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.

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.

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.

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

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

Phix

Mighta gota bit carried away here...

with javascript_semantics
sequence answer
procedure solve(sequence sums,solve_order,firsts,correct_to, integer l,avail,done=0)
    done += 1
    integer d = solve_order[done]
    for ad=firsts[done] to 9 do
        integer m = power(2,ad)
        if and_bits(avail,m) then
            answer[d] = ad
            integer ct = correct_to[done]
            if ct then
                integer carry = 0, bOK = true
                for i=1 to ct do
                    carry += sum(extract(answer,sums[i][1]))
                    if remainder(carry,10)!=answer[sums[i][2]] then
                        bOK = false
                        exit
                    end if
                    carry = floor(carry/10)
                end for
                if bOK then
                    if ct=length(sums) then
                        if carry=0 then
                            ?answer
                        end if
                    else
                        solve(sums,solve_order,firsts,correct_to,l,avail-m,done)
                    end if
                end if
            else
                solve(sums,solve_order,firsts,correct_to,l,avail-m,done)
            end if
            answer[d] = -1
        end if
    end for
end procedure

procedure cryptarithm(string s)
    integer eq = find('=',s)
    sequence ans = trim(s[eq+1..$]),
           words = apply(split(s[1..eq-1],'+'),trim),
             res = join(unique(join(words,"")&ans,"STABLE"),"")
    integer l = length(res)
    for i,w in words do
        words[i] = apply(true,find,{w,{res}})
    end for
    ans = apply(true,find,{ans,{res}})
    sequence sums = {},
      solve_order = {}
    for i=1 to length(ans) do
        sequence set = {}
        for w in words do
            if length(w)>=i then
                integer wi = w[-i]
                set &= wi
                if not find(wi,solve_order) then
                    solve_order &= wi
                end if
            end if
        end for
        integer ai = ans[-i]
        if not find(ai,solve_order) then
            solve_order &= ai
        end if
        sums = append(sums,{set,ai})
    end for
    assert(length(solve_order)=l)
    sequence firsts = repeat(0,l),
         correct_to = repeat(0,l)
    for f in unique(join(apply(true,extract,{words,{{1}}}),{})&ans[1]) do
        firsts[find(f,solve_order)] = 1
    end for
    integer mm = 0
    for i,fs in apply(sums,flatten) do
        integer m = max(apply(true,find,{fs,{solve_order}}))
        mm = max(m,mm)
        correct_to[mm] = i
    end for
    assert(correct_to[$]=length(sums))
    answer = repeat(-1,l)
    printf(1,"%s - %s is ",{s,res})
    solve(sums,solve_order,firsts,correct_to,l,0b1_111_111_111)
end procedure

constant tests = {
`SEND+MORE=MONEY`,
`TO+GO=OUT`,
`SEND + A + TAD + MORE = MONEY`,
`ABRA + CADABRA + ABRA + CADABRA = HOUDINI`,
`I + GUESS + THE + TRUTH = HURTS`,
`THATS + THE + THEORY = ANYWAY`,
-- tad slow, 5.8s vs 0.2s for all above:
`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`}
papply(tests,cryptarithm)

Output:

SEND+MORE=MONEY - SENDMORY is {9,5,6,7,1,0,8,2}
TO+GO=OUT - TOGU is {2,1,8,0}
SEND + A + TAD + MORE = MONEY - SENDATMORY is {9,2,8,3,7,4,1,0,6,5}
ABRA + CADABRA + ABRA + CADABRA = HOUDINI - ABRCDHOUIN is {7,4,5,1,9,3,6,0,8,2}
I + GUESS + THE + TRUTH = HURTS - IGUESTHR is {5,2,6,8,1,4,7,9}
THATS + THE + THEORY = ANYWAY - THASEORYNW is {8,6,9,7,3,2,4,1,5,0}
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 - SOMANYRETH is {3,1,2,7,6,4,8,0,9,5}

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

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 int $s = 7;
while ++$s <= 9 {
    next if $s == 0;

    my int $e = -1;
    while ++$e <= 9 {
        next if $e == $s;

        my int $n = -1;
        while ++$n <= 9 {
            next if $n == $s;
            next if $n == $e;

            my int $d = -1;
            while ++$d <= 9 {
                next if $d == $s;
                next if $d == $e;
                next if $d == $n;

                my int $send = $s*1000 + $e*100 + $n*10 + $d;

                my int $m = 1;

                my int $o = -1;
                while ++$o <= 9 {
                    next if $o == $s;
                    next if $o == $e;
                    next if $o == $n;
                    next if $o == $d;
                    next if $o == $m;

                    my int $r = -1;
                    while ++$r <= 9 {
                        next if $r == $s;
                        next if $r == $e;
                        next if $r == $n;
                        next if $r == $d;
                        next if $r == $m;
                        next if $r == $o;

                        my int $more = $m*1000 + $o*100 + $r*10 + $e;

                        my int $y = -1;
                        while ++$y <= 9 {
                            next if $y == $s;
                            next if $y == $e;
                            next if $y == $n;
                            next if $y == $d;
                            next if $y == $m;
                            next if $y == $o;
                            next if $y == $r;

                            my int $money =
                                $m*10000 + $o*1000 + $n*100 + $e*10 + $y;
                            next unless $send + $more == $money;
                            say 'SEND + MORE == MONEY';
                            say "$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

Ring

t1 = clock() // start
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 "Time: "+ clock() - t1 // end
see "done..." + nl

Output:

works...
SEND = 9567 MORE = 1085 MONEY = 10652
done...
Time: 31.9 s

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