# 100 doors

100 doors
You are encouraged to solve this task according to the task description, using any language you may know.

There are 100 doors in a row that are all initially closed.

You make 100 passes by the doors.

The first time through, visit every door and  toggle  the door  (if the door is closed,  open it;   if it is open,  close it).

The second time, only visit every 2nd door   (door #2, #4, #6, ...),   and toggle it.

The third time, visit every 3rd door   (door #3, #6, #9, ...), etc,   until you only visit the 100th door.

Answer the question:   what state are the doors in after the last pass?   Which are open, which are closed?

Alternate: As noted in this page's   discussion page,   the only doors that remain open are those whose numbers are perfect squares.

Opening only those doors is an   optimization   that may also be expressed; however, as should be obvious, this defeats the intent of comparing implementations across programming languages.

## 11l

Translation of: Python
V doors = [0B] * 100L(i) 100   L(j) (i .< 100).step(i + 1)      doors[j] = !doors[j]   print(‘Door ’(i + 1)‘: ’(I doors[i] {‘open’} E ‘close’))

## 360 Assembly

*        100 doors                 13/08/2015HUNDOOR  CSECT         USING  HUNDOOR,R12         LR     R12,R15         LA     R6,0         LA     R8,1               step 1         LA     R9,100LOOPI    BXH    R6,R8,ELOOPI       do ipass=1 to 100 (R6)         LR     R7,R6         SR     R7,R6         LR     R10,R6             step ipass         LA     R11,100LOOPJ    BXH    R7,R10,ELOOPJ      do idoor=ipass to 100 by ipass (R7)         LA     R5,DOORS-1         AR     R5,R7         XI     0(R5),X'01'        doors(idoor)=not(doors(idoor))NEXTJ    B      LOOPJELOOPJ   B      LOOPIELOOPI   LA     R10,BUFFER         R10 address of the buffer         LA     R5,DOORS           R5 address of doors item         LA     R6,1               idoor=1 (R6)         LA     R9,100             loop counterLOOPN    CLI    0(R5),X'01'        if doors(idoor)=1         BNE    NEXTN         XDECO  R6,XDEC            idoor to decimal         MVC    0(4,R10),XDEC+8    move decimal to buffer         LA     R10,4(R10)NEXTN	 LA     R6,1(R6)           idoor=idoor+1         LA     R5,1(R5)         BCT    R9,LOOPN           loopELOOPN   XPRNT  BUFFER,80RETURN   XR     R15,R15         BR     R14DOORS    DC     100X'00'BUFFER   DC     CL80' 'XDEC     DS     CL12         YREGS         END    HUNDOOR
Output:
   1   4   9  16  25  36  49  64  81 100

## 4DOS Batch

 @echo offset doors=%@repeat[C,100]do step = 1 to 100  do door = %step to 100 by %step    set doors=%@left[%@eval[%door-1],%doors]%@if[%@instr[%@eval[%door-1],1,%doors]==C,O,C]%@right[%@eval[100-%door],%doors]  enddoenddo

The SET line consists of three functions:

 %@left[n,string]                      ^: Return n leftmost chars in string%@right[n,string]                     ^: Return n rightmost chars in string%@if[condition,true-val,false-val]    ^: Evaluate condition; return true-val if true, false-val if false

Here @IF is used to toggle between C and O.

## 6502 Assembly

Works with: [www.6502asm.com] version beta

unoptimized Based on BASIC QB64 unoptimized version

; 100 DOORS in  6502 assembly language for: http://www.6502asm.com/beta/index.html; Written for the original MOS Technology, Inc. NMOS version of the 6502, but should work with any version.; Based on BASIC QB64 unoptimized version: http://rosettacode.org/wiki/100_doors#BASIC;; Notes:;    Doors array[1..100] is at $0201..$0264. On the specified emulator, this is in video memory, so tbe results will ; be directly shown as pixels in the display.;    $0200 (door 0) is cleared for display purposes but is not involved in the open/close loops.; Y register holds Stride; X register holds Index; Zero Page address$01 used to add Stride to Index (via A) because there's no add-to-X or add-Y-to-A instruction.   ; First, zero door array    LDA #00    LDX #100Z_LOOP:    STA 200,X    DEX    BNE Z_LOOP    STA 200,X   ; Now do doors repeated open/close    LDY #01        ; Initial value of StrideS_LOOP:    CPY #101    BCS S_DONE    TYA            ; Initial value of IndexI_LOOP:    CMP #101    BCS I_DONE    TAX            ; Use as Door array index    INC $200,X ; Toggle bit 0 to reverse state of door STY 01 ; Add stride (Y) to index (X, via A) ADC 01 BCC I_LOOPI_DONE: INY BNE S_LOOPS_DONE: ; Finally, format array values for output: 0 for closed, 1 for open LDX #100C_LOOP: LDA$200,X    AND #$01 STA$200,X    DEX    BNE C_LOOP

48. bytes of code; the specified emulator does not report cycles.

Works with: [6502asm.com] version 1.2

optimized Largely inspired by the optimized C implementation - makes use of the fact that finally only the doors whose numbers are squares of integers are open, as well as the fact that

$n^{2}=1+3+5+\ldots +(2n-1)$.


## AutoHotkey

### Standard Approach

Loop, 100  Door%A_Index% := "closed" Loop, 100 {  x := A_Index, y := A_Index  While (x <= 100)  {    CurrentDoor := Door%x%    If CurrentDoor contains closed    {      Door%x% := "open"      x += y    }    else if CurrentDoor contains open    {      Door%x% := "closed"      x += y    }  }} Loop, 100 {   CurrentDoor := Door%A_Index%   If CurrentDoor contains open      Res .= "Door " A_Index " is openn"}MsgBox % Res

### Alternative Approach

Making use of the identity:

$\sum _{i=1}^{n}(2i-1)=n^{2}$

increment := 3, square := 1 Loop, 100     If (A_Index = square)         outstring .= "nDoor " A_Index " is open"         ,square += increment, increment += 2 MsgBox,, Succesfull, % SubStr(outstring, 2)

### Optimized

While (Door := A_Index ** 2) <= 100   Result .= "Door " Door " is openn"MsgBox, %Result%

## AutoIt

 #include <array.au3>$doors = 100 ;door array, 0 = closed, 1 = openLocal$door[$doors +1] For$ii = 1 To $doors For$i = $ii To$doors Step $ii$door[$i] = Not$door[$i] nextNext ;display to screenFor$i = 1 To $doors ConsoleWrite (Number($door[$i])& " ") If Mod($i,10) = 0 Then ConsoleWrite(@CRLF)Next 

## Axiom

Unoptimized:
(open,closed,change,open?) := (true,false,not,test);doors := bits(100,closed);for i in 1..#doors repeat  for j in i..#doors by i repeat    doors.j := change doors.j[i for i in 1..#doors | open? doors.i] 
Optimized:
[i for i in 1..100 | perfectSquare? i] -- or[i^2 for i in 1..sqrt(100)::Integer]

## AWK

unoptimized

BEGIN {  for(i=1; i <= 100; i++)  {    doors[i] = 0 # close the doors  }  for(i=1; i <= 100; i++)  {    for(j=i; j <= 100; j += i)    {      doors[j] = (doors[j]+1) % 2    }  }  for(i=1; i <= 100; i++)  {    print i, doors[i] ? "open" : "close"  }}

optimized

BEGIN {  for(i=1; i <= 100; i++) {    doors[i] = 0 # close the doors  }  for(i=1; i <= 100; i++) {    if ( int(sqrt(i)) == sqrt(i) ) {      doors[i] = 1    }  }  for(i=1; i <= 100; i++)  {    print i, doors[i] ? "open" : "close"  }}

## B

Works with: The Amsterdam Compiler Kit - B version V6.1pre1
main(){  auto doors; /* != 0 means open */  auto pass, door;   door = 0;  while( door<100 ) doors[door++] = 0;   pass = 0;  while( pass<100 )  {    door = pass;    while( door<100 )    {      doors[door] = !doors[door];      door =+ pass+1;    }    ++pass;  }   door = 0;  while( door<100 )  {    printf("door #%d is %s.*n", door+1, doors[door] ? "open" : "closed");    ++door;  }   return(0);}

## BASIC

### Applesoft BASIC

Based on the Sinclair ZX81 BASIC implementation.

  100 : 110  REM  100 DOORS PROBLEM 120 : 130  DIM D(100) 140  FOR P = 1 TO 100 150  FOR T = P TO 100 STEP P 160  D(T) =  NOT D(T): NEXT T 170  NEXT P 180  FOR I = 1 TO 100 190  IF D(I) THEN  PRINT I;" "; 200  NEXT I 
Output:

]RUN
1 4 9 16 25 36 49 64 81 100

### BASIC256

# 100 doors problemdim d(100) # simple solutionprint "simple solution"gosub initializefor t = 1 to 100   for j = t to 100 step t      d[j-1] = not d[j-1]   next jnext tgosub showopen # more optimized solutionprint "more optimized solution"gosub initializefor t = 1 to 10      d[t^2-1] = truenext tgosub showopenend initialize:for t = 1 to d[?]   d[t-1] = false	 # closednext treturn showopen:for t = 1 to d[?]   print d[t-1]+ " ";   if t%10 = 0 then printnext treturn

### Commodore BASIC

Based on the Sinclair ZX81 BASIC implementation.

10 DIM D(100)20 FOR I=1 TO 10030 FOR J=I TO 100 STEP I40 D(J) = NOT D(J)50 NEXT J60 NEXT I70 FOR I=1 TO 10080 IF D(I) THEN PRINT I,90 NEXT I

### IS-BASIC

100 PROGRAM "100doors.bas"110 NUMERIC D(1 TO 100)120 FOR I=1 TO 100130   LET D(I)=0140 NEXT150 FOR I=1 TO 100160   FOR J=I TO 100 STEP I170     LET D(J)=NOT D(J)180   NEXT 190 NEXT200 FOR I=1 TO 100210   IF D(I) THEN PRINT I220 NEXT

Optimized:

100 PROGRAM "100doors.bas"110 LET NR=1:LET D=3120 DO130   PRINT NR140   LET NR=NR+D:LET D=D+2150 LOOP WHILE NR<=100

### QBASIC

Works with: QBASIC, QB64

unoptimized

REM "100 Doors" program FOR QB64 BASIC (http://www.qb64.net/), a QuickBASIC-like compiler.REM Author: G. A. TipperyREM Date: 12-Feb-2014REMREM   Unoptimized (naive) version, per specifications at http://rosettacode.org/wiki/100_doors DEFINT A-ZCONST N = 100DIM door(N) FOR stride = 1 TO N    FOR index = stride TO N STEP stride        LET door(index) = NOT (door(index))    NEXT indexNEXT stride PRINT "Open doors:"FOR index = 1 TO N    IF door(index) THEN PRINT indexNEXT index END
Works with: QuickBasic version 4.5

unoptimized

DIM doors(0 TO 99)FOR pass = 0 TO 99	FOR door = pass TO 99 STEP pass + 1		PRINT doors(door)		PRINT NOT doors(door)		doors(door) = NOT doors(door)	NEXT doorNEXT passFOR i = 0 TO 99	PRINT "Door #"; i + 1; " is ";	IF NOT doors(i) THEN		PRINT "closed"	ELSE		PRINT "open"	END IFNEXT i

optimized

DIM doors(0 TO 99)FOR door = 0 TO 99	IF INT(SQR(door)) = SQR(door) THEN doors(door) = -1NEXT doorFOR i = 0 TO 99	PRINT "Door #"; i + 1; " is ";	IF NOT doors(i) THEN		PRINT "closed"	ELSE		PRINT "open"	END IFNEXT i

optimized

 'lrcvs 04.11.12CLSx = 1 : y = 3 : z = 0PRINT x + " Open"DOz = x + yPRINT z + " Open"x = z : y = y + 2UNTIL z >= 100END 

### Sinclair ZX81 BASIC

Works with only 1k of RAM, although it doesn't leave too much to play with.

10 DIM D(100)20 FOR I=1 TO 10030 FOR J=I TO 100 STEP I40 LET D(J)=NOT D(J)50 NEXT J60 NEXT I70 FOR I=1 TO 10080 IF D(I) THEN PRINT I,90 NEXT I

## BaCon

 OPTION BASE 1 DECLARE doors FOR size = 1 TO 100    FOR pass = 0 TO 100 STEP size	doors[pass] = NOT(doors[pass])    NEXTNEXT FOR which = 1 TO 100    IF doors[which] THEN PRINT whichNEXT 
Output:
1
4
9
16
25
36
49
64
81
100


## Batch File

unoptimized

 @echo offsetlocal enableDelayedExpansion:: 0 = closed:: 1 = open:: SET /A treats undefined variable as 0:: Negation operator ! must be escaped because delayed expansion is enabledfor /l %%p in (1 1 100) do for /l %%d in (%%p %%p 100) do set /a "door%%d=^!door%%d"for /l %%d in (1 1 100) do if !door%%d!==1 (  echo door %%d is open) else echo door %%d is closed 

optimized

 @echo offsetlocal enableDelayedExpansionset /a square=1, incr=3for /l %%d in (1 1 100) do (  if %%d neq !square! (echo door %%d is closed) else (    echo door %%d is open    set /a square+=incr, incr+=2  )) 

## BBC BASIC

      DIM doors%(100)       FOR pass% = 1 TO 100        FOR door% = pass% TO 100 STEP pass%          doors%(door%) = NOT doors%(door%)        NEXT door%      NEXT pass%       FOR door% = 1 TO 100        IF doors%(door%) PRINT "Door " ; door% " is open"      NEXT door%

## bc

/* 0 means door is closed, 1 means door is open */for (i = 0; i < 100; i++) {    for (j = i; j < 100; j += (i + 1)) {        d[j] = 1 - d[j]     /* Toggle door */    }} "Open doors:"for (i = 0; i < 100; i++) {    if (d[i] == 1) (i + 1)}

## Befunge

### Befunge-93

#### Unoptimized

Requires an interpreter with working read-write memory support. Padding the code page with extra blank lines can sometimes help.

>"d">:00p1-:>:::9%\9/9+g2%!\:9v$.v_^#!$::$_^#"c":+g00p+9/9\%<::<[email protected]#$:\*:+55:+1p27g1g+9/9\%9 

#### Optimized

Just calculates the first 10 perfect squares.

1+:::*.9#@_

### Befunge-98

Works with: CCBI version 2.1
108p0>:18p;;>:9g!18g9p08g]*!0\|+relet|-1*aap81::+];::+1<r]!g9;>$08g1+:08paa[*#@_^._aa ## BlitzMax Works with: BlitzMax version 1.37 optimized Graphics 640,480i=1While ((i*i)<=100) a$=i*i	DrawText a$,10,20*i Print i*i i=i+1 WendFlip WaitKey  ## BlooP The currently available BlooP interpreters don't really allow iterating over cells with any level of ease, so instead I loop over each door in turn, running it through all 100 cycles and toggling it when it is a multiple of the step number.  DEFINE PROCEDURE ''DIVIDE'' [A,B]:BLOCK 0: BEGIN IF A < B, THEN: QUIT BLOCK 0; CELL(0) <= 1; OUTPUT <= 1; LOOP AT MOST A TIMES: BLOCK 2: BEGIN IF OUTPUT * B = A, THEN: QUIT BLOCK 0; OUTPUT <= OUTPUT + 1; IF OUTPUT * B > A, THEN: BLOCK 3: BEGIN OUTPUT <= CELL(0); QUIT BLOCK 0; BLOCK 3: END; CELL(0) <= OUTPUT; BLOCK 2: END;BLOCK 0: END. DEFINE PROCEDURE ''MINUS'' [A,B]:BLOCK 0: BEGIN IF A < B, THEN: QUIT BLOCK 0; LOOP AT MOST A TIMES: BLOCK 1: BEGIN IF OUTPUT + B = A, THEN: QUIT BLOCK 0; OUTPUT <= OUTPUT + 1; BLOCK 1: END;BLOCK 0: END. DEFINE PROCEDURE ''MODULUS'' [A,B]:BLOCK 0: BEGIN CELL(0) <= DIVIDE[A,B]; OUTPUT <= MINUS[A,CELL(0) * B];BLOCK 0: END. DEFINE PROCEDURE ''TOGGLE'' [DOOR]:BLOCK 0: BEGIN IF DOOR = 1, THEN: QUIT BLOCK 0; OUTPUT <= 1;BLOCK 0: END. DEFINE PROCEDURE ''NUMBERS'' [DOOR, COUNT]:BLOCK 0: BEGIN CELL(0) <= 1; /*each number*/ OUTPUT <= 0; /*current door state*/ LOOP COUNT TIMES: BLOCK 1: BEGIN IF MODULUS[DOOR, CELL(0)] = 0, THEN: OUTPUT <= TOGGLE[OUTPUT]; CELL(0) <= CELL(0) + 1; BLOCK 1: END; BLOCK 0: END. DEFINE PROCEDURE ''DOORS'' [COUNT]:BLOCK 0: BEGIN CELL(0) <= 1; /*each door*/ LOOP COUNT TIMES: BLOCK 1: BEGIN CELL(1) <= NUMBERS[CELL(0), COUNT]; /*iterate over the states of this door to get its final state*/ IF CELL(1) = 1, THEN: /*door state = open*/ PRINT[CELL(0), ' ']; CELL(0) <= CELL(0) + 1; BLOCK 1: END;BLOCK 0: END. DOORS;  Output:  > 1 > 4 > 9 > 16 > 25 > 36 > 49 > 64 > 81 > 100  ## Bracmat Bracmat is not really at home in tasks that involve addressing things by index number. Here are four solutions that each do the task, but none should win a price for cleanliness. Solution 1. Use an indexable array. Local variables are stored in stacks. Each stack corresponds to one variable name and vice versa. Stacks can also be used as arrays, but because of how local variables are implemented, arrays cannot be declared as local variables. ( 100doors-tbl= door step . tbl$(doors.101) { Create an array. Indexing is 0-based. Add one extra for addressing element nr. 100 }    & 0:?step    &   whl      ' ( 1+!step:~>100:?step   { ~> means 'not greater than', i.e. 'less than or equal' }        & 0:?door        &   whl          ' ( !step+!door:~>100:?door            & 1+-1*!(!door$doors):?doors { <number>$<variable> sets the current index, which stays the same until explicitly changed. }            )        )    & 0:?door    &   whl      ' ( 1+!door:~>100:?door        &   out          $( door !door is ( !(!door$doors):1&open              | closed              )            )        )    & tbl$(doors.0) { clean up the array }) Solution 2. Use one variable for each door. In Bracmat, a variable name can be any non-empty string, even a number, so we use the numbers 1 .. 100 as variable names, but also as door numbers. When used as variable an extra level of indirection is needed. See the occurrences of ?! and !! in the following code. ( 100doors-var= step door . 0:?door & whl ' ( 1+!door:~>100:?door & closed:?!door { this creates a variable and assigns a value 'closed' to it } ) & 0:?step & whl ' ( 1+!step:~>100:?step & 0:?door & whl ' ( !step+!door:~>100:?door & ( !!door:closed&open | closed ) : ?!door ) ) & 0:?door & whl ' ( 1+!door:~>100:?door & out$(door !door is !!door)        )    & 0:?door    &   whl      ' ( 1+!door:~>100:?door        & tbl$(!door.0) { cleanup the variable } )) Solution 3. Use a list and a dedicated positioning pattern to address the right door in the list. Create a new list by concatenating the skipped elements with the toggled elements. This solution is computationally unfavourable because of the many concatenations. ( 100doors-list= doors door doorIndex step . :?doors & 0:?door & whl ' ( 1+!door:~>100:?door & closed !doors:?doors ) & 0:?skip & whl ' ( :?ndoors & whl ' ( !doors:?skipped [!skip %?door ?doors { the [<number> pattern only succeeds when the scanning cursor is at position <number> } & !ndoors !skipped ( !door:open&closed | open ) : ?ndoors ) & !ndoors !doors:?doors & 1+!skip:<100:?skip ) & out$!doors)

Solution 4. Use a list of objects. Each object can be changed without the need to re-create the whole list.

( 100doors-obj=   doors door doorIndex step  .   :?doors    & 0:?door    &   whl      ' ( 1+!door:~>100:?door        & new$(=closed) !doors:?doors ) & 0:?skip & whl ' ( !doors:?tododoors & whl ' ( !tododoors:? [!skip %?door ?tododoors & ( !(door.):open&closed | open ) : ?(door.) ) & 1+!skip:<100:?skip ) & out$!doors)

These four functions are called in the following way:

100doors-tbl$& 100doors-var$& 100doors-list$& 100doors-obj$;

## Burlesque

Version using square numbers:

 blsq ) 10ro2?^{1 4 9 16 25 36 49 64 81 100} 

## C

### unoptimized

Uses: C Runtime (Components:printf,)
#include <stdio.h> int main(){  char is_open = { 0 };  int pass, door;   /* do the 100 passes */  for (pass = 0; pass < 100; ++pass)    for (door = pass; door < 100; door += pass+1)      is_open[door] = !is_open[door];   /* output the result */  for (door = 0; door < 100; ++door)    printf("door #%d is %s.\n", door+1, (is_open[door]? "open" : "closed"));   return 0;}

Using defensive programming, pointers, sentinel values and some other standard programming practices,

Uses: C Runtime (Components:printf,)
#include <stdio.h> #define NUM_DOORS 100 int main(int argc, char *argv[]){  int is_open[NUM_DOORS] = { 0 } ;  int * doorptr, * doorlimit = is_open + NUM_DOORS ;  int pass ;   /* do the N passes, go backwards because the order is not important */  for ( pass= NUM_DOORS ; ( pass ) ; -- pass ) {    for ( doorptr= is_open + ( pass-1 ); ( doorptr < doorlimit ) ; doorptr += pass ) {      ( * doorptr ) ^= 1 ;    }  }   /* output results */  for ( doorptr= is_open ; ( doorptr != doorlimit ) ; ++ doorptr ) {    printf("door #%ld is %s\n", ( doorptr - is_open ) + 1, ( * doorptr ) ? "open" : "closed" ) ;  }}

### optimized

This optimized version makes use of the fact that finally only the doors with square index are open, as well as the fact that $n^{2}=1+3+5+\ldots +(2n-1)$.

Uses: C Runtime (Components:printf,)
#include <stdio.h> int main(){  int square = 1, increment = 3, door;  for (door = 1; door <= 100; ++door)  {    printf("door #%d", door);    if (door == square)    {      printf(" is open.\n");      square += increment;      increment += 2;    }    else      printf(" is closed.\n");  }  return 0;}

The following ultra-short optimized version demonstrates the flexibility of C loops, but isn't really considered good C style:

#include <stdio.h> int main(){  int door, square, increment;  for (door = 1, square = 1, increment = 1; door <= 100; door++ == square && (square += increment += 2))    printf("door #%d is %s.\n", door, (door == square? "open" : "closed"));  return 0;}
Or really optimize it -- square of an integer is, well, computable:
#include <stdio.h> int main(){	int i;	for (i = 1; i * i <= 100; i++)		printf("door %d open\n", i * i); 	return 0;}

## C++

Works with: GCC version 4.1.2 20061115 (prerelease) (SUSE Linux)

unoptimized

#include <iostream> int main(){  bool is_open = { false };   // do the 100 passes  for (int pass = 0; pass < 100; ++pass)    for (int door = pass; door < 100; door += pass+1)      is_open[door] = !is_open[door];   // output the result  for (int door = 0; door < 100; ++door)    std::cout << "door #" << door+1 << (is_open[door]? " is open." : " is closed.") << std::endl;  return 0;}

optimized This optimized version makes use of the fact that finally only the doors with square index are open, as well as the fact that $(n+1)^{2}=1+3+5+\ldots +(2n+1)$.

#include <iostream> int main(){  int square = 1, increment = 3;  for (int door = 1; door <= 100; ++door)  {    std::cout << "door #" << door;    if (door == square)    {      std::cout << " is open." << std::endl;      square += increment;      increment += 2;    }    else      std::cout << " is closed." << std::endl;  }  return 0;}

The only calculation that's really needed:

#include <iostream> //compiled with "Dev-C++" , from RaptorOne int main(){    for(int i=1; i*i<=100; i++)            std::cout<<"Door "<<i*i<<" is open!"<<std::endl;}

Compile time computation using C++17 to produce fastest runtime.

#include <iostream>    // compiled with clang (tags/RELEASE_600/final)#include <type_traits> // or g++ (GCC) 7.3.1 20180406 -- from hare1039namespace functional_list // basic building block for template meta programming{struct NIL{	using head = NIL;	using tail = NIL;	friend std::ostream& operator << (std::ostream& os, NIL const) { return os; }}; template <typename H, typename T = NIL>struct list{	using head = H;	using tail = T;}; template <int i>struct integer{	static constexpr int value = i;	friend std::ostream& operator << (std::ostream& os, integer<i> const) { os << integer<i>::value; return os;}}; template <typename L, int nTH> constexprauto at(){	if constexpr (nTH == 0)		return (typename L::head){};	else if constexpr (not std::is_same_v<typename L::tail, NIL>) 		return at<typename L::tail, nTH - 1>();	else		return NIL{};}template <typename L, int nTH>using at_t = decltype(at<L, nTH>()); template <typename L, typename elem> constexprauto prepend() { return list<elem, L>{}; } template <typename L, typename elem>using prepend_t = decltype(prepend<L, elem>()); template <int Size, typename Dat = integer<0>> constexprauto gen_list(){	if constexpr (Size == 0)		return NIL{};	else	{		using next = decltype(gen_list<Size - 1, Dat>());		return prepend<next, Dat>();	}}template <int Size, typename Dat = integer<0>>using gen_list_t = decltype(gen_list<Size, Dat>()); } namespace fl = functional_list; constexpr int door_amount = 101; // index from 1 to 100 template <typename L, int current, int moder> constexprauto construct_loop(){	using val_t = fl::at_t<L, current>;	if constexpr (std::is_same_v<val_t, fl::NIL>)		return fl::NIL{};	else	{		constexpr int val = val_t::value;		using val_add_t = fl::integer<val + 1>;		using val_old_t = fl::integer<val>; 		if constexpr (current == door_amount)		{			if constexpr(current % moder == 0)				return fl::list<val_add_t>{};			else				return fl::list<val_old_t>{};		}		else		{			using sub_list = decltype(construct_loop<L, current + 1, moder>());			if constexpr(current % moder == 0)				return fl::prepend<sub_list, val_add_t>();			else				return fl::prepend<sub_list, val_old_t>();		}	}} template <int iteration> constexprauto construct(){	if constexpr (iteration == 1) // door index = 1	{		using l = fl::gen_list_t<door_amount>;		return construct_loop<l, 0, iteration>();	}	else	{		using prev_iter_list = decltype(construct<iteration - 1>());		return construct_loop<prev_iter_list, 0, iteration>();	}} template <typename L, int pos> constexprvoid show_ans(){	if constexpr (std::is_same_v<typename L::head, fl::NIL>)		return;	else	{		if constexpr (L::head::value % 2 == 1)			std::cout << "Door " << pos << " is opened.\n";		show_ans<typename L::tail, pos + 1>();	}} int main(){	using result = decltype(construct<100>());	show_ans<result, 0>();}

## C#

### Unoptimized with Modulus % Operator

namespace ConsoleApplication1{    using System;    class Program    {        static void Main(string[] args)        {            bool[] doors = new bool;             //Close all doors to start.            for (int d = 0; d < 100; d++) doors[d] = false;             //For each pass...            for (int p = 0; p < 100; p++)//number of passes            {                //For each door to toggle...                for (int d = 0; d < 100; d++)//door number                {                    if ((d + 1) % (p + 1) == 0)                    {                        doors[d] = !doors[d];                    }                }            }             //Output the results.            Console.WriteLine("Passes Completed!!!  Here are the results: \r\n");            for (int d = 0; d < 100; d++)            {                if (doors[d])                {                    Console.WriteLine(String.Format("Door #{0}: Open", d + 1));                }                else                {                    Console.WriteLine(String.Format("Door #{0}: Closed", d + 1));                }            }            Console.ReadKey(true);        }    }}

### Optimized for Orthogonality

(This version demonstrates a different thought pattern during development, where operation and presentation are separated. It could easily be refactored so that the operations to determine which doors are opened and to display the list of doors would be in separate methods, at which point it would become simple to extract them to separate classes and employ a DI pattern to switch the algorithm or display mechanism being used. It also keeps the calculation clear and concise.)

namespace ConsoleApplication1{    using System;    class Program    {        static void Main(string[] args)        {            //Perform the operation.            bool[] doors = new bool;            int n = 0;            int d;            while ((d = (++n * n)) <= 100)                doors[d - 1] = true;             //Perform the presentation.            for (d = 0; d < doors.Length; d++)                Console.WriteLine("Door #{0}: {1}", d + 1, doors[d] ? "Open" : "Closed");            Console.ReadKey(true);        }    }}

### Unoptimized but Concise

namespace ConsoleApplication1{    using System;    class Program    {        static void Main()        {            bool[] doors = new bool;             //The number of passes can be 1-based, but the number of doors must be 0-based.            for (int p = 1; p <= 100; p++)                for (int d = p - 1; d < 100; d += p)                    doors[d] = !doors[d];            for (int d = 0; d < 100; d++)                Console.WriteLine("Door #{0}: {1}", d + 1, doors[d] ? "Open" : "Closed");            Console.ReadKey(true);        }    }}

### Optimized for brevity

namespace ConsoleApplication1{    using System;    class Program    {        static void Main()        {            double n;             //If the current door number is the perfect square of an integer, say it is open, else say it is closed.            for (int d = 1; d <= 100; d++)                Console.WriteLine("Door #{0}: {1}", d, (n = Math.Sqrt(d)) == (int)n ? "Open" : "Closed");            Console.ReadKey(true);        }    }}

## Ceylon

shared void run() {    print("Open doors (naive):     naive()           Open doors (optimized): optimized()"); } shared {Integer*} naive(Integer count = 100) {    variable value doors = [ for (_ in 1..count) closed ];    for (step in 1..count) {        doors = [for (i->door in doors.indexed) let (index = i+1) if (step == 1 || step.divides(index)) then door.toggle() else door ];    }    return doors.indexesWhere((door) => door == opened).map(1.plusInteger);} shared {Integer*} optimized(Integer count = 100) =>        { for (i in 1..count) i*i }.takeWhile(count.notSmallerThan);  shared abstract class Door(shared actual String string) of opened | closed {    shared formal Door toggle();}object opened extends Door("opened") { toggle() => closed; }object closed extends Door("closed") { toggle() => opened; }

Output:

Open doors (naive):     { 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 }
Open doors (optimized): { 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 }

## C1R

100_doors

## Caché ObjectScript

  for i=1:1:100 {	 set doors(i) = 0 } for i=1:1:100 {	 for door=i:i:100 {		  Set doors(door)='doors(door)	 } } for i = 1:1:100 {	if doors(i)=1 write i_": open",! } 

Output:

 1: open4: open9: open16: open25: open36: open49: open64: open81: open100: open 

## Clarion

     program     map    end MAX_DOOR_NUMBER         equate(100)CRLF                    equate('<13,10>') Doors                   byte,dim(MAX_DOOR_NUMBER)Pass                    byteDoorNumber              byteDisplayString           cstring(2000) ResultWindow            window('Result'),at(,,133,291),center,double,auto                            prompt('Door states:'),at(8,4),use(?PromptTitle)                            text,at(8,16,116,266),use(DisplayString),boxed,vscroll,font('Courier New',,,,CHARSET:ANSI),readonly                        end     code     Doors :=: false    loop Pass = 1 to MAX_DOOR_NUMBER        loop DoorNumber = Pass to MAX_DOOR_NUMBER by Pass            Doors[DoorNumber] = choose(Doors[DoorNumber], false, true)        end    end     clear(DisplayString)    loop DoorNumber = 1 to MAX_DOOR_NUMBER        DisplayString = DisplayString & format(DoorNumber, @n3) & ' is ' & choose(Doors[DoorNumber], 'opened', 'closed') & CRLF    end    open(ResultWindow)    accept    end    close(ResultWindow)     return 

## Clio

Unoptimized

fn visit-doors doors step:  if step > 100: doors  else:    [1:100]      -> * fn index:            if index % step: doors[(index - 1)]            else: not doors[(index - 1)]      -> visit-doors (step + 1) [1:100] -> * n: false -> visit-doors 1 => doors[1:100] -> * (@eager) fn i:  doors[(i - 1)]    -> if = true: #open            else: #closed    -> print #Door i #is @

Optimized

[1:100] -> * (@eager) fn i:  i ^ 0.5    -> eq @ (transform i: floor)    -> if = true: #open            else: #closed    -> print #Door i #is @

## CLIPS

Unoptimized

(deffacts initial-state  (door-count 100)) (deffunction toggle  (?state)  (switch ?state    (case "open" then "closed")    (case "closed" then "open")  )) (defrule create-doors-and-visits  (door-count ?count)  =>  (loop-for-count (?num 1 ?count) do    (assert (door ?num "closed"))    (assert (visit-from ?num ?num))  )  (assert (doors initialized))) (defrule visit  (door-count ?max)  ?visit <- (visit-from ?num ?step)  ?door <- (door ?num ?state)  =>  (retract ?visit)  (retract ?door)  (assert (door ?num (toggle ?state)))  (if    (<= (+ ?num ?step) ?max)    then    (assert (visit-from (+ ?num ?step) ?step))  )) (defrule start-printing  (doors initialized)  (not (visit-from ? ?))  =>  (printout t "These doors are open:" crlf)  (assert (print-from 1))) (defrule print-door  (door-count ?max)  ?pf <- (print-from ?num)  (door ?num ?state)  =>  (retract ?pf)  (if    (= 0 (str-compare "open" ?state))    then    (printout t ?num " ")  )  (if    (< ?num ?max)    then    (assert (print-from (+ ?num 1)))    else    (printout t crlf "All other doors are closed." crlf)  ))

Optimized

(deffacts initial-state  (door-count 100)) (deffunction is-square  (?num)  (= (sqrt ?num) (integer (sqrt ?num)))) (defrule check-doors  (door-count ?count)  =>  (printout t "These doors are open:" crlf)  (loop-for-count (?num 1 ?count) do    (if (is-square ?num) then      (printout t ?num " ")    )  )  (printout t crlf "All other doors are closed." crlf))

## Clojure

Unoptimized / mutable array

(defn doors []  (let [doors (into-array (repeat 100 false))]    (doseq [pass   (range 1 101)             i      (range (dec pass) 100 pass) ]      (aset doors i (not (aget doors i))))    doors))    (defn open-doors [] (for [[d n] (map vector (doors) (iterate inc 1)) :when d] n)) (defn print-open-doors []  (println     "Open doors after 100 passes:"    (apply str (interpose ", " (open-doors)))))

Unoptimized / functional

(defn doors []  (reduce (fn [doors toggle-idx] (update-in doors [toggle-idx] not))          (into [] (repeat 100 false))          (for [pass   (range 1 101)                i      (range (dec pass) 100 pass) ]            i))) (defn open-doors [] (for [[d n] (map vector (doors) (iterate inc 1)) :when d] n)) (defn print-open-doors []  (println     "Open doors after 100 passes:"    (apply str (interpose ", " (open-doors)))))

Alternative Unoptimized / functional

(defn open-doors []  (->> (for [step (range 1 101), occ (range step 101 step)] occ)       frequencies       (filter (comp odd? val))       keys       sort)) (defn print-open-doors []  (println     "Open doors after 100 passes:"    (apply str (interpose ", " (open-doors)))))

Optimized / functional

(defn doors []	(reduce (fn [doors idx] (assoc doors idx true)) 	        (into [] (repeat 100 false))	        (map #(dec (* % %)) (range 1 11)))) (defn open-doors [] (for [[d n] (map vector (doors) (iterate inc 1)) :when d] n)) (defn print-open-doors []  (println     "Open doors after 100 passes:"    (apply str (interpose ", " (open-doors)))))

Alternative Optimized / functional

(defn open-doors [] (->> (iterate inc 1) (map #(* % %)) (take-while #(<= % 100)))) (defn print-open-doors []  (println     "Open doors after 100 passes:"    (apply str (interpose ", " (open-doors)))))

## COBOL

       IDENTIFICATION DIVISION.       PROGRAM-ID. 100Doors.        DATA DIVISION.       WORKING-STORAGE SECTION.       01 Current-n      PIC 9(3).       01 StepSize       PIC 9(3).       01 DoorTable.          02 Doors       PIC 9(1)   OCCURS 100 TIMES.             88 ClosedDoor          VALUE ZERO.       01 Idx            PIC 9(3).        PROCEDURE DIVISION.       Begin.           INITIALIZE DoorTable           PERFORM VARYING StepSize FROM 1 BY 1 UNTIL StepSize > 100             PERFORM VARYING Current-n FROM StepSize BY StepSize                     UNTIL Current-n > 100               SUBTRACT Doors (Current-n) FROM 1 GIVING Doors (Current-n)             END-PERFORM           END-PERFORM            PERFORM VARYING Idx FROM 1 BY 1                   UNTIL Idx > 100             IF ClosedDoor (Idx)               DISPLAY Idx " is closed."             ELSE               DISPLAY Idx " is open."             END-IF           END-PERFORM            STOP RUN           .

## Coco

We use the naive algorithm.

doors = [false] * 100 for pass til doors.length    for i from pass til doors.length by pass + 1        ! = doors[i] for i til doors.length    console.log 'Door %d is %s.', i + 1, if doors[i] then 'open' else 'closed'

## CoffeeScript

unoptimized:

doors = [] for pass in [1..100]  for i in [pass..100] by pass    doors[i] = !doors[i] console.log "Doors #{index for index, open of doors when open} are open" # matrix outputconsole.log doors.map (open) -> +open 

optimized:

isInteger = (i) -> Math.floor(i) == i console.log door for door in [1..100] when isInteger Math.sqrt door

ultra-optimized:

console.log Math.pow(i,2) for i in [1..10]

## ColdFusion

Basic Solution: Returns List of 100 values: 1=open 0=closed

 	doorCount = 1;	doorList = "";	// create all doors and set all doors to open	while (doorCount LTE 100) {		doorList = ListAppend(doorList,"1");		doorCount = doorCount + 1;	}	loopCount = 2;	doorListLen = ListLen(doorList);	while (loopCount LTE 100) {		loopDoorListCount = 1;		while (loopDoorListCount LTE 100) {			testDoor = loopDoorListCount / loopCount;			if (testDoor EQ Int(testDoor)) {				checkOpen = ListGetAt(doorList,loopDoorListCount);				if (checkOpen EQ 1) {					doorList = ListSetAt(doorList,loopDoorListCount,"0");				} else {					doorList = ListSetAt(doorList,loopDoorListCount,"1");				}			}			loopDoorListCount = loopDoorListCount + 1;		}		loopCount = loopCount + 1;	} 

Squares of Integers Solution: Returns List of 100 values: 1=open 0=closed

 	doorCount = 1;	doorList = "";	loopCount = 1;	while (loopCount LTE 100) {		if (Sqr(loopCount) NEQ Int(Sqr(loopCount))) {			doorList = ListAppend(doorList,0);		} else {			doorList = ListAppend(doorList,1);		}		loopCount = loopCount + 1;	} 

Display only

// Display all doors<cfloop from="1" to="100" index="x">    Door #x# Open: #YesNoFormat(ListGetAt(doorList,x))#<br /></cfloop> // Output only open doors<cfloop from="1" to="100" index="x">    <cfif ListGetAt(doorList,x) EQ 1>        #x#<br />    </cfif></cfloop>

Another Route

<Cfparam name="doorlist" default=""><cfloop from="1" to="100" index="i">    <Cfset doorlist = doorlist & 'c,'></cfloop><cfloop from="1" to="100" index="i">    <Cfloop from="1" to="100" index="door" step="#i#">    <Cfif listgetat(doorlist, door) eq 'c'>        <Cfset doorlist = listsetat(doorlist, door, 'O')>    <Cfelse>        <Cfset doorlist = listsetat(doorlist, door, 'c')>    </Cfif>    </Cfloop></cfloop><Cfoutput>#doorlist#</Cfoutput>

 10 D=100: DIMD(D): P=120 PRINT CHR$(147);"PASS: ";P22 FOR I=P TO D STEP P: D(I)=NOTD(I): NEXT30 IF P=100 THEN 4032 P=P+1: GOTO2040 PRINT: PRINT"THE FOLLOWING DOORS ARE OPEN: "42 FOR I=1 TO D: IF D(I)=-1 THEN PRINTI;44 NEXT  ## Common Lisp Unoptimized / functional This is a very unoptimized version of the problem, using recursion and quite considerable list-copying. It emphasizes the functional way of solving this problem. (defun visit-door (doors doornum value1 value2) "visits a door, swapping the value1 to value2 or vice-versa" (let ((d (copy-list doors)) (n (- doornum 1))) (if (eql (nth n d) value1) (setf (nth n d) value2) (setf (nth n d) value1)) d)) (defun visit-every (doors num iter value1 value2) "visits every 'num' door in the list" (if (> (* iter num) (length doors)) doors (visit-every (visit-door doors (* num iter) value1 value2) num (+ 1 iter) value1 value2))) (defun do-all-visits (doors cnt value1 value2) "Visits all doors changing the values accordingly" (if (< cnt 1) doors (do-all-visits (visit-every doors cnt 1 value1 value2) (- cnt 1) value1 value2))) (defun print-doors (doors) "Pretty prints the doors list" (format T "~{~A ~A ~A ~A ~A ~A ~A ~A ~A ~A~%~}~%" doors)) (defun start (&optional (size 100)) "Start the program" (let* ((open "_") (shut "#") (doors (make-list size :initial-element shut))) (print-doors (do-all-visits doors size open shut)))) Unoptimized, imperative This is a version that closely follows the problem description and is still quite short. Of all the presented solutions it might be closest to "idiomatic Common Lisp". (define-modify-macro toggle () not) (defun 100-doors () (let ((doors (make-array 100))) (dotimes (i 100) (loop for j from i below 100 by (1+ i) do (toggle (svref doors j)))) (dotimes (i 100) (format t "door ~a: ~:[closed~;open~]~%" (1+ i) (svref doors i))))) Unoptimized, n-doors. (defun doors (z &optional (w (make-list z)) (n 1)) (if (> n z) w (doors z (toggle w n z) (1+ n)))) (defun toggle (w m z) (loop for a in w for n from 1 to z collect (if (zerop (mod n m)) (not a) a))) > (doors 100)(T NIL NIL T NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T) Optimized, n-doors. (defun doors (n) (loop for a from 1 to n collect (zerop (mod (sqrt a) 1)))) > (doors 100)(T NIL NIL T NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T) Optimized This is an optimized version, using the perfect square algorithm. (defun 100-doors () (let ((doors (make-array 100))) (dotimes (i 10) (setf (svref doors (* i i)) t)) (dotimes (i 100) (format t "door ~a: ~:[closed~;open~]~%" (1+ i) (svref doors i))))) Optimized 2 Another optimized version, with finer granular separation of functionality (might be a bit excessive). (defun perfect-square-list (n) "Generates a list of perfect squares from 0 up to n" (loop for i from 1 to (isqrt n) collect (expt i 2))) (defun print-doors (doors) "Pretty prints the doors list" (format T "~{~A ~A ~A ~A ~A ~A ~A ~A ~A ~A~%~}~%" doors)) (defun open-door (doors num open) "Sets door at num to open" (setf (nth (- num 1) doors) open)) (defun visit-all (doors vlist open) "Visits and opens all the doors indicated in vlist" (dolist (dn vlist doors) (open-door doors dn open))) (defun start2 (&optional (size 100)) "Start the program" (print-doors (visit-all (make-list size :initial-element '\#) (perfect-square-list size) '_))) Optimized (2) This version displays a much more functional solution through the use of MAPCAR. (let ((i 0)) (mapcar (lambda (x) (if (zerop (mod (sqrt (incf i)) 1)) "_" "#")) (make-list 100))) ## Component Pascal BlackBox Component Builder  MODULE Doors100;IMPORT StdLog; PROCEDURE Do*;VAR i,j: INTEGER; closed: ARRAY 101 OF BOOLEAN;BEGIN (* initialization of closed to true *) FOR i := 0 TO LEN(closed) - 1 DO closed[i] := TRUE END; (* process *) FOR i := 1 TO LEN(closed) DO; j := 1; WHILE j < LEN(closed) DO IF j MOD i = 0 THEN closed[j] := ~closed[j] END;INC(j) END END; (* print results *) i := 1; WHILE i < LEN(closed) DO IF (i - 1) MOD 10 = 0 THEN StdLog.Ln END; IF closed[i] THEN StdLog.String("C ") ELSE StdLog.String("O ") END; INC(i) END;END Do;END Doors100.  Execute: ^Q Doors100.Do Output: O C C O C C C C O C C C C C C O C C C C C C C C O C C C C C C C C C C O C C C C C C C C C C C C O C C C C C C C C C C C C C C O C C C C C C C C C C C C C C C C O C C C C C C C C C C C C C C C C C C O  ## Coq Basic solution: Require Import List. Fixpoint rep {A} (a : A) n := match n with | O => nil | S n' => a::(rep a n') end. Fixpoint flip (l : list bool) (n k : nat) : list bool := match l with | nil => nil | cons h t => match k with | O => (negb h) :: (flip t n n) | S k' => h :: (flip t n k') end end. Definition flipeach l n := flip l n n. Fixpoint flipwhile l n := match n with | O => flipeach l 0 | S n' => flipwhile (flipeach l (S n')) n' end. Definition prison cells := flipwhile (rep false cells) cells. Optimized version ((n+1)^2 = n^2 + 2n + 1): Require Import List. Fixpoint prisoo' nd n k accu := match nd with | O => rev accu | S nd' => let ra := match k with | O => (true, S n, (n + n)) | S k' => (false, n, k') end in prisoo' nd' (snd (fst ra)) (snd ra) ((fst (fst ra))::accu) end. Definition prisoo cells := prisoo' cells 1 0 nil. Unit test: Goal prison 100 = prisoo 100. compute. reflexivity. Qed. Full proof at github: Goal forall n, prison n = prisoo n. Abort. ## Crystal doors = Array.new(100, false) 1.upto(100) do |i| i.step(by: i, limit: 100) do |j| doors[j - 1] = !doors[j - 1] endend doors.each_with_index do |open, i| puts "Door #{i + 1} is #{open ? "open" : "closed"}"end ## D import std.stdio, std.algorithm, std.range; enum DoorState : bool { closed, open }alias Doors = DoorState[]; Doors flipUnoptimized(Doors doors) pure nothrow { doors[] = DoorState.closed; foreach (immutable i; 0 .. doors.length) for (ulong j = i; j < doors.length; j += i + 1) if (doors[j] == DoorState.open) doors[j] = DoorState.closed; else doors[j] = DoorState.open; return doors;} Doors flipOptimized(Doors doors) pure nothrow { doors[] = DoorState.closed; for (int i = 1; i ^^ 2 <= doors.length; i++) doors[i ^^ 2 - 1] = DoorState.open; return doors;} void main() { auto doors = new Doors(100); foreach (const open; [doors.dup.flipUnoptimized, doors.dup.flipOptimized]) iota(1, open.length + 1).filter!(i => open[i - 1]).writeln;} Output: [1, 4, 9, 16, 25, 36, 49, 64, 81, 100] [1, 4, 9, 16, 25, 36, 49, 64, 81, 100] Unoptimized. Demonstrates very basic language syntax/features. Program output allows to see what the code is doing:  import std.stdio; void printAllDoors(bool[] doors){ // Prints the state of all the doors foreach(i, door; doors) { writeln("#: ", i + 1, (door) ? " open" : " closed"); }}void main(){ bool doors = false; //Create 100 closed doors for(int a = 0; a < 100; ++a) { writefln("Pass #%s; visiting every %s door.", a + 1, a + 1); // Optional for(int i = a; i < 100; i += (a + 1)) { writefln("Visited door %s", i + 1); //Optional doors[i] = !doors[i]; } writeln(); // Optional } printAllDoors(doors); // Prints the state of each door}  ## Dafny The InitializeDoors function demonstrates some of Dafny's advanced features.  datatype Door = Closed | Open method InitializeDoors(n:int) returns (doors:array<Door>) // Precondition: n must be a valid array size. requires n >= 0 // Postcondition: doors is an array, which is not an alias for any other // object, with a length of n, all of whose elements are Closed. The "fresh" // (non-alias) condition is needed to allow doors to be modified by the // remaining code. ensures doors != null && fresh(doors) && doors.Length == n ensures forall j :: 0 <= j < doors.Length ==> doors[j] == Closed;{ doors := new Door[n]; var i := 0; // Invariant: i is always a valid index inside the loop, and all doors less // than i are Closed. These invariants are needed to ensure the second // postcondition. while i < doors.Length invariant i <= doors.Length invariant forall j :: 0 <= j < i ==> doors[j] == Closed; { doors[i] := Closed; i := i + 1; }} method Main (){ var doors := InitializeDoors(100); var pass := 1; while pass <= doors.Length { var door := pass; while door < doors.Length { doors[door] := if doors[door] == Closed then Open else Closed; door := door + pass; } pass := pass + 1; } var i := 0; while i < doors.Length { print i, " is ", if doors[i] == Closed then "closed\n" else "open\n"; i := i + 1; }}  ## Dart unoptimized main() { for (var k = 1, x = new List(101); k <= 100; k++) { for (int i = k; i <= 100; i += k) x[i] = !x[i]; if (x[k]) print("$k open");    }}

optimized version (including generating squares without multiplication)

main() {  for(int i=1,s=3;i<=100;i+=s,s+=2)    print("door $i is open");} comprehensible (not "code golf") version for a pedestrian language import 'dart:io'; final numDoors = 100;final List<bool> doorClosed = List(numDoors); String stateToString(String message) { var res = ''; for (var i = 0; i < numDoors; i++) { res += (doorClosed[i] ? 'X' : '\u2610'); } return res + " " + message;} main() { for (var i = 0; i < numDoors; i++) { doorClosed[i] = true; } stdout.writeln(stateToString("after initialization")); for (var step = 1; step <= numDoors; step++) { final start = step - 1; for (var i = start; i < numDoors; i += step) { doorClosed[i] = !doorClosed[i]; } stdout.writeln(stateToString("after toggling with step =$step"));  }}
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX after initialization
☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐ after toggling with step = 1
☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X after toggling with step = 2
☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX after toggling with step = 3
☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐ after toggling with step = 4
☐XX☐X☐☐☐X☐☐X☐X☐☐☐☐☐XXX☐XXXX☐☐X☐☐XXXX☐XXX☐☐☐☐☐X☐X☐☐X☐☐☐X☐XX☐☐☐XX☐X☐☐☐X☐☐X☐X☐☐☐☐☐XXX☐XXXX☐☐X☐☐XXXX☐XXX after toggling with step = 5
☐XX☐XX☐☐X☐☐☐☐X☐☐☐X☐XXX☐☐XXX☐☐☐☐☐XXX☐☐XXX☐X☐☐☐X☐☐☐☐X☐☐XX☐XX☐X☐XX☐XX☐☐X☐☐☐☐X☐☐☐X☐XXX☐☐XXX☐☐☐☐☐XXX☐☐XXX after toggling with step = 6
☐XX☐XXX☐X☐☐☐☐☐☐☐☐X☐X☐X☐☐XXXX☐☐☐☐XX☐☐☐XXX☐☐☐☐☐X☐☐X☐X☐☐XXXXX☐X☐X☐☐XX☐☐XX☐☐☐X☐☐XX☐XXX☐XXXX☐☐☐X☐XXX☐☐☐XX after toggling with step = 7
☐XX☐XXXXX☐☐☐☐☐☐X☐X☐X☐X☐XXXXX☐☐☐XXX☐☐☐XX☐☐☐☐☐☐X☐XX☐X☐☐XX☐XX☐X☐X☐XXX☐☐XX☐X☐X☐☐XX☐☐XX☐XXXXX☐☐X☐XXXX☐☐XX after toggling with step = 8
☐XX☐XXXX☐☐☐☐☐☐☐X☐☐☐X☐X☐XXX☐X☐☐☐XXX☐X☐XX☐☐☐☐☐XX☐XX☐X☐☐☐X☐XX☐X☐XXXXX☐☐XX☐☐☐X☐☐XX☐☐☐X☐XXXXX☐XX☐XXXX☐☐☐X after toggling with step = 9
☐XX☐XXXX☐X☐☐☐☐☐X☐☐☐☐☐X☐XXX☐X☐X☐XXX☐X☐XXX☐☐☐☐XX☐XXXX☐☐☐X☐XX☐☐☐XXXXX☐☐X☐☐☐☐X☐☐XX☐X☐X☐XXXXX☐☐X☐XXXX☐☐☐☐ after toggling with step = 10
☐XX☐XXXX☐XX☐☐☐☐X☐☐☐☐☐☐☐XXX☐X☐X☐X☐X☐X☐XXX☐☐☐XXX☐XXXX☐☐☐☐☐XX☐☐☐XXXX☐☐☐X☐☐☐☐X☐☐☐X☐X☐X☐XXXX☐☐☐X☐XXXX☐☐X☐ after toggling with step = 11
☐XX☐XXXX☐XXX☐☐☐X☐☐☐☐☐☐☐☐XX☐X☐X☐X☐X☐☐☐XXX☐☐☐XXX☐☐XXX☐☐☐☐☐XX☐X☐XXXX☐☐☐X☐☐X☐X☐☐☐X☐X☐X☐☐XXX☐☐☐X☐XXX☐☐☐X☐ after toggling with step = 12
☐XX☐XXXX☐XXXX☐☐X☐☐☐☐☐☐☐☐X☐☐X☐X☐X☐X☐☐☐X☐X☐☐☐XXX☐☐XXXX☐☐☐☐XX☐X☐XXX☐☐☐☐X☐☐X☐X☐☐☐☐☐X☐X☐☐XXX☐☐☐☐☐XXX☐☐☐X☐ after toggling with step = 13
☐XX☐XXXX☐XXXXX☐X☐☐☐☐☐☐☐☐X☐☐☐☐X☐X☐X☐☐☐X☐X☐X☐XXX☐☐XXXX☐☐☐XXX☐X☐XXX☐☐☐☐XX☐X☐X☐☐☐☐☐X☐X☐XXXX☐☐☐☐☐XXX☐☐XX☐ after toggling with step = 14
☐XX☐XXXX☐XXXXXXX☐☐☐☐☐☐☐☐X☐☐☐☐☐☐X☐X☐☐☐X☐X☐X☐X☐X☐☐XXXX☐☐☐XXX☐☐☐XXX☐☐☐☐XX☐X☐XX☐☐☐☐X☐X☐XXXX☐☐X☐☐XXX☐☐XX☐ after toggling with step = 15
☐XX☐XXXX☐XXXXXX☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐X☐☐☐X☐X☐X☐X☐X☐XXXXX☐☐☐XXX☐☐☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐☐X☐XXXX☐☐X☐☐XXXX☐XX☐ after toggling with step = 16
☐XX☐XXXX☐XXXXXX☐X☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐X☐X☐X☐X☐XXX☐X☐☐☐XXX☐☐☐XX☐☐☐☐XXX☐X☐XX☐☐☐☐☐☐X☐X☐XX☐☐X☐☐XXXX☐XX☐ after toggling with step = 17
☐XX☐XXXX☐XXXXXX☐XX☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐XXX☐☐☐XX☐☐☐☐XXX☐☐☐XX☐☐☐☐☐☐X☐X☐XX☐☐☐☐☐XXXX☐XX☐ after toggling with step = 18
☐XX☐XXXX☐XXXXXX☐XXX☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐☐☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐☐☐XX☐☐☐☐XXX☐☐☐XXX☐☐☐☐☐X☐X☐XX☐☐☐☐☐XX☐X☐XX☐ after toggling with step = 19
☐XX☐XXXX☐XXXXXX☐XXXX☐☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐XX☐☐☐☐XXX☐☐☐XXX☐☐☐X☐X☐X☐XX☐☐☐☐☐XX☐X☐XXX after toggling with step = 20
☐XX☐XXXX☐XXXXXX☐XXXXX☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐☐☐☐☐XXX☐☐☐XXX☐☐☐X☐X☐☐☐XX☐☐☐☐☐XX☐X☐XXX after toggling with step = 21
☐XX☐XXXX☐XXXXXX☐XXXXXX☐☐X☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐X☐XXX☐X☐X☐X☐X☐X☐X☐☐☐X☐XXX☐☐☐XXX☐☐☐X☐X☐☐☐XXX☐☐☐☐XX☐X☐XXX after toggling with step = 22
☐XX☐XXXX☐XXXXXX☐XXXXXXX☐X☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐XXX☐X☐X☐X☐X☐X☐X☐☐☐X☐X☐X☐☐☐XXX☐☐☐X☐X☐☐☐XXX☐☐☐XXX☐X☐XXX after toggling with step = 23
☐XX☐XXXX☐XXXXXX☐XXXXXXXXX☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐XX☐X☐X☐X☐X☐X☐X☐☐☐X☐X☐X☐X☐XXX☐☐☐X☐X☐☐☐XXX☐☐☐XXX☐☐☐XXX after toggling with step = 24
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐X☐X☐X☐X☐X☐X☐☐☐X☐X☐X☐X☐X☐X☐☐☐X☐X☐☐☐XXX☐☐☐XXX☐☐☐XX☐ after toggling with step = 25
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐X☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐X☐X☐X☐X☐X☐☐☐X☐X☐X☐X☐X☐X☐X☐X☐X☐☐☐XXX☐☐☐XXX☐☐☐XX☐ after toggling with step = 26
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XX☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐X☐X☐X☐X☐☐☐X☐X☐X☐X☐X☐X☐X☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XX☐ after toggling with step = 27
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXX☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐X☐X☐X☐☐☐X☐X☐X☐X☐X☐X☐X☐XXX☐X☐XXX☐☐☐XXX☐☐☐XX☐ after toggling with step = 28
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXX☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐X☐☐☐X☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐☐☐XXX☐☐☐XX☐ after toggling with step = 29
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXX☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐X☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐XXX☐☐☐XX☐ after toggling with step = 30
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXX☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐☐☐XX☐ after toggling with step = 31
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXX☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐X☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐XX☐ after toggling with step = 32
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXX☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 33
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 34
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 35
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 36
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 37
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XX☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 38
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXX☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 39
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXX☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐XX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 40
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXX☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 41
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXX☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 42
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXX☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 43
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXX☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐X☐X☐X☐X☐X☐☐ after toggling with step = 44
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXX☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐X☐X☐X☐☐ after toggling with step = 45
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXX☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐X☐X☐☐ after toggling with step = 46
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐X☐☐ after toggling with step = 47
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐ after toggling with step = 48
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐ after toggling with step = 49
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 50
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XX☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 51
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXX☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 52
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXX☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 53
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXX☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 54
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXX☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 55
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXX☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 56
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXX☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 57
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXX☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 58
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXX☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 59
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXX☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 60
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXX☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 61
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 62
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 63
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 64
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 65
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XX☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 66
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXX☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 67
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXX☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 68
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXX☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 69
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXX☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 70
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXX☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 71
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXX☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 72
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXX☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 73
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXX☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 74
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXX☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 75
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXX☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 76
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXX☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 77
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXX☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 78
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 79
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 80
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 81
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 82
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 83
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 84
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 85
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 86
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXX☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 87
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXX☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 88
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXX☐☐☐☐☐☐☐☐☐☐X after toggling with step = 89
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXX☐☐☐☐☐☐☐☐☐X after toggling with step = 90
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXX☐☐☐☐☐☐☐☐X after toggling with step = 91
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXX☐☐☐☐☐☐☐X after toggling with step = 92
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXX☐☐☐☐☐☐X after toggling with step = 93
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXX☐☐☐☐☐X after toggling with step = 94
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXX☐☐☐☐X after toggling with step = 95
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXXX☐☐☐X after toggling with step = 96
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐☐X after toggling with step = 97
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXXX☐X after toggling with step = 98
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXXXXX after toggling with step = 99
☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXXXX☐ after toggling with step = 100

## DCL

 $! doors.com$! Excecute by running @doors at prompt.$square = 1$ incr = 3$count2 = 0$ d = 1$LOOP2:$       count2 = count2 + 1$IF (d .NE. square)$               THEN WRITE SYS$OUTPUT "door ''d' is closed"$       ELSE WRITE SYS$OUTPUT "door ''d' is open"$               square = incr + square$incr = incr + 2$       ENDIF$d = d + 1$       IF (count2 .LT. 100) THEN GOTO LOOP2 

See Pascal

## Déjà Vu

local :open-doors [ rep 101 false ] for i range 1 100:	local :j i	while <= j 100:		set-to open-doors j not open-doors! j		set :j + j i !print\ "Open doors: "for i range 1 100:	if open-doors! i:		!print$$to-str i " " ) Output: Open doors: 1 4 9 16 25 36 49 64 81 100  ## DUP 100[][0^:1-]# {initialize doors}%[s;[101<][;~\:s;+]#%]d: {function d, switch door state function}1s:[s;101<][d;!s;1+s:]# {increment step width from 1 to 100, execute function d each time}1[101<][.' ,;['o,'p,'e,'n,10,]['c,'l,'o,'s,'e,'d,10,]?1+]# {loop through doors, print door number and state} Result: 1 open2 closed3 closed4 open5 closed6 closed7 closed8 closed9 open10 closed11 closed12 closed...94 closed95 closed96 closed97 closed98 closed99 closed100 open Compare this solution to the FALSE solution of this problem. ## DWScript Unoptimized var doors : array [1..100] of Boolean;var i, j : Integer; for i := 1 to 100 do for j := i to 100 do if (j mod i) = 0 then doors[j] := not doors[j];F for i := 1 to 100 do if doors[i] then PrintLn('Door '+IntToStr(i)+' is open'); ## Dyalect Outputs only open doors to save up space: var doors = Array.empty(100, false) for p in 0..99 { for d in 0..99 { if (d + 1) % (p + 1) == 0 { doors[d] = !doors[d]; } }} for d in doors.indices() when doors[d] { print("Door \(d+1): Open")} Output: Door 1: Open Door 4: Open Door 9: Open Door 16: Open Door 25: Open Door 36: Open Door 49: Open Door 64: Open Door 81: Open Door 100: Open ## Dylan Unoptimized define method doors() let doors = make(<array>, fill: #f, size: 100); for (x from 0 below 100) for (y from x below 100 by x + 1) doors[y] := ~doors[y] end end; for (x from 1 to 100) if (doors[x - 1]) format-out("door %d open\n", x) end endend ## E Graphical Works with: E-on-Java This version animates the changes of the doors (as checkboxes). #!/usr/bin/env rune var toggles := []var gets := [] # Set up GUI (and data model)def frame := <swing:makeJFrame>("100 doors")frame.getContentPane().setLayout(<awt:makeGridLayout>(10, 10))for i in 1..100 { def component := <import:javax.swing.makeJCheckBox>(E.toString(i)) toggles with= fn { component.setSelected(!component.isSelected()) } gets with= fn { component.isSelected() } frame.getContentPane().add(component)} # Set up termination conditiondef doneframe.addWindowListener(def _ { to windowClosing(event) { bind done := true } match _ {}}) # Open and close doorsdef loop(step, i) { toggles[i] <- () def next := i + step timer.whenPast(timer.now() + 10, fn { if (next >= 100) { if (step >= 100) { # Done. } else { loop <- (step + 1, step) } } else { loop <- (step, i + step) } })}loop(1, 0) frame.pack()frame.show()interp.waitAtTop(done) ## EasyLang len d[] 101for p = 1 to 100 i = p while i <= 100 d[i] = 1 - d[i] i += p ..for i = 1 to 100 if d[i] = 1 print i .. ## EchoLisp The result is obviously the same in we run the process backwards. So, we check the state of each door during the 100-th step (opening/closing every door)  ; initial state = closed = #f(define doors (make-vector 101 #f)); run pass 100 to 1(for* ((pass (in-range 100 0 -1)) (door (in-range 0 101 pass))) (when (and (vector-set! doors door (not (vector-ref doors door))) (= pass 1)) (writeln door "is open"))) 1 "is open" 4 "is open" 9 "is open" 16 "is open" 25 "is open" 36 "is open" 49 "is open" 64 "is open" 81 "is open" 100 "is open"  ## ECL optimized version  Doors := RECORD UNSIGNED1 DoorNumber; STRING6 State;END; AllDoors := DATASET([{0,0}],Doors); Doors OpenThem(AllDoors L,INTEGER Cnt) := TRANSFORM SELF.DoorNumber := Cnt; SELF.State := IF((CNT * 10) % (SQRT(CNT)*10)<>0,'Closed','Opened');END; OpenDoors := NORMALIZE(AllDoors,100,OpenThem(LEFT,COUNTER)); OpenDoors;  unoptimized version - demonstrating LOOP  Doors := RECORD UNSIGNED1 DoorNumber; STRING6 State;END; AllDoors := DATASET([{0,'0'}],Doors); //first build the 100 doors Doors OpenThem(AllDoors L,INTEGER Cnt) := TRANSFORM SELF.DoorNumber := Cnt; SELF.State := 'Closed';END; ClosedDoors := NORMALIZE(AllDoors,100,OpenThem(LEFT,COUNTER)); //now iterate through them and use door logic loopBody(DATASET(Doors) ds, UNSIGNED4 c) := PROJECT(ds, //ds=original input TRANSFORM(Doors, SELF.State := CASE((COUNTER % c) * 100, 0 => IF(LEFT.STATE = 'Opened','Closed','Opened') ,LEFT.STATE); SELF.DoorNumber := COUNTER; //PROJECT COUNTER )); g1 := LOOP(ClosedDoors,100,loopBody(ROWS(LEFT),COUNTER)); OUTPUT(g1);  unoptimized version - using ITERATE This is a bit more efficient than the LOOP version  DoorSet := DATASET(100,TRANSFORM({UNSIGNED1 DoorState},SELF.DoorState := 1));SetDoors := SET(DoorSet,DoorState); Doors := RECORD UNSIGNED1 Pass; SET OF UNSIGNED1 DoorSet;END; StartDoors := DATASET(100,TRANSFORM(Doors,SELF.Pass := COUNTER,SELF.DoorSet := SetDoors)); Doors XF(Doors L, Doors R) := TRANSFORM ds := DATASET(L.DoorSet,{UNSIGNED1 DoorState}); NextDoorSet := PROJECT(ds, TRANSFORM({UNSIGNED1 DoorState}, SELF.DoorState := CASE((COUNTER % R.Pass) * 100, 0 => IF(LEFT.DoorState = 1,0,1), LEFT.DoorState))); SELF.DoorSet := IF(L.Pass=0,R.DoorSet,SET(NextDoorSet,DoorState)); SELF.Pass := R.Pass END; Res := DATASET(ITERATE(StartDoors,XF(LEFT,RIGHT)).DoorSet,{UNSIGNED1 DoorState});PROJECT(Res,TRANSFORM({STRING20 txt},SELF.Txt := 'Door ' + COUNTER + ' is ' + IF(LEFT.DoorState=1,'Open','Closed')));  ## EDSAC order code Since there are only 100 doors, we'll keep things simple and use a whole EDSAC location for each door. A single bit would be enough, but that would make the code much longer. The program works through the array of doors by modifying its own orders (instructions). This would be considered bad practice today, but was quite usual on the EDSAC.  [Hundred doors problem from Rosetta Code website][EDSAC program, Initial Orders 2] [Library subroutine M3. Prints header and is then overwritten.Here, the last character sets the teleprinter to figures.] [email protected]@E8FEZPF @&*[email protected]&# ..PZ [blank tape, needed to mark end of header text] [Library subroutine P6. Prints strictly positive integer.32 locations; working locations 1, 4, 5] T56K [define load address for subroutine] [email protected]@[email protected]@[email protected] [email protected] [email protected]@[email protected]@J995FJF!F T88K [define load address for main program] GK [set @ (theta) for relative addresses] [The 100 doors are at locations 200..299.Doors are numbered 0..99 internally, and 1..100 for output.The base address and the number of doors can be varied.The value of a door is 0 if open, negative if closed.] [Constants. Program also uses order 'P 1 F' which is permanently at absolute address 2.]  P200F [address of door #0]  P100F [number of doors, as an address]  UF [makes S order from T, since 'S' = 'T' + 'U']  MF [makes A order from T, since 'A' = 'T' + 'M']  V2047D [all 1's for "closed" (any negative value will do)]  &F [line feed]  @F [carriage return]  K4096F [teleprinter null[ [Variables]  PF [pass number; step when toggling doors]  PF [door number, as address, 0-based]  PF [order referring to door 0] [Enter with acc = 0] [Part 1 : close all the doors]  [email protected] [pass := 0 (used in part 2)] [email protected] [door number := 0] [email protected] [load 'T F' order] [email protected] [add base address] [email protected] [store T order for door #0]  TF [clear acc; also serves as constant] [email protected] [load door number] [email protected] [make T order] [email protected] [plant in code] [email protected] [load value for "closed"]  TF [store in current door] [email protected] [load door number] A2F [add 1] [email protected] [update door number] [email protected] [done all doors yet?] [email protected] [if not, loop back] [Part 2 : 100 passes, toggling the doors]  TF [clear acc] [email protected] [load pass number] A2F [add 1] [email protected] [save updated pass number] S2F [make -1] [email protected] [door number := -1] [email protected] [add pass number to get first door toggled on this pass] [email protected] [gone beyond end?] [email protected] [if so, move on to part 3]  [email protected] [restore acc after test] [email protected] [store current door number] [email protected] [make T order to load status] [email protected] [plant T order for first door in pass] [email protected] [convert to S order] [email protected] [plant S order] [email protected] [load value for "closed"]  SF [subtract status; toggles status]  TF [update status] [email protected] [load door number just toggled] [email protected] [add pass number to get next door in pass] [email protected] [gone beyond end?] [email protected] [no, loop to do next door] [email protected] [yes, loop to do next pass] [Part 3 : Print list of open doors. Header has set teleprinter to figures.]  TF [clear acc] [email protected] [door nr := 0] [email protected] [T order for door 0] [email protected] [convert to A order] [email protected]  TF [email protected] [load door number] [email protected] [make A order to load value] [email protected] [plant in next order]  AF [acc := 0 if open, < 0 if closed] [email protected] [skip if closed] [email protected] [door number as address] A2F [add 1 for 1-based output] RD [shift 1 right, address --> integer] TF [store integer at 0 for printing]  [email protected] [for return from subroutine] G56F [call subroutine to print door number] [email protected] [followed by CRLF] [email protected]  TF [clear acc] [email protected] [load door number] A2F [add 1] [email protected] [update door number] [email protected] [done all doors yet?] [email protected] [if not, loop back]  [email protected] [output null to flush teleprinter buffer] ZF [stop] E11Z [define relative start address] PF  Output: THE OPEN DOORS ARE 1 4 9 16 25 36 49 64 81 100  ## Eero  #import <Foundation/Foundation.h> int main() square := 1, increment = 3 for int door in 1 .. 100 printf("door #%d", door) if door == square puts(" is open.") square += increment increment += 2 else puts(" is closed.") return 0  ## Egel  import "prelude.eg" using Systemusing List data open, closed def toggle = [ open N -> closed N | closed N -> open N ] def doors = [ N -> map [ N -> closed N ] (fromto 1 N) ] def toggleK = [ K nil -> nil | K (cons (D N) DD) -> let DOOR = if (N%K) == 0 then toggle (D N) else D N in cons DOOR (toggleK K DD) ] def toggleEvery = [ nil DOORS -> DOORS | (cons K KK) DOORS -> toggleEvery KK (toggleK K DOORS) ] def run = [ N -> toggleEvery (fromto 1 N) (doors N) ] def main = run 100  ## EGL  program OneHundredDoors function main() doors boolean[] = new boolean; n int = 100; for (i int from 1 to n) for (j int from i to n by i) doors[j] = !doors[j]; end end for (i int from 1 to n) if (doors[i]) SysLib.writeStdout( "Door " + i + " is open" ); end end end end  ## Eiffel This is my first RosettaCode submission, as well as a foray into Eiffel for myself. I've tried to adhere to the description of the problem statement, as well as showcase a few Eiffelisms shown in the documentation. The replacement code below took the original code and has made improvements in some ways, such as: 1. Removal of "magic" many magic numbers and strings. 2. Refactor of various code blocks to routines (commands and queries with good CQS). 3. Utilization/Demonstration of full, secret, and selective feature exporting. 4. Utilization/Demonstration of constants as expanded type constants and once-functions. 5. Utilization/Demonstration of static-references (e.g. {APPLICATION}.min_door_count). 6. Utilization/Demonstration of "like" keyword type anchoring (e.g. a_index_address: like {DOOR}.address). 7. Utilization/Demonstration of semi-strict logical implication (e.g. consistency: is_open implies not Is_closed). 8. Utilization/Demonstration of contracts, including require, ensure, and class invariant. 9. Utilization/Demonstration of agent and do_all' call on ITERABLE type. 10. Utilization/Demonstration of various forms of across including "loop" and "all". ... as well as other Eiffel-ism's and some coding standards/best-practices. file: application.e note description: "100 Doors problem" date: "08-JUL-2015" revision: "1.1" class APPLICATION create make feature {NONE} -- Initialization make -- Main application routine. do initialize_closed_doors toggle_doors output_door_states end feature -- Access doors: ARRAYED_LIST [DOOR] -- A set of doors (self-initialized to capacity of max_door_count'). attribute create Result.make (max_door_count) end feature -- Basic Operations initialize_closed_doors -- Initialize all doors'. do across min_door_count |..| max_door_count as ic_address_list loop doors.extend (create {DOOR}.make_closed (ic_address_list.item)) end ensure has_all_closed_doors: across doors as ic_doors_list all not ic_doors_list.item.is_open end end toggle_doors -- Toggle all doors'. do across min_door_count |..| max_door_count as ic_addresses_list loop across doors as ic_doors_list loop if is_door_to_toggle (ic_doors_list.item.address, ic_addresses_list.item) then ic_doors_list.item.toggle_door end end end end output_door_states -- Output the state of all doors'. do doors.do_all (agent door_state_out) end feature -- Status Report is_door_to_toggle (a_door_address, a_index_address: like {DOOR}.address): BOOLEAN -- Is the door at a_door_address' needing to be toggled, when compared to a_index_address'? do Result := a_door_address \\ a_index_address = 0 ensure only_modulus_zero: Result = (a_door_address \\ a_index_address = 0) end feature -- Outputs door_state_out (a_door: DOOR) -- Output the state of a_door'. do print ("Door " + a_door.address.out + " is ") if a_door.is_open then print ("open.") else print ("closed.") end io.new_line end feature {DOOR} -- Constants min_door_count: INTEGER = 1 -- Minimum number of doors. max_door_count: INTEGER = 100 -- Maximum number of doors. end file: door.e note description: "A door with an address and an open or closed state." date: "08-JUL-2015" revision: "1.1" class DOOR create make_closed, make feature {NONE} -- initialization make_closed (a_address: INTEGER) -- Initialize Current {DOOR} at a_address' and state of Is_closed'. require positive: a_address >= {APPLICATION}.min_door_count and a_address >= Min_door_count do make (a_address, Is_closed) ensure closed: is_open = Is_closed end make (a_address: INTEGER; a_status: BOOLEAN) -- Initialize Current {DOOR} with a_address' and a_status', denoting position and is_open' or Is_closed'. require positive: a_address >= {APPLICATION}.min_door_count and a_address >= Min_door_count do address := a_address is_open := a_status ensure address_set: address = a_address status_set: is_open = a_status end feature -- access address: INTEGER -- address' of Current {DOOR}. is_open: BOOLEAN assign set_open -- is_open' (or not) status of Current {DOOR}. feature -- Setters set_open (a_status: BOOLEAN) -- Set status' with a_status' do is_open := a_status ensure open_updated: is_open = a_status end feature {APPLICATION} -- Basic Operations toggle_door -- Toggle Current {DOOR} from is_open' to not is_open'. do is_open := not is_open ensure toggled: is_open /= old is_open end feature {NONE} -- Implementation: Constants Is_closed: BOOLEAN = False -- State of being not is_open'. Min_door_count: INTEGER = 1 -- Minimum door count. invariant one_or_more: address >= 1 consistency: is_open implies not Is_closed end ## Ela Standard Approach open generic type Door = Open | Closed deriving Show gate [] _ = []gate (x::xs) (y::ys) | x == y = Open :: gate xs ys | else = Closed :: gate xs ys run n = gate [1..n] [& k*k \\ k <- [1..]] Alternate Approach open listrun n = takeWhile (<n) [& k*k \\ k <- [1..]] ## Elena ELENA 4.0 : import system'routines;import extensions; public program(){ var Doors := Array.allocate(100).populate:(n=>false); for(int i := 0, i < 100, i := i + 1) { for(int j := i, j < 100, j := j + i + 1) { Doors[j] := Doors[j].Inverted } }; for(int i := 0, i < 100, i := i + 1) { console.printLine("Door #",i + 1," :",Doors[i].iif("Open","Closed")) }; console.readChar()} ## Elixir defmodule HundredDoors do def doors(n \\ 100) do List.duplicate(false, n) end def toggle(doors, n) do List.update_at(doors, n, &(!&1)) end def toggle_every(doors, n) do Enum.reduce( Enum.take_every((n-1)..99, n), doors, fn(n, acc) -> toggle(acc, n) end ) endend # unoptimizedfinal_state = Enum.reduce(1..100, HundredDoors.doors, fn(n, acc) -> HundredDoors.toggle_every(acc, n) end) open_doors = Enum.with_index(final_state) |> Enum.filter_map(fn {door,_} -> door end, fn {_,index} -> index+1 end) IO.puts "All doors are closed except these: #{inspect open_doors}" # optimized final_state = Enum.reduce(1..10, HundredDoors.doors, fn(n, acc) -> HundredDoors.toggle(acc, n*n-1) end) open_doors = Enum.with_index(final_state) |> Enum.filter_map(fn {door,_} -> door end, fn {_,index} -> index+1 end) IO.puts "All doors are closed except these: #{inspect open_doors}" Output: All doors are closed except these: [1, 4, 9, 16, 25, 36, 49, 64, 81, 100] ## Elm -- Unoptimizedimport List exposing (indexedMap, foldl, repeat, range)import Html exposing (text)import Debug exposing (toString) type Door = Open | Closed toggle d = if d == Open then Closed else Open toggleEvery : Int -> List Door -> List DoortoggleEvery k doors = indexedMap (\i door -> if modBy k (i+1) == 0 then toggle door else door) doors n = 100 main = text (toString (foldl toggleEvery (repeat n Closed) (range 1 n)))  ## Emacs Lisp Unoptimized (defun create-doors () "Returns a list of closed doors Each door only has two status: open or closed.If a door is closed it has the value 0, if it's open it has the value 1." (let ((return_value '(0)) ;; There is already a door in the return_value, so k starts at 1 ;; otherwise we would need to compare k against 99 and not 100 in ;; the while loop (k 1)) (while (< k 100) (setq return_value (cons 0 return_value)) (setq k (+ 1 k))) return_value)) (defun toggle-single-door (doors) "Toggle the stat of the door at the car' position of the DOORS list DOORS is a list of integers with either the value 0 or 1 and it representsa row of doors. Returns a list where the car' of the list has it's value toggled (if openit becomes closed, if closed it becomes open)." (if (= (car doors) 1) (cons 0 (cdr doors)) (cons 1 (cdr doors)))) (defun toggle-doors (doors step original-step) "Step through all elements of the doors' list and toggle a door when step is 1 DOORS is a list of integers with either the value 0 or 1 and it representsa row of doors.STEP is the number of doors we still need to transverse before we arriveat a door that has to be toggled.ORIGINAL-STEP is the value of the argument step when this function iscalled for the first time. Returns a list of doors" (cond ((null doors) '()) ((= step 1) (cons (car (toggle-single-door doors)) (toggle-doors (cdr doors) original-step original-step))) (t (cons (car doors) (toggle-doors (cdr doors) (- step 1) original-step))))) (defun main-program () "The main loop for the program" (let ((doors_list (create-doors)) (k 1) ;; We need to define max-specpdl-size and max-specpdl-size to big ;; numbers otherwise the loop reaches the max recursion depth and ;; throws an error. ;; If you want more information about these variables, press Ctrl ;; and h at the same time and then press v and then type the name ;; of the variable that you want to read the documentation. (max-specpdl-size 5000) (max-lisp-eval-depth 2000)) (while (< k 101) (setq doors_list (toggle-doors doors_list k k)) (setq k (+ 1 k))) doors_list)) (defun print-doors (doors) "This function prints the values of the doors into the current buffer. DOORS is a list of integers with either the value 0 or 1 and it representsa row of doors." ;; As in the main-program function, we need to set the variable ;; max-lisp-eval-depth to a big number so it doesn't reach max recursion ;; depth. (let ((max-lisp-eval-depth 5000)) (unless (null doors) (insert (int-to-string (car doors))) (print-doors (cdr doors))))) ;; Returns a list with the final solution(main-program) ;; Print the final solution on the buffer(print-doors (main-program)) ## Erlang non-optimized  -module(hundoors). -export([go/0]). toggle(closed) -> open;toggle(open) -> closed. go() -> go([closed || _ <- lists:seq(1, 100)],[], 1, 1).go([], L, N, _I) when N =:= 101 -> lists:reverse(L);go([], L, N, _I) -> go(lists:reverse(L), [], N + 1, 1);go([H|T], L, N, I) -> H2 = case I rem N of 0 -> toggle(H); _ -> H end, go(T, [H2|L], N, I + 1).  optimized doors() -> F = fun(X) -> Root = math:pow(X,0.5), Root == trunc(Root) end, Out = fun(X, true) -> io:format("Door ~p: open~n",[X]); (X, false)-> io:format("Door ~p: close~n",[X]) end, [Out(X,F(X)) || X <- lists:seq(1,100)]. ## ERRE  ! "100 Doors" program for ERRE LANGUAGE! Author: Claudio Larini! Date: 21-Nov-2014!! PC Unoptimized version translated from a QB version PROGRAM 100DOORS !INTEGER CONST N=100 DIM DOOR[N] BEGIN FOR STRIDE=1 TO N DO FOR INDEX=STRIDE TO N STEP STRIDE DO DOOR[INDEX]=NOT(DOOR[INDEX]) END FOREND FOR PRINT("Open doors:";)FOR INDEX=1 TO N DO IF DOOR[INDEX] THEN PRINT(INDEX;) END IFEND FORPRINT END PROGRAM  ## Euler Math Toolbox  >function Doors () ... doors:=zeros(1,100); for i=1 to 100 for j=i to 100 step i doors[j]=!doors[j]; end; end; return doorsendfunction>nonzeros(Doors()) [ 1 4 9 16 25 36 49 64 81 100 ]  ## Euphoria unoptimised -- doors.exinclude std/console.esequence doorsdoors = repeat( 0, 100 ) -- 1 to 100, initialised to false for pass = 1 to 100 do for door = pass to 100 by pass do --printf( 1, "%d", doors[door] ) --printf( 1, "%d", not doors[door] ) doors[door] = not doors[door] end forend for sequence oc for i = 1 to 100 do if doors[i] then oc = "open" else oc = "closed" end if printf( 1, "door %d is %s\n", { i, oc } )end for  ## Excel Note: The use of Auto Fill saves a lot of time when entering this code. One can refer to Excel help pages to learn about Auto Fill features. Create a labelling column (A) and row (1) labelling the number of the door (column A, labelling starts in row 2 with a "1" and continues counting up to "100" in row 101) and the number of the pass (row 1, labelling starts in column B with a "0" and continues counting up to "100" in column CX). Additonally, you can label cell A1 as "Door/Pass" or so. Closed doors are represented by zeroes ("0"), open doors are represented by ones ("1"). To represent the initial condition fill rows 2 to 101 in column B (pass "0") with zeroes. Starting in column C, row 2, you enter code as shown in the examples below. The examples show the code to be entered in cells C2, C3, and D2. Continue to write code for the rest of the 4245 data cells, accordingly. Excel Auto Fill feature is best used for this. Cell C2:  =IF(A2/C1=INT(A2/C1),IF(B2=0,1,IF(B2=1,0)),B2)  Cell C3:  =IF(A3/C1=INT(A3/C1),IF(B3=0,1,IF(B3=1,0)),B3)  Cell D2:  =IF(A2/D1=INT(A2/D1),IF(C2=0,1,IF(C2=1,0)),C2)  The last column (column CX, labelled "100") shows a "1" for each door (labelled by the rows in column A) that is open after the 100th pass. It shows a "1" for the following doors: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. ## F# Requires #light in versions of F# prior to 2010 beta. let answerDoors = let ToggleNth n (lst:bool array) = // Toggle every n'th door [(n-1) .. n .. 99] // For each appropriate door |> Seq.iter (fun i -> lst.[i] <- not lst.[i]) // toggle it let doors = Array.create 100 false // Initialize all doors to closed Seq.iter (fun n -> ToggleNth n doors) [1..100] // toggle the appropriate doors for each pass doors // Initialize all doors to closed  Unoptimized / functional  let modifier doors skip = let rec modifierInner doors skip counter = match doors with | [] -> [] //base case: end of hall | first::rest when counter >= skip -> //case: reached door marked for change not first::(modifierInner rest skip 0) // open or close that door | first::rest -> //case: reached door to skip first::(modifierInner rest skip (counter+1)) // skip it modifierInner doors skip 0 //Initial state for walkthrough let answerDoors doors = let rec modifyDoors skipRange doors modifier = //fold each door result to the next with List.fold modifier doors skipRange //with an increasing skip modifyDoors [0..99] doors modifier //Initial starting state let initDoors = Array.create 100 false |> Array.toList //Initialize all doors to closed (false) answerDoors initDoors |> printfn "%A" //print answer (false is closed door)  Tail-Recursive Optimized/Functional  let modifier doors skip = let rec modifier' doors skip counter result = match doors with | [] -> result |> List.rev //base case: end of hall | first::rest when counter >= skip -> //case: reached door marked for change modifier' rest skip 0 ((not first)::result) // open or close that door | first::rest -> //case: reached door to skip modifier' rest skip (counter+1) (first::result) // skip it modifier' doors skip 0 [] //Initial state for walkthrough  Following is the solution using perfect squares. The coercions in PerfectSquare are, I believe, slightly different in versions prior to 2010 beta and, again, #light is required in those versions. open Systemlet answer2 = let PerfectSquare n = let sqrt = int(Math.Sqrt(float n)) n = sqrt * sqrt [| for i in 1..100 do yield PerfectSquare i |] Simple single line solution using nothing but List  [1..100] |> List.fold (fun doors pass->List.mapi (fun i x->if ((i + 1) % pass)=0 then not x else x) doors) (List.init 100 (fun _->false))  ## Factor Unoptimized USING: bit-arrays formatting fry kernel math math.rangessequences ;IN: rosetta.doors CONSTANT: number-of-doors 100 : multiples ( n -- range ) 0 number-of-doors rot <range> ; : toggle-multiples ( n doors -- ) [ multiples ] dip '[ _ [ not ] change-nth ] each ; : toggle-all-multiples ( doors -- ) [ number-of-doors [1,b] ] dip '[ _ toggle-multiples ] each ; : print-doors ( doors -- ) [ swap "open" "closed" ? "Door %d is %s\n" printf ] each-index ; : main ( -- ) number-of-doors 1 + <bit-array> [ toggle-all-multiples ] [ print-doors ] bi ; main Optimized  USING: formatting math math.primes.factors math.ranges sequences ;IN: rosetta-doors2 : main ( -- ) 100 [1,b] [ divisors length odd? ] filter "Open %[%d, %]\n" printf ;  ## Falcon Unoptimized code doors = arrayBuffer( 101, false ) for pass in [ 0 : doors.len() ] for door in [ 0 : doors.len() : pass+1 ] doors[ door ] = not doors[ door ] endend for door in [ 1 : doors.len() ] // Show Output > "Door ", door, " is: ", ( doors[ door ] ) ? "open" : "closed"end  Optimized code  for door in [ 1 : 101 ]: > "Door ", door, " is: ", fract( door ** 0.5 ) ? "closed" : "open" ## FALSE 100[][0 1ø:1-]# {initialize doors}%[s;[101\>][;~\:s;+]#%]d: {function d, switch door state function}1s:[s;101\>][d;!s;1+s:]# {increment step width from 1 to 100, execute function d each time}1[101\>][." ";["open"]?~["closed"]?1+]# {loop through doors, print door number and state} Result: 1 open2 closed3 closed4 open5 closed6 closed7 closed8 closed9 open10 closed...98 closed99 closed100 open Compare this solution to the DUP solution of this problem. ## Fantom Unoptimized  states := (1..100).toList 100.times |i| { states = states.map |state| { state % (i+1) == 0 ? -state : +state } } echo("Open doors are " + states.findAll { it < 0 }.map { -it })  Optimized  echo("Open doors are " + (1..100).toList.findAll { it.toFloat.pow(0.5f).toInt.pow(2) == it})  ## FBSL Unoptimised #AppType Console DIM doors[], n AS INTEGER = 100 FOR DIM i = 1 TO n FOR DIM j = i TO n STEP i doors[j] = NOT doors[j] NEXTNEXT FOR i = 1 TO n IF doors[i] THEN PRINT "Door ", i, " is open"NEXT Pause Optimised (by ML) #APPTYPE CONSOLE DIM i = 0, j = 0, door = 1 WHILE INCR(i) < 101 IF i = door THEN PRINT "Door ", door, " open" INCR(door, INCR((INCR(j) << 1))) END IFWEND PAUSE ## Fish Unoptimized 1001-p01.>0101-p02.>101-g001-g+:::aa*)?v101-p03.>02-g?v1}02-p02. >05. >0}02-p02.>~~~0101-p001-g:1+001-paa*)?v02. >07.>0101-p08.>101-g::02-g?v >1+:101-paa*=?; >n" "o^ ## friendly interactive shell Unoptimized # Set doors to empty listset doors # Initialize doors arraysfor i in (seq 100) set doors[i] 0end for i in (seq 100) set j i while test j -le 100 # Logical not on doors set doors[j] (math !doors[j]) set j (math j + i) endend # Print every doorfor i in (seq (count doors)) echo -n "i " if test doors[i] -eq 0 echo closed else echo open endend  Optimized # Set doors to empty listset doors for i in (seq 100) set doors[(math "i * i")] 1 echo -n "i " if test doors[i] -eq 1 echo open else echo closed endend ## Forth Unoptimized : toggle ( c-addr -- ) \ toggle the byte at c-addr dup [email protected] 1 xor swap c! ; 100 1+ ( 1-based indexing ) constant ndoorscreate doors ndoors allot : init ( -- ) doors ndoors erase ; \ close all doors : pass ( n -- ) \ toggle every nth door ndoors over do doors i + toggle dup ( n ) +loop drop ; : run ( -- ) ndoors 1 do i pass loop ;: display ( -- ) \ display open doors ndoors 1 do doors i + [email protected] if i . then loop cr ; init run display Optimized : squared ( n -- n' ) dup * ;: doors ( n -- ) 1 begin 2dup squared >= while dup squared . 1+ repeat 2drop ;100 doors ## Fōrmulæ In this page you can see the solution of this task. Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text (more info). Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for transportation effects more than visualization and edition. The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code. ## Fortran Works with: Fortran 90 unoptimized program doors implicit none integer, allocatable :: door(:) character(6), parameter :: s(0:1) = ["closed", "open "] integer :: i, n print "(A)", "Number of doors?" read *, n allocate (door(n)) door = 1 do i = 1, n door(i:n:i) = 1 - door(i:n:i) print "(A,G0,2A)", "door ", i, " is ", s(door(i)) end doend program optimized PROGRAM DOORS INTEGER, PARAMETER :: n = 100 ! Number of doors INTEGER :: i LOGICAL :: door(n) = .TRUE. ! Initially closed DO i = 1, SQRT(REAL(n)) door(i*i) = .FALSE. END DO DO i = 1, n WRITE(*,"(A,I3,A)", ADVANCE="NO") "Door ", i, " is " IF (door(i)) THEN WRITE(*,"(A)") "closed" ELSE WRITE(*,"(A)") "open" END IF END DO END PROGRAM DOORS ## FreeBASIC ### Toggle ' version 27-10-2016' compile with: fbc -s console #Define max_doors 100 Dim As ULong c, n, n1, door(1 To max_doors) ' toggle, at start all doors are closed (0)' 0 = door closed, 1 = door openFor n = 1 To max_doors For n1 = n To max_doors Step n door(n1) = 1 - door(n1) NextNext ' count the doors that are open (1)Print "doors that are open nr: ";For n = 1 To max_doors If door(n) = 1 Then Print n; " "; c = c + 1 End IfNext Print : PrintPrint "There are " + Str(c) + " doors open" ' empty keyboard bufferWhile InKey <> "" : WendPrint : Print "hit any key to end program"SleepEnd Output: doors that are open nr: 1 4 9 16 25 36 49 64 81 100 There are 10 doors open ### Count ' version 27-10-2016' compile with: fbc -s console #Define max_doors 100 Dim As ULong c, n, n1, door(1 To max_doors) ' at start all doors are closed' simple add 1 each time we open or close a door' doors with odd numbers are open' doors with even numbers are closedFor n = 1 To max_doors For n1 = n To max_doors Step n door(n1) += 1 NextNext Print "doors that are open nr: ";For n = 1 To max_doors If door(n) And 1 Then Print n; " "; c = c + 1 End IfNext Print : PrintPrint "There are " + Str(c) + " doors open" ' empty keyboard bufferWhile InKey <> "" : WendPrint : Print "hit any key to end program"SleepEnd Output is the same as the first version. ### Optimized ' version 27-10-2016' compile with: fbc -s console #Define max_doors 100 Dim As ULong c, n Print "doors that are open nr: ";For n = 1 To 10 Print n * n; " "; c = c + 1Next Print : PrintPrint "There are " + Str(c) + " doors open" ' empty keyboard bufferWhile InKey <> "" : WendPrint : Print "hit any key to end program"SleepEnd Output is the same as the first version. ## Free Pascal  program OneHundredIsOpen; const DoorCount = 100; var IsOpen: array[1..DoorCount] of boolean; Door, Jump: integer; begin // Close all doors for Door := 1 to DoorCount do IsOpen[Door] := False; // Iterations for Jump := 1 to DoorCount do begin Door := Jump; repeat IsOpen[Door] := not IsOpen[Door]; Door := Door + Jump; until Door > DoorCount; end; // Show final status for Door := 1 to DoorCount do begin Write(Door, ' '); if IsOpen[Door] then WriteLn('open') else WriteLn('closed'); end; // Wait for <enter> Readln;end.  ## Frink  doors = new array[, false]for pass=1 to 100 for door=pass to 100 step pass [email protected] = ! [email protected] print["Open doors: "]for door=1 to 100 if [email protected] print["door "]  ## FunL ### Unoptimized for i <- 1..100 r = foldl1( \a, b -> a xor b, [(a|i) | a <- 1..100] ) println( i + ' ' + (if r then 'open' else 'closed') ) ### Optimized import math.sqrt for i <- 1..100 println( i + ' ' + (if sqrt(i) is Integer then 'open' else 'closed') ) ## Futhark  let main(n: i32): [n]bool = loop is_open = replicate n false for i < n do let js = map (*i+1) (iota n) let flips = map (\j -> if j < n then unsafe !is_open[j] else true -- Doesn't matter. ) js in scatter is_open js flips  ## FutureBasic  include "ConsoleWindow" dim as short door, square : square = 1dim as short increment : increment = 3 for door = 1 to 100 if (door == square) print "Door"; door; " is open." square += increment increment += 2 else print "Door"; door; " is closed." end ifnext  Output: Door 1 is open. Door 2 is closed. Door 3 is closed. Door 4 is open. Door 5 is closed. Door 6 is closed. Door 7 is closed. Door 8 is closed. Door 9 is open. Door 10 is closed. Door 11 is closed. Door 12 is closed. Door 13 is closed. Door 14 is closed. Door 15 is closed. Door 16 is open. Door 17 is closed. Door 18 is closed. Door 19 is closed. Door 20 is closed. Door 21 is closed. Door 22 is closed. Door 23 is closed. Door 24 is closed. Door 25 is open. Door 26 is closed. Door 27 is closed. Door 28 is closed. Door 29 is closed. Door 30 is closed. Door 31 is closed. Door 32 is closed. Door 33 is closed. Door 34 is closed. Door 35 is closed. Door 36 is open. Door 37 is closed. Door 38 is closed. Door 39 is closed. Door 40 is closed. Door 41 is closed. Door 42 is closed. Door 43 is closed. Door 44 is closed. Door 45 is closed. Door 46 is closed. Door 47 is closed. Door 48 is closed. Door 49 is open. Door 50 is closed. Door 51 is closed. Door 52 is closed. Door 53 is closed. Door 54 is closed. Door 55 is closed. Door 56 is closed. Door 57 is closed. Door 58 is closed. Door 59 is closed. Door 60 is closed. Door 61 is closed. Door 62 is closed. Door 63 is closed. Door 64 is open. Door 65 is closed. Door 66 is closed. Door 67 is closed. Door 68 is closed. Door 69 is closed. Door 70 is closed. Door 71 is closed. Door 72 is closed. Door 73 is closed. Door 74 is closed. Door 75 is closed. Door 76 is closed. Door 77 is closed. Door 78 is closed. Door 79 is closed. Door 80 is closed. Door 81 is open. Door 82 is closed. Door 83 is closed. Door 84 is closed. Door 85 is closed. Door 86 is closed. Door 87 is closed. Door 88 is closed. Door 89 is closed. Door 90 is closed. Door 91 is closed. Door 92 is closed. Door 93 is closed. Door 94 is closed. Door 95 is closed. Door 96 is closed. Door 97 is closed. Door 98 is closed. Door 99 is closed. Door 100 is open.  ## FUZE BASIC READ x,y,zPRINT "Open doors: ";x;" ";CYCLE z=x+y PRINT z;" "; x=z y=y+2REPEAT UNTIL z>=100DATA 1,3,0END ## Gambas Public Sub Main()Dim bDoor As New BooleanDim siCount1, siCount2, siStart As Short For siCount1 = 1 To 100 Inc siStart For siCount2 = siStart To 100 Step siCount1 bDoor[siCount2] = Not bDoor[siCount2] NextNext For siCount1 = 1 To 100 If bDoor[siCount1] Then Print siCount1;;Next End Output: 1 4 9 16 25 36 49 64 81 100  ## GAP doors := function(n) local a,j,s; a := [ ]; for j in [1 .. n] do a[j] := 0; od; for s in [1 .. n] do j := s; while j <= n do a[j] := 1 - a[j]; j := j + s; od; od; return Filtered([1 .. n], j -> a[j] = 1);end; doors(100);# [ 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 ] ## Genie  // 100 doors problem// Author: Sinuhe masan (2019)init // 100 elements array of boolean type doors:bool for var i = 1 to 100 doors[i] = false // set all doors closed for var i = 1 to 100 j:int = i while j <= 100 do doors[j] = not doors[j] j = j + i print("Doors open: ") for var i = 1 to 100 if doors[i] stdout.printf ("%d ", i)  ## Glee 100 *=0=>d  create vector 1..100, create bit pattern d, marking all equal to 0:for (1..100[.s]){  loop s from 1 to 100 d^(100 %s *=0 )=>d;}  d = d xor (bit pattern of vector 1..100 % s)d  output d  The resulting output is the bit pattern showing the state of the 100 doors: Result:10010000 10000001 00000000 10000000 00010000 00000000 10000000 00000001 00000000 00000000 10000000 00000000 0001 ## GML var doors,a,i;//Sets up the array for all of the doors.for (i = 1; i<=100; i += 1) { doors[i]=0; } //This first for loop goes through and passes the interval down to the next for loop.for (i = 1; i <= 100; i += 1;) { //This for loop opens or closes the doors and uses the interval(if interval is 2 it only uses every other etc..) for (a = 0; a <= 100; a += i;) { //Opens or closes a door. doors[a] = !doors[a]; } }open_doors = ''; //This for loop goes through the array and checks for open doors.//If the door is open it adds it to the string then displays the string.for (i = 1; i <= 100; i += 1;) { if (doors[i] == 1) { open_doors += "Door Number "+string(i)+" is open#"; } }show_message(open_doors);game_end(); ## Go unoptimized package main import "fmt" func main() { doors := bool{} // the 100 passes called for in the task description for pass := 1; pass <= 100; pass++ { for door := pass-1; door < 100; door += pass { doors[door] = !doors[door] } } // one more pass to answer the question for i, v := range doors { if v { fmt.Print("1") } else { fmt.Print("0") } if i%10 == 9 { fmt.Print("\n") } else { fmt.Print(" ") } }} Output: 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1  optimized package main import "fmt" func main() { var door int = 1 var incrementer = 0 for current := 1; current <= 100; current++ { fmt.Printf("Door %d ", current) if current == door { fmt.Printf("Open\n") incrementer++ door += 2*incrementer + 1 } else { fmt.Printf("Closed\n") } }} ## Golfscript 100:c;[{0}c*]:d;c,{.c,>$$%{.d<\.d=1^\)d>++:d;}/}/[c,{)"door "\+" is"+}%d{{"open"}{"closed"}if}%]zip{" "*puts}/

optimized with sqrt (Original version of GolfScript has no sqrt operator, but it can be added easily; the code was tested using a work-in-progress C interpreter for a language compatible enough with Golfscript)

100,{)}%{:d.sqrt 2?={"open"}{"close"}if"door "d+" is "+\+puts}/

optimized without sqrt

[{"close"}100*]:d;10,{)2?(.d<\["open"]\)d>++:d;}/[100,{)"door "\+" is"+}%d]zip{" "*puts}/

## Gosu

unoptimized

 uses java.util.Arrays var doors = new booleanArrays.fill( doors, false ) for( pass in 1..100 ) {    var counter = pass-1    while( counter < 100 ) {        doors[counter] = !doors[counter]        counter += pass  }} for( door in doors index i ) {    print( "door ${i+1} is${door ? 'open' : 'closed'}" )}

optimized

 var door = 1var delta = 0 for( i in 1..100 ) {    if( i == door ) {        print( "door ${i} is open" ) delta++ door += 2*delta + 1 } else { print( "door${i} is closed" )    }}

## Groovy

unoptimized

doors = [false] * 100(0..99).each {   it.step(100, it + 1) {      doors[it] ^= true   }}(0..99).each {   println("Door #${it + 1} is${doors[it] ? 'open' : 'closed'}.")}

optimized a Using square roots

(1..100).each {   println("Door #${it} is${Math.sqrt(it).with{it==(int)it} ? 'open' : 'closed'}.")}

optimized b Without using square roots

doors = ['closed'] * 100(1..10).each { doors[it**2 - 1] = 'open' }(0..99).each {   println("Door #${it + 1} is${doors[it]}.")}

## GW-BASIC

10 DIM A(100)20 FOR OFFSET = 1 TO 10030      FOR I = 0 TO 100 STEP OFFSET40              A(I) = A(I) + 150      NEXT I60 NEXT OFFSET70 ' Print "opened" doors80 FOR I = 1 TO 10090      IF A(I) MOD 2 = 1 THEN PRINT I100 NEXT I

Output:

1
4
9
16
25
36
49
64
81
100


## Harbour

Unoptimized code:

#define ARRAY_ELEMENTS 100PROCEDURE Main()   LOCAL aDoors := Array( ARRAY_ELEMENTS )   LOCAL i, j    AFill( aDoors, .F. )   FOR i := 1 TO ARRAY_ELEMENTS      FOR j := i TO ARRAY_ELEMENTS STEP i         aDoors[ j ] = ! aDoors[ j ]      NEXT   NEXT   AEval( aDoors, {|e, n| QQout( Padl(n,3) + " is " + Iif(aDoors[n], "*open*", "closed" ) + "|" ), Iif( n%5 == 0, Qout(), e:=NIL) } )   RETURN

Optimized code

#define ARRAY_ELEMENTS 100PROCEDURE Main()   LOCAL aDoors := Array( ARRAY_ELEMENTS )    AFill( aDoors, .F. )   AEval( aDoors, {|e, n| aDoors[n] := e := Iif( Int(Sqrt(n))==Sqrt(n), .T., .F. ) } )   AEval( aDoors, {|e, n| QQout( Padl(n,3) + " is " + Iif(aDoors[n], "*open*", "closed" ) + "|" ), Iif( n%5 == 0, Qout(), e:=NIL )} )   RETURN

Output:

 1 is *open*|  2 is closed|  3 is closed|  4 is *open*|  5 is closed|
6 is closed|  7 is closed|  8 is closed|  9 is *open*| 10 is closed|
11 is closed| 12 is closed| 13 is closed| 14 is closed| 15 is closed|
16 is *open*| 17 is closed| 18 is closed| 19 is closed| 20 is closed|
21 is closed| 22 is closed| 23 is closed| 24 is closed| 25 is *open*|
26 is closed| 27 is closed| 28 is closed| 29 is closed| 30 is closed|
31 is closed| 32 is closed| 33 is closed| 34 is closed| 35 is closed|
36 is *open*| 37 is closed| 38 is closed| 39 is closed| 40 is closed|
41 is closed| 42 is closed| 43 is closed| 44 is closed| 45 is closed|
46 is closed| 47 is closed| 48 is closed| 49 is *open*| 50 is closed|
51 is closed| 52 is closed| 53 is closed| 54 is closed| 55 is closed|
56 is closed| 57 is closed| 58 is closed| 59 is closed| 60 is closed|
61 is closed| 62 is closed| 63 is closed| 64 is *open*| 65 is closed|
66 is closed| 67 is closed| 68 is closed| 69 is closed| 70 is closed|
71 is closed| 72 is closed| 73 is closed| 74 is closed| 75 is closed|
76 is closed| 77 is closed| 78 is closed| 79 is closed| 80 is closed|
81 is *open*| 82 is closed| 83 is closed| 84 is closed| 85 is closed|
86 is closed| 87 is closed| 88 is closed| 89 is closed| 90 is closed|
91 is closed| 92 is closed| 93 is closed| 94 is closed| 95 is closed|
96 is closed| 97 is closed| 98 is closed| 99 is closed|100 is *open*|


unoptimized

data Door  = Open  | Closed  deriving (Eq, Show) toggle :: Door -> Doortoggle Open = Closedtoggle Closed = Open toggleEvery :: Int -> [Door] -> [Door]toggleEvery k = zipWith toggleK [1 ..]  where    toggleK n door      | n mod k == 0 = toggle door      | otherwise = door run :: Int -> [Door]run n = foldr toggleEvery (replicate n Closed) [1 .. n] main :: IO ()main = print $filter ((== Open) . snd)$ zip [1 ..] (run 100)
Output:
[(1,Open),(4,Open),(9,Open),(16,Open),(25,Open),(36,Open),(49,Open),(64,Open),(81,Open),(100,Open)]

optimized (without using square roots)

gate :: Eq a => [a] -> [a] -> [Door]gate (x:xs) (y:ys) | x == y  =  Open   : gate xs ysgate (x:xs) ys               =  Closed : gate xs ysgate []     _                =  [] run n = gate [1..n] [k*k | k <- [1..]]

alternatively, returning a list of all open gates, it's a one-liner:

run n = takeWhile (< n) [k*k | k <- [1..]]

## Haxe

class RosettaDemo{    static public function main()    {        findOpenLockers(100);    }     static function findOpenLockers(n : Int)    {        var i = 1;         while((i*i) <= n)        {            Sys.print(i*i + "\n");            i++;        }    }}

## HicEst

Unoptimized

REAL :: n=100, open=1, door(n) door = 1 - open ! = closedDO i = 1, n  DO j = i, n, i    door(j) = open - door(j)  ENDDOENDDODLG(Text=door, TItle=SUM(door)//" doors open")

Optimized

door = 1 - open ! = closedDO i = 1, n^0.5  door(i*i) = openENDDODLG(Text=door, TItle=SUM(door)//" doors open")

## HolyC

Translation of: C
U8 is_open;U8 pass = 0, door = 0; /* do the 100 passes */for (pass = 0; pass < 100; ++pass)  for (door = pass; door < 100; door += pass + 1)    is_open[door] = !is_open[door]; /* output the result */for (door = 0; door < 100; ++door)  if (is_open[door])    Print("Door #%d is open.\n", door + 1);  else    Print("Door #%d is closed.\n", door + 1);

## Huginn

optimized

package require Tcl 8.5set doors [lrepeat [expr {$n + 1}] closed]for {set i 1} {$i <= sqrt($n)} {incr i} { lset doors [expr {$i ** 2}] open}for {set i 1} {$i <=$n} {incr i} {    puts [format "door %d is %s" $i [lindex$doors $i]]} graphical Library: Tk Inspired by the E solution, here's a visual representation package require Tcl 8.5package require Tk array set door_status {} # create the guiset doors [list x]for {set i 0} {$i < 10} {incr i} {    for {set j 0} {$j < 10} {incr j} { set k [expr {1 +$j + 10*$i}] lappend doors [radiobutton .d_$k -text $k -variable door_status($k) \                         -indicatoron no -offrelief flat -width 3 -value open]        grid [lindex $doors$k] -column $j -row$i    }} # create the controlsbutton .start -command go -text Startlabel .i_label -text " door:"entry .i -textvariable i -width 4label .step_label -text " step:"entry .step -textvariable step -width 4grid .start - .i_label - .i - .step_label - .step - -row $igrid configure .start -sticky ewgrid configure .i_label .step_label -sticky egrid configure .i .step -sticky w proc go {} { global doors door_status i step # initialize the door_status (all closed) for {set d 1} {$d <= 100} {incr d} {        set door_status($d) closed } # now, begin opening and closing for {set step 1} {$step <= 100} {incr step} {        for {set i 1} {$i <= 100} {incr i} { if {$i % $step == 0} { [lindex$doors $i] [expr {$door_status($i) eq "open" ? "deselect" : "select"}] update after 50 } } }} ## TI-83 BASIC ### Naive seq(0,X,1,100 For(X,1,100 0 or Ans-not(fPart(cumSum(1 or Ans)/A End Pause Ans  A-1cumsum(1 or Ans should be able to replace cumsum(1 or Ans)/A (saving a byte because of the unnecessary closing parenthesis) but it falls victim to a rounding error that causes X^(-1)*X to be stored as 0.99999999999999... (although it's still displayed as the original X). When the fPart( [fractional part] command evaluates this, it returns .999999999, which not( turns to 0 (meaning a closed door). Regular division, as shown, isn't prone to this. ### Optimized Pause not(fPart(√(seq(X,X,1,100  ## TI-89 BASIC Define doors(fast) = Func Local doors,i,j seq(false,x,1,100) ? doors If fast Then For i,1,10,1 true ? doors[i^2] EndFor Else For i,1,100,1 For j,i,100,i not doors[j] ? doors[j] EndFor EndFor EndIf Return doorsEndFunc ## TorqueScript for(%steps = 1; %a <= 100; %a++) for(%current = %steps; %current <= 100; %current += %steps) %door[%current] = !%door[%current];for(%a = 1; %a <= 100; %a++) echo("Door #" @ %a @ " is" SPC %door[%current] ? "Open" : "Closed" @ "."); ## TSE SAL  // library: math: get: task: door: open: close100 <description></description> <version control></version control> <version>1.0.0.0.11</version> <version control></version control> (filenamemacro=getmaocl.s) [<Program>] [<Research>] [kn, ri, mo, 31-12-2012 22:03:16]PROC PROCMathGetTaskDoorOpenClose( INTEGER doorMaxI, INTEGER passMaxI ) // e.g. PROC Main() // e.g. PROCMathGetTaskDoorOpenClose( 100, 100 ) // e.g. END // e.g. // e.g. <F12> Main() // // === // // The output will be: // // door 1 is open // door 4 is open // door 9 is open // door 16 is open // door 25 is open // door 36 is open // door 49 is open // door 64 is open // door 81 is open // door 100 is open // all other doors are closed // // === // INTEGER passMinI = 1 INTEGER passI = 0 // INTEGER doorminI = 1 INTEGER doorI = 0 // STRING s = "" // INTEGER bufferI = 0 // PushPosition() bufferI = CreateTempBuffer() PopPosition() // FOR doorI = doorMinI TO doorMaxI // SetGlobalInt( Format( "doorsI", doorI ), 0 ) // ENDFOR // FOR passI = passMinI TO passMaxI // doorI = passI - passI // REPEAT // doorI = doorI + passI // SetGlobalInt( Format( "doorsI", doorI ), NOT( GetGlobalInt( Format( "doorsI", doorI ) ) ) ) // UNTIL ( doorI >= doorMaxI ) // ENDFOR // FOR doorI = doorMinI TO doorMaxI // IF ( GetGlobalInt( Format( "doorsI", doorI ) ) > 0 ) // s = "open" // AddLine( Format( "door", " ", doorI, " ", "is", " ", s ), bufferI ) // ELSE // s = "closed" // ENDIF // ENDFOR // AddLine( "all other doors are closed", bufferI ) // GotoBufferId( bufferI ) //END PROC Main() PROCMathGetTaskDoorOpenClose( 100, 100 )END  ## True BASIC  ! Optimized solution with True BASIC OPTION NOLETx = 1 y = 3 z = 0PRINT STR$(x) & " Open"DO UNTIL z >= 100z = x + yPRINT STR$(z) & " Open"x = z y = y + 2LOOP END  ## TUSCRIPT $$MODE TUSCRIPTDICT doors createCOMPILELOOP door=1,100 LOOP pass=1,100 SET go=MOD (door,pass) DICT doors lookup door,num,cnt,status IF (num==0) THEN SET status="open" DICT doors add door,num,cnt,status ELSE IF (go==0) THEN IF (status=="closed") THEN SET status="open" ELSE SET status="closed" ENDIF DICT doors update door,num,cnt,status ENDIF ENDIF ENDLOOPENDLOOPENDCOMPILEDICT doors unload door,num,cnt,status  Output (variable status):  status = * 1 = open 2 = closed 3 = closed 4 = open 5 = closed 6 = closed 7 = closed 8 = closed 9 = open 10 = closed 11 = closed 12 = closed 13 = closed 14 = closed 15 = closed 16 = open 17 = closed 18 = closed 19 = closed 20 = closed 21 = closed 22 = closed 23 = closed 24 = closed 25 = open 26 = closed 27 = closed 28 = closed 29 = closed 30 = closed 31 = closed 32 = closed 33 = closed 34 = closed 35 = closed 36 = open 37 = closed 38 = closed 39 = closed 40 = closed 41 = closed 42 = closed 43 = closed 44 = closed 45 = closed 46 = closed 47 = closed 48 = closed 49 = open 50 = closed 51 = closed 52 = closed 53 = closed 54 = closed 55 = closed 56 = closed 57 = closed 58 = closed 59 = closed 60 = closed 61 = closed 62 = closed 63 = closed 64 = open 65 = closed 66 = closed 67 = closed 68 = closed 69 = closed 70 = closed 71 = closed 72 = closed 73 = closed 74 = closed 75 = closed 76 = closed 77 = closed 78 = closed 79 = closed 80 = closed 81 = open 82 = closed 83 = closed 84 = closed 85 = closed 86 = closed 87 = closed 88 = closed 89 = closed 90 = closed 91 = closed 92 = closed 93 = closed 94 = closed 95 = closed 96 = closed 97 = closed 98 = closed 99 = closed 100 = open  ## TXR (defun hyaku-mai-tobira () (let ((doors (vector 100))) (each ((i (range 0 99))) (each ((j (range i 99 (+ i 1)))) (flip [doors j]))) doors)) (each ((counter (range 1)) (door (hyaku-mai-tobira))) (put-line door @counter is @(if door "open" "closed"))) ## uBasic/4tH Translation of: BBC BASIC Deliberately unoptimized. FOR p = 1 TO 100 FOR d = p TO 100 STEP p @(d) = @(d) = 0 NEXT dNEXT p FOR d= 1 TO 100 IF @(d) PRINT "Door ";d;" is open"NEXT d ## Uniface unoptimized Works with: Uniface 9.6  entry LP_DO_IT variables string V_DOORS boolean V_DOOR_STATE string V_DOOR_STATE_S numeric V_IDX numeric V_TOTAL_DOORS string V_DOOR_STATE_LIST numeric V_LOOP_COUNT endvariables V_TOTAL_DOORS = 100 putitem V_DOORS, V_TOTAL_DOORS, 0 V_DOORS =$replace (V_DOORS, 1, "·;", "·;0", -1)     putitem/id V_DOOR_STATE_LIST, "1", "Open"    putitem/id V_DOOR_STATE_LIST, "0", "Close"     V_LOOP_COUNT = 1    while (V_LOOP_COUNT <= V_TOTAL_DOORS)        V_IDX = 0        V_IDX = V_IDX + V_LOOP_COUNT         getitem V_DOOR_STATE, V_DOORS, V_IDX        while (V_IDX <= V_TOTAL_DOORS)             V_DOOR_STATE = !V_DOOR_STATE            getitem/id V_DOOR_STATE_S, V_DOOR_STATE_LIST, $number(V_DOOR_STATE) putitem V_DOORS, V_IDX, V_DOOR_STATE V_IDX = V_IDX + V_LOOP_COUNT getitem V_DOOR_STATE, V_DOORS, V_IDX endwhile V_LOOP_COUNT = V_LOOP_COUNT + 1 endwhile V_IDX = 1 getitem V_DOOR_STATE, V_DOORS, V_IDX while (V_IDX <= V_TOTAL_DOORS) getitem/id V_DOOR_STATE_S, V_DOOR_STATE_LIST,$number(V_DOOR_STATE)        if (V_DOOR_STATE)            putmess "Door %%V_IDX%%% is finally %%V_DOOR_STATE_S%%%"        endif         V_IDX = V_IDX + 1        getitem V_DOOR_STATE, V_DOORS, V_IDX    endwhile end ; LP_DO_IT  
Output:
Door 1 is finally Open
Door 4 is finally Open
Door 9 is finally Open
Door 16 is finally Open
Door 25 is finally Open
Door 36 is finally Open
Door 49 is finally Open
Door 64 is finally Open
Door 81 is finally Open
Door 100 is finally Open



## UNIX Shell

Works with: Bourne Again SHell
#! /bin/bash declare -a doorsfor((i=1; i <= 100; i++)); do    doors[$i]=0done for((i=1; i <= 100; i++)); do for((j=i; j <= 100; j += i)); do echo$i $j doors[$j]=$(( doors[j] ^ 1 )) donedone for((i=1; i <= 100; i++)); do if [[${doors[$i]} -eq 0 ]]; then op="closed" else op="open" fi echo$i $opdone Optimised version #!/bin/bash for i in {1..100}; do door[$i*$i]=1 [ -z${door[$i]} ] && echo "$i closed" || echo "\$i open"done

## Ursa

 ## 100 doors# decl int i jdecl boolean<> doors # append 101 boolean values to doors streamfor (set i 0) (or (< i 100) (= i 100)) (inc i)        append false doorsend for # loop through, opening and closing doorsfor (set i 1) (or (< i 100) (= i 100)) (inc i)        for (set j i) (or (< j 100) (= j 100)) (inc j)                if (= (mod j i) 0)                        set doors<j> (not doors<j>)                end if        end forend for # loop through and output which doors are openfor (set i 1) (or (< i 100) (= i 100)) (inc i)        out "Door " i ": " console        if doors<i>                out "open" endl console        else                out "closed&quo`