S2T2

Jim Randell 10:38 am on 11 October 2019 Permalink Reply
Tags: by: Andrew Skidmore ( 85 )   

• 

  Jim Randell 10:39 am on 11 October 2019 Permalink | Reply

  This is a straightforward alphametic sum.

  We can solve it using the [[ SubstitutedSum() ]] solver from the enigma.py library.

  The following command executes in 164ms.

  Run: [ @repl.it ]

  % python -m enigma SubstitutedSum "SEVEN + THREE + TWO = TWELVE"
  (SEVEN + THREE + TWO = TWELVE)
  (82524 + 19722 + 106 = 102352) / E=2 H=9 L=3 N=4 O=6 R=7 S=8 T=1 V=5 W=0
  (82526 + 19722 + 104 = 102352) / E=2 H=9 L=3 N=6 O=4 R=7 S=8 T=1 V=5 W=0
  

  Solution: LETTERS = 3211278.

  The values for N and O can be interchanged, but we are asked for the value of LETTERS, so the solution is unique.

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• 

  GeoffR 11:01 am on 12 October 2019 Permalink | Reply

  
  % A Solution in MiniZinc
  
  %   S E V E N
  %   T H R E E
  %       T W O
  % -----------
  % T W E L V E
  % -----------
  include "globals.mzn";
   
  var 1..9:S; var 0..9:E; var 0..9:V; var 0..9:N;
  var 1..9:T; var 0..9:H; var 0..9:R; var 0..9:W;   
  var 0..9:O; var 0..9:L;
  
  % Carry digits for adding columns
  var 0..2: carry1; var 0..2: carry2; var 0..2: carry3; 
  var 0..2: carry4; var 0..2: carry5; 
   
  constraint all_different([S, E, V, N, T, H, R, W, O, L]);
  
  % Working left from the right hand column
  constraint (N + E + O) mod 10 == E 
  /\ (N + E + O) div 10 == carry1;
  
  constraint (2*E + W + carry1) mod 10 == V 
  /\ (2*E + W + carry1) div 10 == carry2;
  
  constraint (V + R + T + carry2) mod 10 == L 
  /\ (V + R + T + carry2) div 10 == carry3;
  
  constraint (E + H + carry3) mod 10 == E 
  /\ (E + H + carry3) div 10 == carry4;
  
  constraint (S + T + carry4) mod 10 == W 
  /\ (S + T + carry4) div 10 == carry5;
  
  constraint T = carry5;
  
  solve satisfy;
  
  output [ "LETTERS = " ++ show(L),show(E),
  show(T),show(T),show(E), show(R),show(S) ]
  
  ++ ["\n" ++ "SEVEN = " ++  show(S),show(E),
  show(V),show(E),show(N)]
  ++ [", THREE = " ++  show(T),show(H),show(R),
  show(E),show(E) ]
  ++ [", TWO = " ++  show(T),show(W),show(O) ]
  ++ [", TWELVE = " ++  show(T),show(W),show(E),
  show(L),show(V),show(E)];
  
  % LETTERS = 3211278
  % SEVEN = 82526, THREE = 19722, TWO = 104, TWELVE = 102352
  % -----------------
  % LETTERS = 3211278
  % SEVEN = 82524, THREE = 19722, TWO = 106, TWELVE = 102352
  % Finished in 161msec
  
  
  

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