S2T2

Jim Randell 10:09 am on 9 August 2019 Permalink Reply
Tags: by: Graham Smithers ( 82 )   

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  Jim Randell 10:10 am on 9 August 2019 Permalink | Reply

  We can easily use the [[ SubstitutedExpression() ]] solver from the enigma.py library to solve the alphametic sums, and we can use [[ --code ]] parameters to provide the additional check that none of the numbers consist of a set of consecutive digits. The numbers are all composed of different digits, so that makes things a bit simpler.

  This run file executes in 139ms.

  Run: [ @repl.it ]

  #! python -m enigma -rr
  
  SubstitutedExpression
  
  --answer="FIFTEEN"
  
  "ONE + ONE = TWO"
  "ONE + FOUR = FIVE"
  
  # check the words in each sum do not consist of consecutive digits
  "check(ONE) and check(TWO)"
  "check(FOUR) and check(FIVE)"
  
  # function to check a sorted sequence of distinct numbers is increasing consecutive 
  --code="is_consecutive = lambda s: s[-1] - s[0] == len(s) - 1"
  
  # function to check a word does not consist of consecutive digits
  --code="check = lambda w: not is_consecutive(sorted(nsplit(w)))"
  

  Solution: FIFTEEN = 9594663.

  We have:

  ONE = 236, TWO = 472, FOUR = 9280, FIVE = 9516

  There is one other solution to the alphametic sums that is eliminated because FOUR is composed from a set of (numerically) consecutive digits:

  ONE = 286, TWO = 572, FOUR = 3210, FIVE = 3496

  So we could just generate both solutions to the alphametic sums, and remove the non-viable solution by inspection.

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• 

  GeoffR 3:05 pm on 11 August 2019 Permalink | Reply

  % A Solution in MiniZinc
  include "globals.mzn";
   
  var 1..9: O; var 0..9: N; var 1..9: F; var 0..9: R;
  var 0..9: E; var 1..9: T; var 0..9: W; var 0..9: I; 
  var 0..9: V; var 0..9: U;   
  
  constraint all_different([U, O, N, E, F, R, T, W, I, V]); 
  
  % check ONE for non-consecutive digits
  var set of int : s1 = {O,N,E};
  constraint max ([O,N,E]) - min([O,N,E]) != card(s1) - 1;
  var 100..999: ONE = 100*O + 10*N + E; 
  
  % check TWO for non-consecutive digits
  var set of int : s2 = {T,W,O};
  constraint max ([T,W,O]) - min([T,W,O]) != card(s2) - 1;
  var 100..999: TWO = 100*T + 10*W + O;
  
  % check FOUR for non-consecutive digits
  var set of int : s3 = {F,O,U,R};
  constraint max ([F,O,U,R]) - min([F,O,U,R]) != card(s3) - 1;
  var 1000..9999: FOUR = 1000*F + 100*O + 10*U + R;
  
  % check FIVE for non-consecutive digits
  var set of int : s4 = {F,I,V,E};
  constraint max ([F,I,V,E]) - min([F,I,V,E]) != card(s4) - 1;
  var 1000..9999: FIVE = 1000*F + 100*I + 10*V + E;
  
  constraint ONE + ONE == TWO;
  constraint ONE + FOUR == FIVE;
  
  solve  satisfy;
  
  output [ "ONE = " ++  show(ONE) ] ++ [ ", TWO = " ++  show(TWO) ]  
  ++ [ ", FOUR = " ++  show(FOUR) ] ++ [ ", FIVE = " ++  show(FIVE) ]
  ++ [ "\nFIFTEEEN = " ++ show(F),show(I),show(F),show(T),show(E),show(E),show(N)];   
  
  % ONE = 236, TWO = 472, FOUR = 9280, FIVE = 9516
  % FIFTEEEN = 9594663
  % time elapsed: 0.02 s
  % ----------
  % ==========
  % Finished in 231msec
  
  

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