SEND + MORE = MONEY

SEND + MORE = MONEY is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Write a program in your language to solve SEND + MORE = MONEY: A Great Puzzle.

ALGOL 68

Translation of: Julia

This task can be solved without using seven nested loops but then again, it can be solved with them - so why not?.
Uses the observations of the Julia sample (unsuprisingly as this is a translation of the Julia sample).

BEGIN # solve the SEND+MORE=MONEY puzzle - translation of the Julia sample #
  INT m = 1;
  OP C = ( INT n )CHAR: REPR ( ABS "0" + n ); # convert integer to a digit #
  FOR s FROM 8 TO 9 DO
    FOR e FROM 0 TO 9 DO
      IF e /= m AND e/= s THEN
        FOR n FROM 0 TO 9 DO
          IF n /= m AND n /= s AND n /= e THEN
            FOR d FROM 0 TO 9 DO
              IF d /= m AND d /= s AND d /= e AND d /= n THEN
                FOR o FROM 0 TO 9 DO
                  IF o /= m AND o /= s AND o /= e AND o /= n AND o /= d THEN
                    FOR r FROM 0 TO 9 DO
                      IF r /= m AND r /= s AND r /= e AND r /= n AND r /= d AND r /= o THEN
                        FOR y FROM 0 TO 9 DO
                          IF y /= m AND y /= s AND y /= e AND y /= n AND y /= d AND y /= o AND y /= r THEN
                            IF ( 1000 * ( s + m ) ) + ( 100 * ( e + o ) ) + ( 10 * ( n + r ) ) + ( d + e )
                             = ( 10 000 * m ) + ( 1000 * o ) + ( 100 * n ) + ( 10 * e ) + y
                            THEN
                              print( ( C s, C e, C n, C d, " + ", C m, C o, C r, C e, " = ", C m, C o, C n, C e, C y
                                     )
                                   )
                            FI
                          FI
                        OD
                      FI
                    OD
                  FI
                OD
              FI
            OD
          FI
        OD
      FI
    OD
  OD
END

Output:

9567 + 1085 = 10652

BASIC

Rosetta Code problem: https://rosettacode.org/wiki/SEND_%2B_MORE_%3D_MONEY

by Jjuanhdez, 02/2023

BASIC256

Translation of: FreeBASIC

Works with: Run BASIC

Works with: Just BASIC

Works with: Liberty BASIC

m = 1
for s = 8 to 9
  for e = 0 to 9
    if e <> m and e <> s then
      for n = 0 to 9
        if n <> m and n <> s and n <> e then
          for d = 0 to 9
            if d <> m and d <> s and d <> e and d <> n then
              for o = 0 to 9
                if o <> m and o <> s and o <> e and o <> n and o <> d then
                  for r = 0 to 9
                    if r <> m and r <> s and r <> e and r <> n and r <> d and r <> o then
                      for y = 0 to 9
                        if y <> m and y <> s and y <> e and y <> n and y <> d and y <> o then
                          if ((1000*(s+m)) + (100*(e+o)) + (10*(n+r)) + (d+e)) = ((10000* m) + (1000*o) + (100*n) + (10*e) + y) then
                            print s;e;n;d; " + "; m;o;r;e; " = "; m;o;n;e;y
                          end if
                        end if
                      next y
                    end if
                  next r
                end if
              next o
            end if
          next d
        end if
      next n
    end if
  next e
next s

Output:

Same as FreeBASIC entry.

Gambas

Translation of: FreeBASIC

Public Sub Main()

  Dim m, s, e, n, d, o, r, y As Byte
  
  m = 1
  For s = 8 To 9
    For e = 0 To 9
      If e <> m And e <> s Then
        For n = 0 To 9
          If n <> m And n <> s And n <> e Then
            For d = 0 To 9
              If d <> m And d <> s And d <> e And d <> n Then
                For o = 0 To 9
                  If o <> m And o <> s And o <> e And o <> n And o <> d Then
                    For r = 0 To 9
                      If r <> m And r <> s And r <> e And r <> n And r <> d And r <> o Then
                        For y = 0 To 9
                          If y <> m And y <> s And y <> e And y <> n And y <> d And y <> o Then
                            If ((1000*(s+m)) + (100*(e+o)) + (10*(n+r)) + (d+e)) =  ((10000* m) + (1000*o) + (100*n) + (10*e) + y) Then
                              Print s & e & n & d & " + " & m & o & r & e & " = " &  m & o & n & e & y
                            End If
                          End If
                        Next
                      End If
                    Next
                  End If
                Next
              End If
            Next
          End If
        Next
      End If
    Next
  Next

End

Output:

Same as FreeBASIC entry.

Run BASIC

Works with: Just BASIC

Works with: Liberty BASIC

PureBasic

OpenConsole()
m.i = 1
For s.i = 8 To 9
  For e.i = 0 To 9
    If e <> m And e <> s
      For n.i = 0 To 9
        If n <> m And n <> s And n <> e
          For d.i = 0 To 9
            If d <> m And d <> s And d <> e And d <> n
              For o.i = 0 To 9
                If o <> m And o <> s And o <> e And o <> n And o <> d
                  For r.i = 0 To 9
                    If r <> m And r <> s And r <> e And r <> n And r <> d And r <> o
                      For y.i = 0 To 9
                        If y <> m And y <> s And y <> e And y <> n And y <> d And y <> o
                          If ((1000*(s+m))+(100*(e+o))+(10*(n+r))+(d+e)) = ((10000*m)+(1000*o)+(100*n)+(10*e)+y)
                            PrintN(Str(s)+Str(e)+Str(n)+Str(d)+" + "+Str(m)+Str(o)+Str(r)+Str(e)+" = "+Str(m)+Str(o)+Str(n)+Str(e)+Str(y))
                          EndIf
                        EndIf
                      Next y
                    EndIf
                  Next r
                EndIf
              Next o
            EndIf
          Next d
        EndIf
      Next n
    EndIf
  Next e
Next s
CloseConsole()

Output:

Same as FreeBASIC entry.

True BASIC

Works with: QBasic version 1.1

LET m = 1
FOR s = 8 TO 9
    FOR e = 0 TO 9
        IF e <> m AND e <> s THEN
           FOR n = 0 TO 9
               IF n <> m AND n <> s AND n <> e THEN
                  FOR d = 0 TO 9
                      IF d <> m AND d <> s AND d <> e AND d <> n THEN
                         FOR o = 0 TO 9
                             IF o <> m AND o <> s AND o <> e AND o <> n AND o <> d THEN
                                FOR r = 0 TO 9
                                    IF r <> m AND r <> s AND r <> e AND r <> n AND r <> d AND r <> o THEN
                                       FOR y = 0 TO 9
                                           IF y <> m AND y <> s AND y <> e AND y <> n AND y <> d AND y <> o THEN
                                              IF ((1000*(s+m))+(100*(e+o))+(10*(n+r))+(d+e)) = ((10000*m)+(1000*o)+(100*n)+(10*e)+y) THEN
                                                 PRINT STR$(s); STR$(e); STR$(n); STR$(d); " + "; 
                                                 PRINT STR$(m); STR$(o); STR$(r); STR$(e); " = ";
                                                 PRINT STR$(m); STR$(o); STR$(n); STR$(e); STR$(y)
                                              END IF
                                           END IF
                                       NEXT y
                                    END IF
                                NEXT r
                             END IF
                         NEXT o
                      END IF
                  NEXT d
               END IF
           NEXT n
        END IF
    NEXT e
NEXT s
END

Output:

Same as FreeBASIC entry.

Yabasic

Translation of: FreeBASIC

m = 1
for s = 8 to 9
  for e = 0 to 9
    if e <> m and e <> s then
      for n = 0 to 9
        if n <> m and n <> s and n <> e then
          for d = 0 to 9
            if d <> m and d <> s and d <> e and d <> n then
              for o = 0 to 9
                if o <> m and o <> s and o <> e and o <> n and o <> d then
                  for r = 0 to 9
                    if r <> m and r <> s and r <> e and r <> n and r <> d and r <> o then
                      for y = 0 to 9
                        if y <> m and y <> s and y <> e and y <> n and y <> d and y <> o then
                          if ((1000*(s+m)) + (100*(e+o)) + (10*(n+r)) + (d+e)) = ((10000* m) + (1000*o) + (100*n) + (10*e) + y)  ? str$(s), str$(e), str$(n), str$(d), " + ", str$(m), str$(o), str$(r), str$(e), " = ", str$(m), str$(o), str$(n), str$(e), str$(y)
                        fi
                      next y
                    fi
                  next r
                fi
              next o
            fi
          next d
        fi
      next n
    fi
  next e
next s
end

Output:

Same as FreeBASIC entry.

C

Translation of: Julia

#include <stdio.h>

int main() {
  int m = 1, s, e, n, d, o, r, y, sum1, sum2;
  const char *f = "%d%d%d%d + %d%d%d%d = %d%d%d%d%d\n";
  for (s = 8; s < 10; ++s) {
    for (e = 0; e < 10; ++e) {
      if (e == m || e == s) continue;
      for (n = 0; n < 10; ++n) {
        if (n == m || n == s || n == e) continue;
        for (d = 0; d < 10; ++d) {
          if (d == m || d == s || d == e || d == n) continue;
          for (o = 0; o < 10; ++o) {
            if (o == m || o == s || o == e || o == n || o == d) continue;
            for (r = 0; r < 10; ++r) {
              if (r == m || r == s || r == e || r == n || r == d || r == o) continue;
              for (y = 0; y < 10; ++y) {
                if (y == m || y == s || y == e || y == n || y == d || y == o) continue;
                sum1 = 1000*s + 100*e + 10*n + d + 1000*m + 100*o + 10*r + e;
                sum2 = 10000*m + 1000*o + 100*n + 10*e + y;
                if (sum1 == sum2) {
                  printf(f, s, e, n, d, m, o, r, e, m, o, n, e, y);
                }
              }
            }
          }
        }
      }
    }
  }           
  return 0;
}

Output:

9567 + 1085 = 10652

FreeBASIC

Translation of: Julia

Dim As Byte m = 1, s, e, n, d, o, r, y
For s = 8 To 9
    For e = 0 To 9
        If e <> m And e <> s Then
            For n = 0 To 9
                If n <> m And n <> s And n <> e Then
                    For d = 0 To 9
                        If d <> m And d <> s And d <> e And d <> n Then
                            For o = 0 To 9
                                If o <> m And o <> s And o <> e And o <> n And o <> d Then
                                    For r = 0 To 9
                                        If r <> m And r <> s And r <> e And r <> n And r <> d And r <> o Then
                                            For y = 0 To 9
                                                If y <> m And y <> s And y <> e And y <> n And y <> d And y <> o Then
                                                    If ((1000*(s+m)) + (100*(e+o)) + (10*(n+r)) + (d+e)) = _
                                                       ((10000* m) + (1000*o) + (100*n) + (10*e) + y) Then
                                                        Print s & e & n & d & " + " & _
                                                        m & o & r & e & " = " &  m & o & n & e & y
                                                    End If
                                                End If
                                            Next y
                                        End If
                                    Next r
                                End If
                            Next o
                        End If
                    Next d
                End If
            Next n
        End If
    Next e
Next s

Sleep

Output:

9567 + 1085 = 10652

Go

Translation of: Wren

package main

import (
    "fmt"
    "time"
)

func contains(a []int, v int) bool {
    for i := 0; i < len(a); i++ {
        if a[i] == v {
            return true
        }
    }
    return false
}

func main() {
    start := time.Now()
    var sends [][4]int
    var ors [][2]int
    m := 1
    digits := []int{0, 2, 3, 4, 5, 6, 7, 8, 9}
    for s := 8; s <= 9; s++ {
        for _, e := range digits {
            if e == s {
                continue
            }
            for _, n := range digits {
                if n == s || n == e {
                    continue
                }
                for _, d := range digits {
                    if d == s || d == e || d == n {
                        continue
                    }
                    sends = append(sends, [4]int{s, e, n, d})
                }
            }
        }
    }
    for _, o := range digits {
        for _, r := range digits {
            if r != o {
                ors = append(ors, [2]int{o, r})
            }
        }
    }
    fmt.Println("Solution(s):")
    for _, send := range sends {
        SEND := 1000*send[0] + 100*send[1] + 10*send[2] + send[3]
        for _, or := range ors {
            send2 := send[:]
            or2 := or[:]
            if contains(send2, or[0]) || contains(send2, or[1]) {
                continue
            }
            MORE := 1000*m + 100*or[0] + 10*or[1] + send[1]
            for _, y := range digits {
                if contains(send2, y) || contains(or2, y) {
                    continue
                }
                MONEY := 10000*m + 1000*or[0] + 100*send[2] + 10*send[1] + y
                if SEND+MORE == MONEY {
                    fmt.Printf("%d + %d = %d\n", SEND, MORE, MONEY)
                }
            }
        }
    }
    fmt.Printf("\nTook %s.\n", time.Since(start))
}

Output:

Solution(s):
9567 + 1085 = 10652

Took 1.149804ms.

J

Tacit Solution

SEND=.  10 #.   0 1 2 3&{
MORE=.  10 #.   4 5 6 1&{
MONEY=. 10 #. 4 5 2 1 7&{
M=.                   4&{
   
entry=. 0&{::
try=.   1&{::
   
sample=. (10 ?~ 8:) ; 1 + try NB. counting tries to avoid a premature convergence
   
good=. (not=. -.) (o=.@:) (0 = M) (and=. *.) (SEND + MORE) = MONEY
   
answer=. (": o SEND , ' + ' , ": o MORE , ' = ' , ": o MONEY) o entry
tries=.  ', random tries ' , ": o try
   
while=. ^: (^:_)
   
solve=.  (answer , tries) o (sample while (not o good o entry)) o ( 0 ;~ i.) o 8: f.

Example use:

   solve ''
9567 + 1085 = 10652, random tries 248241
   
   solve ''
9567 + 1085 = 10652, random tries 246504
   
   solve ''
9567 + 1085 = 10652, random tries 3291556

The code is tacit and fixed (in other words, it is point-free):

   _80 [\ (5!:5)<'solve'
((":@:(10 (#.) 0 1 2 3&({ )) , ' + ' , ":@:(10 (#.) 4 5 6 1&({ )) , ' = ' , ":@:
(10 (#.) 4 5 2 1 7&({ )))@:(0&({::)) , ', random tries ' , ":@:(1&({::)))@:(((10
 ?~ 8:) ; 1 + 1&({::))^:(-.@:(-.@:(0 = 4&({ )) *. ((10 (#.) 0 1 2 3&({ )) + 10 (
#.) 4 5 6 1&({ )) = 10 (#.) 4 5 2 1 7&({ ))@:(0&({::)))^:_)@:(0 ;~ i.)@:8:

jq

Works with: jq

Works with gojq, the Go implementation of jq, and with fq

Straight out of the wikipedia page, except for {} instead of [] in the last line of the def:

def send_more_money:
    def choose(m;n;used): ([range(m;n+1)] - used)[];
    def num(a;b;c;d): 1000*a + 100*b + 10*c + d;
    def num(a;b;c;d;e): 10*num(a;b;c;d) + e;
    first(
      1 as $m
      | 0 as $o
      | choose(8;9;[]) as $s
      | choose(2;9;[$s]) as $e
      | choose(2;9;[$s,$e]) as $n
      | choose(2;9;[$s,$e,$n]) as $d
      | choose(2;9;[$s,$e,$n,$d]) as $r
      | choose(2;9;[$s,$e,$n,$d,$r]) as $y
      | select(num($s;$e;$n;$d) + num($m;$o;$r;$e) == num($m;$o;$n;$e;$y))
      | {$s,$e,$n,$d,$m,$o,$r,$e,$m,$o,$n,$e,$y} );

send_more_money

Output:

{"s":9,"e":5,"n":6,"d":7,"m":1,"o":0,"r":8,"y":2}

Julia

A hoary old task, solved with pencil before electricity was a thing.

Since the M in Money is the result of carry in base 10 of two single digits it is a 1 (we exclude 0 here though that would work, but then MONEY would be spelled ONEY).

In addition, the S plus 1 then needs to result in a carry, so S is 8 or 9, depending on whether there is a carry into that column. Pencil and paper can continue, but from here the computer is likely quicker.

let
    m = 1
    for s in 8:9
        for e in 0:9
            e in [m, s] && continue
            for n in 0:9
                n in [m, s, e] && continue
                for d in 0:9
                    d in [m, s, e, n] && continue
                    for o in 0:9
                        o in [m, s, e, n, d] && continue
                        for r in 0:9
                            r in [m, s, e, n, d, o] && continue
                            for y in 0:9
                                y in [m, s, e, n, d, o] && continue
                                if 1000s + 100e + 10n + d + 1000m + 100o + 10r + e ==
                                   10000m + 1000o + 100n + 10e + y
                                    println("$s$e$n$d + $m$o$r$e == $m$o$n$e$y")
                                end
                            end
                        end
                    end
                end
            end
        end
    end
end

Output:

9567 + 1085 == 10652

Nim

Translation of: Julia

import std/strformat

let m = 1
for s in 8..9:
  for e in 0..9:
    if e in [m, s]: continue
    for n in 0..9:
      if n in [m, s, e]: continue
      for d in 0..9:
        if d in [m, s, e, n]: continue
        for o in 0..9:
          if o in [m, s, e, n, d]: continue
          for r in 0..9:
            if r in [m, s, e, n, d, o]: continue
            for y in 0..9:
              if y in [m, s, e, n, d, o]: continue
              if 1000 * s + 100 * e + 10 * n + d + 1000 * m + 100 * o + 10 * r + e ==
                 10000 * m + 1000 * o + 100 * n + 10 * e + y:
                echo &"{s}{e}{n}{d} + {m}{o}{r}{e} = {m}{o}{n}{e}{y}"

Output:

9567 + 1085 = 10652

Pascal

Free Pascal

simple brute force. Permutation stolen by nQueens.

program SymbolToDigit;
{$IFDEF FPC}{$MODE DELPHI}{$Optimization ON,All}{$ENDIF}
{$IFDEF Windows}{$APPTYPE CONSOLE}{$ENDIF}
uses
  sysutils;// TDatetime
const
  nmax = 9;
  maxLen = 7;

type
 tFreeDgt = array[0..nmax+1] of Int32;
 tSymbWord = String[maxLen];
  
 tDgtWord =  record
               DW_DgtsIdx: array[1..maxLen] of UInt8;
               DW_maxIdx: Uint8;
             end;
             
 tDgtFront  =  record
                 DW_DgtsIdx: array[1..nmax+1] of UInt8;
                 DW_maxIdx: Uint8;
               end;             
  tInUse = set of 0..nmax+1;           
const
{
  maxIDx = 2;
  cSumWords : array[0..maxIDx] of tSymbWord =('SEND','MORE','MONEY');
}  
{
  maxIDx = 4;  
  cSumWords : array[0..maxIDx]  of tSymbWord =('ABRA','CADABRA','ABRA','CADABRA','HOUDINI');
}

//MANYOTHERS=M2A7N6Y4O1T9H5E0R8S3
  maxIDx = 41;
  cSumWords : array[0..maxIDx] of tSymbWord =(
    'SO','MANY','MORE','MEN','SEEM','TO','SAY','THAT',
    'THEY','MAY','SOON','TRY','TO','STAY','AT','HOME',
    'SO','AS','TO','SEE','OR','HEAR','THE','SAME','ONE',
    'MAN','TRY','TO','MEET','THE','TEAM','ON','THE',
    'MOON','AS','HE','HAS','AT','THE','OTHER','TEN',
    'TESTS');

var
{$ALIGN 32}
  DigitSample,
  DigitSampleSolution : tFreeDgt;
  SymbInUse : array[0..10] of char;
  Words :array[0..maxIDx] of tSymbWord;
  DgtWords : array[0..maxIDx] of tDgtWord;
  DgtFrontWords :tDgtFront;
  SymbInUseCount,gblCount : Uint32;
  fullStop: boolean;
  ch : char;

procedure OneSol(idx:int32;const DS:tFreeDgt);
var
  i,symbolIdx : Int32;
begin
  For i := maxlen downto 1 do
  begin
    symbolIdx :=  DgtWords[idx].DW_DgtsIdx[i];
    if symbolIdx = 0 then
      write(' ')
    else
      write(DS[symbolIdx]);
  end;
  writeln(cSumWords[idx]:maxLen+2);
end;

procedure RevString(var s:tSymbWord);
var
  i,j: NativeInt;
begin
  i := 1;
  j := Length(s);
  while j>i do
  begin
    ch:= s[i];s[i]:= s[j];s[j] := ch;
    inc(i);dec(j);
  end;
end;

procedure GetSymbols;
var
  //CHR(ORD('A')-1) = '@' is placeholder for no Symbol
  SymbToIdx : array['@'..'Z'] of byte;
  FrontSymbols :tInUse;
  i,j : Int32;
Begin
  fillchar(SymbToIdx,SizeOf(SymbToIdx),#255);
  SymbToIdx['@'] := 0;
  SymbInUseCount := 1;//['@'] is always zero

  For i := 0 to maxIDx do
  begin
    Words[i] := cSumWords[i];
    j := length(Words[i]);
    //position of highest symbol
    DgtWords[i].DW_maxIdx := j;
    // extend by '@' aka zero
    RevString(Words[i]);
    setlength(Words[i],maxlen);
    For j := j+1 to maxLen do
      Words[i][j] := Low(SymbToIdx);
  end;
  // find all symbols
  for j := 1 to High(tSymbWord) do
  Begin
    For i := 0 to maxIdx do
    begin
      ch := Words[i][j];
      if SymbToIdx[ch] = 255 then
      begin
        SymbToIdx[ch] := SymbInUseCount;
        SymbInUse[SymbInUseCount] := ch;
        inc(SymbInUseCount);
      end;
    end;
  end;
  dec(SymbInUseCount);
  For i := 1 to SymbInUseCount do
    write(SymbInUse[i]);
  writeln(SymbInUseCount:4,' symbols');

  //get index for every symbol in word
  For i := 0 to maxIdx do
    with DgtWords[i] do
      for j := 1 to High(tSymbWord) do
        DW_DgtsIdx[j]:= SymbToIdx[Words[i][j]];
        
  //find all first symbols
  FrontSymbols := [];
  For i := 0 to maxIDx do
    with DgtWords[i] do
      include(FrontSymbols,DW_DgtsIdx[DW_maxIdx]);

  j := 1;  
  For i := 0 to nmax+1 do
    if i in FrontSymbols then
    Begin
      DgtFrontWords.DW_DgtsIdx[j] := i;
      inc(j);
    end;   
  DgtFrontWords.DW_maxIdx := j-1;
end;

function AddWords(const DS:tFreeDgt):boolean;
var
  col,row,
  sum,carry : NativeUInt;
begin
  // check for zero in first symbols of words
  with DgtFrontWords do
    For col := DW_maxIdx downto 1 do
    begin
      if DS[DW_DgtsIdx[col]] = 0 then 
        EXIT(false);
    end;
    
  carry := 0;
  For col := 1 to maxLen do
  Begin
    sum := carry;
    carry := 0;
    // add one column
    For row := maxIdx-1 downto 0 do
      sum := sum+DS[DgtWords[row].DW_DgtsIdx[col]];
      
    if sum > 9 then
    begin
      carry := sum DIV 10;
      sum := sum - 10 * carry;
    end;  
    //digit of sum
    if sum <> DS[DgtWords[maxIDx].DW_DgtsIdx[col]] then
      EXIT(false);
  end;
  If Carry = 0 then
    DigitSampleSolution := DS; 
  EXIT(true);
end;

procedure NextPermute(Row:nativeInt;var DS:tFreeDgt);
var
  i,Col : nativeInt;
begin
  if fullStop then   EXIT;
  IF row <= 10 then
  begin
    NextPermute(Row+1,DS);
    For i := row+1 to 10 do
    begin
      //swap
      Col := DS[i];
      DS[i] := DS[Row];
      DS[Row] := Col;
        NextPermute(Row+1,DS);
      //Undo swap
      DS[Row] := DS[i];
      DS[i] := Col;
    end
  end
else
  begin
    fullStop :=  AddWords(DS);
    inc(gblCount);
  end
end;

var
  T1,T0: TDateTime;
  i,j : Uint32;

begin
  DigitSample[0] := 0;
  For i := 0 to nmax do
    DigitSample[i+1] := i;
  GetSymbols;

  t0 := time;
  gblCount := 0;
  fullStop := false;
  NextPermute(1,DigitSample);
  t1:= time;
  IF maxIDx < 10 then
    For i := 0 to High(DgtWords)do 
      OneSol(i,DigitSampleSolution);
  writeln;
  For i := 1 to SymbInUseCount do
  begin  
     j := DigitSampleSolution[i];
     write(SymbInUse[i],'=',j,' ');
  end;   
  writeln;
  WriteLn(gblCount,' checks ',FormatDateTime(' NN:SS.ZZZ',T1-t0),' secs');
end.

@TIO.RUN:

DEYNROSM   8 symbols
   9567     SEND
   1085     MORE
  10652    MONEY

D=7 E=5 Y=2 N=6 R=8 O=0 S=9 M=1 
2704147 checks  00:00.043 secs
//shorthened    'SO','MANY','MORE','MEN','SEEM','TO','SAY',
OYENMTSRAH  10 symbols

O=1 Y=4 E=0 N=6 M=2 T=9 S=3 R=8 A=7 H=5 
496179 checks  00:00.013 secs

Perl

Translation of: Raku

Exhaustive

use v5.36;
use enum <D E M N O R S Y>;
use Algorithm::Combinatorics <combinations permutations>;

sub solve {
  for my $p (map { permutations $_ } combinations [0..9], 8) {
    return $p if @$p[M] > 0 and join('',@$p[S,E,N,D])+join('',@$p[M,O,R,E]) == join('',@$p[M,O,N,E,Y]);
  }
}

printf "SEND + MORE == MONEY\n%d + %d == %d", join('',@$_[S,E,N,D]), join('',@$_[M,O,R,E]), join '',@$_[M,O,N,E,Y]) for solve();

Output:

SEND + MORE == MONEY
9567 + 1085 == 10652

Fine-tuned

use v5.36;

my $s = 7;
while (++$s <= 9) {
    my $e = -1;
    while (++$e <= 9) {
        next if $e == $s;
        my $n = -1;
        while (++$n <= 9) {
            next if grep { $n == $_ } $s,$e;
            my $d = -1;
            while (++$d <= 9) {
                next if grep { $d == $_ } $s,$e,$n;
                my $send = $s*10**3 + $e*10**2 + $n*10 + $d;
                my ($m, $o) = (1, -1);
                while (++$o <= 9) {
                    next if grep { $o == $_ } $s,$e,$n,$d,$m;
                    my $r = -1;
                    while (++$r <= 9) {
                        next if grep { $r == $_ } $s,$e,$n,$d,$m,$o;
                        my $more = $m*10**3 + $o*10**2 + $r*10 + $e;
                        my $y = -1;
                        while (++$y <= 9) {
                            next if grep { $y == $_ } $s,$e,$n,$d,$m,$o,$r;
                            my $money = $m*10**4 + $o*10**3 + $n*10**2 + $e*10 + $y;
                            next unless $send + $more == $money;
                            say "SEND + MORE == MONEY\n$send + $more == $money";
                        }
                    }
                }
            }
        }
    }
}

Output:

SEND + MORE == MONEY
9567 + 1085 == 10652

Phix

atom t0 = time()
constant mp = new_dict() -- keys 'A'..'Z', values 0..9
sequence front, -- 1 if wordstart, else 0, for (0|1)..9
         multh, -- multiplier hash, see below
         used

-- mp ends up holding the (first) acceptable solution.
-- Letters which start any word cannot be 0 (in the rules).
-- In SEND+MORE=MONEY, 'E' is 100 + 1 - 10 = 91 from the 
-- three places E occurs in the puzzle, stored in multh.
-- Hence sum(letter_values*multh)==0 means it is solved.
-- Obviously used stops us using digits more than once.

function solve_rec(string uniq, int i, atom s)
    -- Aside: integer s is fine on 64-bit, but reaches
    --  a high of 13,304,757,742 & crashes on 32-bit.
    if i > length(uniq) then return s==0 end if
    integer chdx = uniq[i]-'A'+1
    for v=front[chdx] to 9 do
        if not used[v+1] then
            used[v+1] = true
            if solve_rec(uniq,i+1,s+v*multh[chdx]) then 
                setd(uniq[i],v,mp)
                return true
            end if
            used[v+1] = false
        end if
    end for
    return false
end function

function solve(string puzzle)
    destroy_dict(mp,true) -- empty, but keep
    used = repeat(false,10) -- nb [1..10] for 0..9
    multh = repeat(0,26) -- see above
    front = repeat(0,26) -- 1 if 1st in any word
    string uniq = ""
    sequence words = split_any(puzzle," +=\n")
    for iw,word in words do
        front[word[1]-'A'+1] = 1
        integer l = length(word),
                m = iff(iw=length(words)?-1:+1)
        for i,ch in word do
            multh[ch-'A'+1] += m*power(10,l-i)
            if not find(ch,uniq) then
                uniq &= ch
            end if
        end for
    end for
    if not solve_rec(uniq,1,0) then
        return "no solution"
    end if
    for i,ch in puzzle do
        if ch>='A' and ch<='Z' then
            puzzle[i] = getd(ch,mp)+'0'
        end if
    end for
    return puzzle
end function
        
constant tests = {
    "SEND + MORE == MONEY",
    "I + BB == ILL",
    "A == B",
    "ACA + DD == BD",
    "A + A + A + A + A + A + A + A + A + A + A + B == BCC",
    "AS + A == MOM",
    "NO + NO + TOO == LATE",
    "HE + SEES + THE == LIGHT",
    "AND + A + STRONG + OFFENSE + AS + A + GOOD == DEFENSE",
    "SIX + SEVEN + SEVEN = TWENTY",
    "THIS+A+FIRE+THEREFORE+FOR+ALL+HISTORIES+I+TELL+A+TALE+THAT+"&
     "FALSIFIES+ITS+TITLE+TIS+A+LIE+THE+TALE+OF+THE+LAST+FIRE+"&
     "HORSES+LATE+AFTER+THE+FIRST+FATHERS+FORESEE+THE+HORRORS+THE+"&
     "LAST+FREE+TROLL+TERRIFIES+THE+HORSES+OF+FIRE+THE+TROLL+RESTS+"&
     "AT+THE+HOLE+OF+LOSSES+IT+IS+THERE+THAT+SHE+STORES+ROLES+OF+"&
     "LEATHERS+AFTER+SHE+SATISFIES+HER+HATE+OFF+THOSE+FEARS+A+TASTE+"&
     "RISES+AS+SHE+HEARS+THE+LEAST+FAR+HORSE+THOSE+FAST+HORSES+THAT+"&
     "FIRST+HEAR+THE+TROLL+FLEE+OFF+TO+THE+FOREST+THE+HORSES+THAT+"&
     "ALERTS+RAISE+THE+STARES+OF+THE+OTHERS+AS+THE+TROLL+ASSAILS+AT+"&
     "THE+TOTAL+SHIFT+HER+TEETH+TEAR+HOOF+OFF+TORSO+AS+THE+LAST+HORSE"&
     "+FORFEITS+ITS+LIFE+THE+FIRST+FATHERS+HEAR+OF+THE+HORRORS+THEIR+"&
     "FEARS+THAT+THE+FIRES+FOR+THEIR+FEASTS+ARREST+AS+THE+FIRST+FATHERS"&
     "+RESETTLE+THE+LAST+OF+THE+FIRE+HORSES+THE+LAST+TROLL+HARASSES+"&
     "THE+FOREST+HEART+FREE+AT+LAST+OF+THE+LAST+TROLL+ALL+OFFER+THEIR+"&
     "FIRE+HEAT+TO+THE+ASSISTERS+FAR+OFF+THE+TROLL+FASTS+ITS+LIFE+"&
     "SHORTER+AS+STARS+RISE+THE+HORSES+REST+SAFE+AFTER+ALL+SHARE+HOT+"&
     "FISH+AS+THEIR+AFFILIATES+TAILOR+A+ROOFS+FOR+THEIR+SAFE == FORTRESSES",
     "TO + GO = OUT",
     "SEND + A + TAD + MORE = MONEY",
     "ABRA + CADABRA + ABRA + CADABRA = HOUDINI",
     "I + GUESS + THE + TRUTH = HURTS",
     "THATS + THE + THEORY = ANYWAY",
     `SO + MANY + MORE + MEN + SEEM + TO + SAY + THAT +
      THEY + MAY + SOON + TRY + TO + STAY + AT + HOME +
      SO + AS + TO + SEE + OR + HEAR + THE + SAME + ONE +
      MAN + TRY + TO + MEET + THE + TEAM + ON + THE +
      MOON + AS + HE + HAS + AT + THE + OTHER + TEN =TESTS`,
}

for t in tests do
    printf(1,"%s\n%s\n\n",{shorten(t,""),shorten(solve(t),"")})
end for
?elapsed(time()-t0)

Output:

SEND + MORE == MONEY
9567 + 1085 == 10652

I + BB == ILL
1 + 99 == 100

A == B
no solution

ACA + DD == BD
no solution

A + A + A + A + A + ...A + A + A + B == BCC
9 + 9 + 9 + 9 + 9 + ...9 + 9 + 9 + 1 == 100

AS + A == MOM
92 + 9 == 101

NO + NO + TOO == LATE
74 + 74 + 944 == 1092

HE + SEES + THE == LIGHT
54 + 9449 + 754 == 10257

AND + A + STRONG + O... A + GOOD == DEFENSE
503 + 5 + 691208 + 2... 5 + 8223 == 3474064

SIX + SEVEN + SEVEN = TWENTY
650 + 68782 + 68782 = 138214

THIS+A+FIRE+THEREFOR...R+SAFE == FORTRESSES
9874+1+5730+98030563...3+4150 == 5639304404

TO + GO = OUT
21 + 81 = 102

SEND + A + TAD + MORE = MONEY
9283 + 7 + 473 + 1062 = 10825

ABRA + CADABRA + ABRA + CADABRA = HOUDINI
7457 + 1797457 + 7457 + 1797457 = 3609828

I + GUESS + THE + TRUTH = HURTS
5 + 26811 + 478 + 49647 = 76941

THATS + THE + THEORY = ANYWAY
86987 + 863 + 863241 = 951091

SO + MANY + MORE + M...+ OTHER + TEN =TESTS
31 + 2764 + 2180 + 2...+ 19508 + 906 =90393

"4.8s"

Translation of Raku

Quite a bit slower than the above

enum S, E, N, D, M, O, R, Y

function check(sequence p)
    if p[M]!=0 and
       sum(sq_mul(extract(p,{S,E,N,D}),{1000,100,10,1}))+
       sum(sq_mul(extract(p,{M,O,R,E}),{1000,100,10,1}))=
     sum(sq_mul(extract(p,{M,O,N,E,Y}),{10000,1000,100,10,1})) then
        printf(1,"   %d%d%d%d\n",extract(p,{S,E,N,D}))
        printf(1," + %d%d%d%d\n",extract(p,{M,O,R,E}))
        printf(1,"= %d%d%d%d%d\n",extract(p,{M,O,N,E,Y}))
        return false
    end if
    return true -- continue
end function

{} = permutes(tagset(9,0),check,8)

Output:

   9567
 + 1085
= 10652

Python

Translation of: Nim

# SEND + MORE = MONEY by xing216
m = 1
for s in range(8,10):
  for e in range(10):
    if e in [m, s]: continue
    for n in range(10):
      if n in [m, s, e]: continue
      for d in range(10):
        if d in [m, s, e, n]: continue
        for o in range(10):
          if o in [m, s, e, n, d]: continue
          for r in range(10):
            if r in [m, s, e, n, d, o]: continue
            for y in range(10):
              if y in [m, s, e, n, d, o]: continue
              if 1000 * s + 100 * e + 10 * n + d + 1000 * m + 100 * o + 10 * r + e == \
                 10000 * m + 1000 * o + 100 * n + 10 * e + y:
                print(f"{s}{e}{n}{d} + {m}{o}{r}{e} = {m}{o}{n}{e}{y}")

Output:

9567 + 1085 = 10652

Raku

Idiomatic

enum <D E M N O R S Y>;

sub find_solution ( ) {
    for ('0'..'9').combinations(8) -> @c {
        .return with @c.permutations.first: -> @p {
            @p[M] !== 0 and

            @p[  S,E,N,D].join
          + @p[  M,O,R,E].join
         == @p[M,O,N,E,Y].join
        }
    }
}

my @s = find_solution();
say "    {@s[  S,E,N,D].join}";
say " +  {@s[  M,O,R,E].join}";
say "== { @s[M,O,N,E,Y].join}";

Output:

    9567
 +  1085
== 10652

Fast

Alternately, a version written in 2015 by Carl Mäsak. Not very concise but quite speedy. Applying the observation that M must be 1 and S must be either 8 or 9 gets the runtime under a tenth of a second.

my $s = 7;
while ++$s ≤ 9 {
    my $e = -1;
    while ++$e ≤ 9 {
        next if $e == $s;
 
        my $n = -1;
        while ++$n ≤ 9 {
            next if $n == $s|$e;
 
            my $d = -1;
            while ++$d ≤ 9 {
                next if $d == $s|$e|$n;

                my $send = $s×10³ + $e×10² + $n×10 + $d; 
                my ($m, $o) = 1, -1;
                while ++$o ≤ 9 {
                    next if $o == $s|$e|$n|$d|$m;
 
                    my $r = -1;
                    while ++$r ≤ 9 {
                        next if $r == $s|$e|$n|$d|$m|$o;
 
                        my $more = $m×10³ + $o×10² + $r×10 + $e;
                        my $y = -1;
                        while ++$y ≤ 9 {
                            next if $y == $s|$e|$n|$d|$m|$o|$r;

                            my $money = $m×10⁴ + $o×10³ + $n×10² + $e×10 + $y;
                            next unless $send + $more == $money;
                            say 'SEND + MORE == MONEY' ~ "\n$send + $more == $money";
                        }
                    }
                }
            }
        }
    }
}
printf "%.3f elapsed seconds", now - INIT now;

Output:

SEND + MORE == MONEY
9567 + 1085 == 10652
0.080 elapsed seconds

Ring

// Bert Mariani  2023-02-09 | A Monte Carlo method to solve the encryted message | SEND + MORE = MONEY

t1 = clock()          // 
See "Start Clock: "+ t1 +nl
counter    = 1
aSendory   = [["s","-"],["e","-"],["n","-"],["d","-"],["o","-"],["r","-"],["y","-"]]
aRandom    = List(10)                       // 0-9

for j = 1 to 100000000
	aRandom = GenRandomUniq()            // 5 2 0 8 7 1 6 4 3 9 	
	for i = 1 to 7
	    if aRandom[1] != 1               // m = 1
	       aSendory[i][2] = aRandom[1]
	       del(aRandom,1)                // Shorten list, remove value entry picked
	    else
	       del(aRandom,1)
	       i--
	    ok
	next
        if (TrySolution(aSendory)) break  else  counter++   ok  // True=1 = Solution Found      
next
See "End   Clock.: "+ (clock() - t1) +nl
See "Count cycles: "+ counter +nl

Func GenRandomUniq()
throwLimit = 10                      // 0-9, Ring does 1-10
aList = 1:throwLimit
aOut  = []
while len(aOut) != throwLimit
    nSize = len(aList)	
    if nSize > 0
        nIndex = random(nSize)       // Random pointer into list
        if nIndex = 0  nIndex=1 ok   // Ignore 0, Ring Index at 1-10		
        aOut + (aList[nIndex] -1)    // -1 fix value 0-9, Ring +1 Extract list entry content
        del(aList,nIndex)            // Shorten list, remove value entry picked
    else
        aOut + aList[1]
        aList = []
    ok
end
return aOut

Func TrySolution(aTry)
     s1 = ( aTry[1][2]) * 1000      // send   
     e1 = ( aTry[2][2]) *  100         
     n1 = ( aTry[3][2]) *   10        
     d1 = ( aTry[4][2]) *    1        
     nbr1 = s1 + e1 + n1 + d1
     m1 = 1             * 1000      // more
     o1 = ( aTry[5][2]) *  100
     r1 = ( aTry[6][2]) *   10
     e1 = ( aTry[2][2]) *    1 
     nbr2 = m1 + o1 + r1 + e1
     m1 = 1             * 10000     // money
     o1 = ( aTry[5][2]) *  1000
     n1 = ( aTry[3][2]) *   100
     e1 = ( aTry[2][2]) *    10
     y1 = ( aTry[7][2]) *     1
     nbr3 = m1 + o1 +n1 + e1 + y1
     nbr4 = nbr1 + nbr2
     if (nbr3 = nbr4)
        See "Solved: SEND: "+ nbr1 +" MORE: "+ nbr2 +" MONEY: "+ nbr3 +" Check "+ nbr4 +nl
        return (nbr3 = nbr4 )      // True
     ok  
return False

Output:

// Output
// Start Clock: 32
// Solved: SEND: 9567 MORE: 1085 MONEY: 10652 Check 10652
// End   Clock.: 3792
// Count cycles: 28316

original

// Author: Gal Zsolt 2023-02-08 
see "works..." + nl + nl
aListSend = []
aListMore = []

for s = 0 to 9
    for e1 = 0 to 9
        for n = 0 to 9
            for d = 0 to 9
                bool = s!=e1 and s!=n and s!=d and e1!=n and e1!=d and n!=d
                if bool
                   sendmore = s*1000+e1*100+n*10+d
                   add(aListSend,sendmore)
                   add(aListMore,sendmore)
                ok
            next
        next
    next
next

for ind1 = len(aListSend) to 1 step -1 
    for ind2 = 1 to len(aListMore)
        strSend = string(aListSend[ind1])
        strMore = string(aListMore[ind2])
        m = substr(strMore,1,1)
        o = substr(strMore,2,1)
        r = substr(strMore,3,1)
        e2 = substr(strMore,4,1)
        bool1 = substr(strSend,m)
        bool2 = substr(strSend,o)
        bool3 = substr(strSend,r)
        if substr(strSend,2,1) = substr(strMore,4,1)
            bool4 = 0
        else
            bool4 = 1
        ok
        boolSendMore = bool1 + bool2 + bool3 + bool4
        if boolSendMore < 1
           if substr(strSend,2,1) = substr(strMore,4,1)
              for y = 0 to 9
                  strMoney1 = substr(strMore,1,1) + substr(strMore,2,1) + substr(strSend,3,1)
                  strMoney2 = substr(strMore,4,1) + string(y)
                  strMoney = strMoney1 + strMoney2
                  numMoney = number(strMoney)
                  numSend = number(strSend)
                  numMore = number(strMore)
                  y1 = substr(strMoney,5,1)
                  ySend = substr(strSend,y1)
                  yMore = substr(strMore,y1)
                  yCheck = ySend + yMore
                  r = substr(strMore,3,1)
                  rCheck = substr(strSend,r)
                  if (numSend + numMore = numMoney) and yCheck < 1 and rCheck < 1
                      see "SEND = "+strSend+" MORE = "+strMore+" MONEY = "+strMoney+nl+nl              
                      exit 3
                  ok
             next
           ok
        ok
    next
next
see "done..." + nl

Output:

works...
SEND = 9567 MORE = 1085 MONEY = 10652
done...

Ruby

Solving for the string "SEND + 1ORE == 1ONEY" using 'tr' , which translates characters to other characters. The resulting string is brutally evalled.

str = "SEND + 1ORE == 1ONEY"
digits = [0,2,3,4,5,6,7,8,9] # 1 is absent
uniq_chars = str.delete("^A-Z").chars.uniq.join
res = digits.permutation(uniq_chars.size).detect do |perm|
  num_str = str.tr(uniq_chars, perm.join)
  next if num_str.match?(/\b0/) #no words can start with 0
  eval num_str
end
puts str.tr(uniq_chars, res.join)

Output:

9567 + 1085 == 10652

Vala

Translation of: C

void main() {
  int m = 1, s, e, n, d, o, r, y, sum1, sum2;
  string f = "%d%d%d%d + %d%d%d%d = %d%d%d%d%d\n";
  for (s = 8; s < 10; ++s) {
    for (e = 0; e < 10; ++e) {
      if (e == m || e == s) continue;
      for (n = 0; n < 10; ++n) {
        if (n == m || n == s || n == e) continue;
        for (d = 0; d < 10; ++d) {
          if (d == m || d == s || d == e || d == n) continue;
          for (o = 0; o < 10; ++o) {
            if (o == m || o == s || o == e || o == n || o == d) continue;
            for (r = 0; r < 10; ++r) {
              if (r == m || r == s || r == e || r == n || r == d || r == o) continue;
              for (y = 0; y < 10; ++y) {
                if (y == m || y == s || y == e || y == n || y == d || y == o) continue;
                sum1 = 1000*s + 100*e + 10*n + d + 1000*m + 100*o + 10*r + e;
                sum2 = 10000*m + 1000*o + 100*n + 10*e + y;
                if (sum1 == sum2) {
                  print(f, s, e, n, d, m, o, r, e, m, o, n, e, y);
                }
              }
            }
          }
        }
      }
    }
  }           
}

Output:

9567 + 1085 = 10652

Wren

Clearly M = 1 and S must be 8 or 9. Brute force can be used to solve for the other letters.

var start = System.clock
var sends = []
var ors = []
var m = 1
var digits = (0..9).toList
digits.remove(m)
for (s in 8..9) {
    for (e in digits) {
        if (e == s) continue
        for (n in digits) {
            if (n == s || n == e) continue
            for (d in digits) {
                if (d == s || d == e || d == n) continue
                sends.add([s, e, n, d])
            }
        }
    }
}
for (o in digits) {
    for (r in digits) {
        if (r == o) continue
        ors.add([o, r])
    }
}
System.print("Solution(s):")
for (send in sends) {
    var SEND = 1000 * send[0] + 100 * send[1] + 10 * send[2] + send[3]
    for (or in ors) {
        if (send.contains(or[0]) || send.contains(or[1])) continue
        var MORE = 1000 * m + 100 * or[0] + 10 * or[1] + send[1]
        for (y in digits) {
            if (send.contains(y) || or.contains(y)) continue
            var MONEY = 10000 * m + 1000 * or[0] + 100 * send[2] + 10 * send[1] + y
            if (SEND + MORE == MONEY) {
                System.print("%(SEND) + %(MORE) = %(MONEY)")
            }
        }
    }
}
System.print("\nTook %(System.clock - start) seconds.")

Output:

Solution(s):
9567 + 1085 = 10652

Took 0.051735 seconds.

XPL0

include xpllib; \for Print
def M = 1;
int S, E, N, D, O, R, Y;
begin \ Solve the SEND+MORE=MONEY puzzle - Translation of the Algol 68 sample
  for S:= 8 to 9 do
    for E:= 0 to 9 do
      if E # M and E # S then
        for N:= 0 to 9 do
          if N # M and N # S and N # E then
            for D:= 0 to 9 do
              if D # M and D # S and D # E and D # N then
                for O:= 0 to 9 do
                  if O # M and O # S and O # E and O # N and O # D then
                    for R:= 0 to 9 do
                      if R # M and R # S and R # E and R # N and R # D and R # O then
                        for Y:= 0 to 9 do
                          if Y # M and Y # S and Y # E and Y # N and Y # D and Y # O and Y # R then
                            if 1000*(S+M) + 100*(E+O) + 10*(N+R) + D + E = 10_000*M + 1000*O + 100*N + 10*E + Y then
                              Print("%d%d%d%d + %d%d%d%d = %d%d%d%d%d\n", S, E, N, D, M, O, R, E, M, O, N, E, Y);
end

Output:

9567 + 1085 = 10652