S2T2

Jim Randell 10:19 am on 5 August 2021 Permalink Reply
Tags: by: Victor Bryant ( 139 )   

• 

  Jim Randell 10:19 am on 5 August 2021 Permalink | Reply

  We can find the answer using the [[ SubstitutedExpression ]] solver from the enigma.py library.

  The following run file executes in 893ms:

  Run: [ @replit ]

  #! python3 -m enigma -rr
  
  SubstitutedExpression
  
  "SO + DO + WHAT + NOW + ADD + AND + SEND + IN + THIS + AND + THAT < 10000"
  
  --answer="THIS + THAT"
  

  Solution: THIS + THAT = 2123.

  The result of the sum is 9998.

  ---

  To gain a bit more speed we can use the technique implemented in [[ SubstitutedExpression.split_sum() ]], splitting the sum into separate columns with carries between. (See: Teaser 2792).

  Except here we may have to deal with multi digit carries (as there are 11 summands — although with a bit of analysis we can see that single digit carries would be sufficient in this case).

  The following run-file executes in 226ms.

  #! python3 -m enigma -rr
  
  SubstitutedExpression
  
  --symbols="ADEHINOSTWabcdewxyz"
  --distinct="ADEHINOSTW"
  --invalid="0,ADINSTWw"
  --invalid="2-9,ac"
  
  # "SO + DO + WHAT + NOW + ADD + AND + SEND + IN + THIS + AND + THAT = wxyz"
  
  "        W +             S +     T +     T + c + e = w"
  "        H + N + A + A + E +     H + A + H + a + d = ex"
  "S + D + A + O + D + N + N + I + I + N + A + b     = cdy"
  "O + O + T + W + D + D + D + N + S + D + T         =  abz"
  
  --template="(SO + DO + WHAT + NOW + ADD + AND + SEND + IN + THIS + AND + THAT = wxyz)"
  --answer="THIS + THAT"
  

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  • 

    Frits 4:41 pm on 5 August 2021 Permalink | Reply

    To gain more speed in the first program you can also add:

    “W + S + 2 * T < 10"

    For more on this puzzle see:

    [https://brg.me.uk/?page_id=4022]

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  • 

    Jim Randell 5:32 pm on 5 August 2021 Permalink | Reply

    Adding a second level of truncation (without worrying about the exact values of the carries) brings the run time down to 80ms. And there is no need for a third level.

    Run: [ @replit ]

    #! python3 -m enigma -rr
    
    SubstitutedExpression
    
    --invalid="0,ADINSTW"
    
    "W + S + T + T < 10"
    "WH + N + A + A + SE + TH + A + TH < 100"
    "SO + DO + WHAT + NOW + ADD + AND + SEND + IN + THIS + AND + THAT < 10000"
    
    --template="(SO + DO + WHAT + NOW + ADD + AND + SEND + IN + THIS + AND + THAT < 10000)"
    --answer="THIS + THAT"
    

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• 

  GeoffR 12:29 pm on 5 August 2021 Permalink | Reply

  
  % A Solution in MiniZinc 
  include "globals.mzn";
  
  % Digits in main 11 numbers
  var 0..9:S; var 0..9:O; var 0..9:D; var 0..9:W;var 0..9:H;
  var 0..9:A; var 0..9:T; var 0..9:E; var 0..9:N;var 0..9:I;
  
  % Carry digits for sum of 11 numbers
  var 1..7:c1; var 1..7:c2; var 1..7:c3;
  
  % Total of 11 numbers
  var 1..9: a; var 0..9: b; var 0..9: c; var 0..9: d;
  var 1000..9999: total == 1000*a + 100*b + 10*c + d;
  
  constraint S > 0 /\ D > 0 /\ W > 0 /\ N > 0 /\ A > 0 /\ I > 0 /\ T > 0;
  constraint all_different([S, O, D, W, H, A, T, E, N, I]);
  
  % Main sum
  %     S O
  %     D O
  % W H A T
  %   N O W
  %   A D D
  %   A N D
  % S E N D
  %     I N
  % T H I S
  %   A N D 
  % T H A T
  %--------
  % a b c d
  %--------
  
  % Adding 4 columns, with carry digits, starting at right hand column
  constraint c1 == (O + O + T + W + D + D + D + N + S + D + T) div 10
  /\ d == (O + O + T + W + D + D + D + N + S + D + T) mod 10;
  
  constraint c2 == (c1 + S + D + A + O + D + N + N + I + I + N + A) div 10
  /\ c == (c1 + S + D + A + O + D + N + N + I + I + N + A) mod 10;
  
  constraint c3 == (c2 + H + N + A + A + E + H + A + H) div 10
  /\ b == (c2 + H + N + A +A +  E + H + A + H) mod 10;
  
  constraint a == c3  + W + S + T + T;
  
  % Sum 2 -  THIS + THAT
  var 0..1:c4; var 0..2:c5; var 0..2:c6;
  var 1..9: e; var 0..9: f; var 0..9: g; var 0..9: h;
  var 1000..9999: efgh = 1000*e + 100*f + 10*g + h;
  
  %  T H I S
  %  T H A T
  %  -------
  %  e f g h
  %---------
  
  constraint c4 == (S + T) div 10 /\ h == (S + T ) mod 10;
  
  constraint c5 == (c4 + I + A) div 10 /\  g == (c4 + I + A) mod 10;
  
  constraint c6 == (c5 + H + H) div 10 /\ f == (c5 + H + H) mod 10;
  
  constraint e == c6 + T +  T;
  
  constraint efgh == 1000*e + 100*f + 10*g + h;
  
  solve satisfy;
  
  output ["Total of 11 numbers = " ++ show(total ) ++ "\n" 
  ++ "THIS + THAT = " ++ show(efgh) ];
  
  % Total of 11 numbers = 9998
  % THIS + THAT = 2123
  % ----------
  % ==========
  
  

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