S2T2

Jim Randell 9:54 am on 21 August 2019 Permalink Reply
Tags: by: Danny Roth ( 84 )   

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  Jim Randell 9:55 am on 21 August 2019 Permalink | Reply

  We can express the puzzle as a set of alphametic constraints and use the [[ SubstitutedExpression() ]] solver from the enigma.py library to solve it.

  The following run file executes in 81ms.

  Run: [ @repl.it ]

  #! python -m enigma -rr
  
  # solver to use
  SubstitutedExpression
  
  # solver parameters
  --distinct=""
  --invalid=""
  --answer="ABCD"
  
  # 2-digit subsequences are prime
  "is_prime(AB)"
  "is_prime(AC)"
  "is_prime(AD)"
  "is_prime(BC)"
  "is_prime(BD)"
  "is_prime(CD)"
  
  # and all different
  "all_different(AB, AC, AD, BC, BD, CD)"
  
  # and more than 1 of them divides ABCD
  "sum(ABCD % x == 0 for x in (AB, AC, AD, BC, BD, CD)) > 1"
  

  Solution: George’s new extension number is 4371.

  4371 is divisible by 47 and by 31.

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  GeoffR 8:43 am on 22 August 2019 Permalink | Reply

  
  % A Solution in MiniZinc
  include "globals.mzn";
  
  var 1..9:A; var 1..9:B; var 1..9:C;  var 1..9:D;
  
  predicate is_prime(var int: x) = 
  x > 1 /\ forall(i in 2..1 + ceil(sqrt(int2float(ub(x))))) 
  ((i < x) -> (x mod i > 0));
  
  % the four-figure telephone extension number
  var 1000..9999: ABCD = 1000*A + 100*B + 10*C + D;
  
  % six different two-digit numbers
  constraint all_different([AB, AC, AD, BC, BD, CD]);
  
  var 10..99: AB = 10*A + B;
  var 10..99: AC = 10*A + C; 
  var 10..99: AD = 10*A + D;
  var 10..99: BC = 10*B + C;
  var 10..99: BD = 10*B + D;
  var 10..99: CD = 10*C + D;
  
  constraint is_prime(AB) /\ is_prime(AC) /\ is_prime(AD)
  /\ is_prime(BC) /\ is_prime(BD) /\ is_prime(CD);
  
  % more than one two-digit number divides exactly into the extension number
  constraint sum ([ABCD mod AB == 0, ABCD mod AC == 0,
  ABCD mod AD == 0, ABCD mod BC == 0, ABCD mod BD == 0,
  ABCD mod CD == 0]) > 1;
  
  solve satisfy;
  output ["George's Ext No. = " ++ show(ABCD)];
  
  % George's Ext No. = 4371
  % ----------
  % ==========
  
  

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