Steady squares
- Euler Project #284
- Task
The 3-digit number 376 in the decimal numbering system is an example of numbers with the special property that its square ends with the same digits: 376*376 = 141376. Let's call a number with this property a steady square. Find steady squares under 10.000
C
<lang c>#include <stdio.h>
- include <stdbool.h>
bool steady(int n) {
int mask=1; for (int d=n; d; d/=10) mask*=10; return (n*n)%mask == n;
}
int main() {
for (int i=1; i<10000; i++)
if (steady(i))
printf("%4d^2 = %8d\n", i, i*i);
return 0;
}</lang>
- Output:
1^2 = 1 5^2 = 25 6^2 = 36 25^2 = 625 76^2 = 5776 376^2 = 141376 625^2 = 390625 9376^2 = 87909376
CLU
<lang clu>n_digits = proc (n: int) returns (int)
i: int := 0
while n>0 do
i := i+1
n := n/10
end
return(i)
end n_digits
steady = proc (n: int) returns (bool)
sq: int := n ** 2 return (sq // 10**n_digits(n) = n)
end steady
start_up = proc ()
po: stream := stream$primary_output()
for i: int in int$from_to(1, 10000) do
if ~steady(i) then continue end
stream$putright(po, int$unparse(i), 4)
stream$puts(po, "^2 = ")
stream$putright(po, int$unparse(i**2), 8)
stream$putl(po, "")
end
end start_up</lang>
- Output:
1^2 = 1 5^2 = 25 6^2 = 36 25^2 = 625 76^2 = 5776 376^2 = 141376 625^2 = 390625 9376^2 = 87909376
F#
<lang fsharp> // Steady Squares. Nigel Galloway: December 21st., 2021 let rec fG n g=match g with 0->true |g when n%10=g%10->fG(n/10)(g/10) |_->false [for n in 0..999 do for g in [1;5;6]->10*n+g]|>List.filter(fun n->fG(n*n)n)|>List.iter(printf "%d ") </lang>
- Output:
1 5 6 25 76 376 625 9376
Factor
Only checking numbers that end with 1, 5, and 6. See Talk:Steady_Squares for more details.
<lang factor>USING: formatting kernel math math.functions math.functions.integer-logs prettyprint sequences tools.memory.private ;
- steady? ( n -- ? )
[ sq ] [ integer-log10 1 + 10^ mod ] [ = ] tri ;
1000 <iota> { 1 5 6 } [
[ 10 * ] dip + dup steady? [ dup sq commas "%4d^2 = %s\n" printf ] [ drop ] if
] cartesian-each</lang>
- Output:
1^2 = 1 5^2 = 25 6^2 = 36 25^2 = 625 76^2 = 5,776 376^2 = 141,376 625^2 = 390,625 9376^2 = 87,909,376
FreeBASIC
<lang freebasic>function numdig( byval n as uinteger ) as uinteger
'number of decimal digits in n
dim as uinteger d=0
while n
d+=1
n\=10
wend
return d
end function
function is_steady_square( n as const uinteger ) as boolean
dim as integer n2 = n^2 if n2 mod 10^numdig(n) = n then return true else return false
end function
for i as uinteger = 1 to 10000
if is_steady_square(i) then print using "####^2 = ########";i;i^2
next i</lang>
- Output:
1^2 = 1 5^2 = 25 6^2 = 36 25^2 = 625 76^2 = 5776 376^2 = 141376 625^2 = 3906259376^2 = 87909376
Python
<lang python> print("working...") print("Steady squares under 10.000 are:") limit = 10000
for n in range(1,limit):
nstr = str(n)
nlen = len(nstr)
square = str(pow(n,2))
rn = square[-nlen:]
if nstr == rn:
print(str(n) + " " + str(square))
print("done...") </lang>
- Output:
working... Steady squares under 10.000 are: 1 1 5 25 6 36 25 625 76 5776 376 141376 625 390625 9376 87909376 done...
Raku
<lang perl6>.say for ({$++²}…*).kv.grep( {$^v.ends-with: $^k} )[1..10]</lang>
- Output:
(1 1) (5 25) (6 36) (25 625) (76 5776) (376 141376) (625 390625) (9376 87909376) (90625 8212890625) (109376 11963109376)
Ring
<lang ring> see "working..." +nl see "Steady squatres under 10.000 are:" + nl limit = 10000
for n = 1 to limit
nstr = string(n)
len = len(nstr)
square = pow(n,2)
rn = right(string(square),len)
if nstr = rn
see "" + n + " -> " + square + nl
ok
next
see "done..." +nl </lang>
- Output:
working... Steady numbers under 10.000 are: 1 -> 1 5 -> 25 6 -> 36 25 -> 625 76 -> 5776 376 -> 141376 625 -> 390625 9376 -> 87909376 done...
Wren
Although it hardly matters for a small range such as this, one can cut down the numbers to be examined by observing that a steady square must end in 0, 1, 5 or 6. <lang ecmascript>import "./fmt" for Fmt
System.print("Steady squares under 10,000:") var finalDigits = [0, 1, 5, 6] for (i in 1..9999) {
if (!finalDigits.contains(i % 10)) continue
var sq = i * i
if (sq.toString.endsWith(i.toString)) Fmt.print("$,5d -> $,10d", i, sq)
}</lang>
- Output:
Steady squares under 10,000:
1 -> 1
5 -> 25
6 -> 36
25 -> 625
76 -> 5,776
376 -> 141,376
625 -> 390,625
9,376 -> 87,909,376