S2T2

Jim Randell 2:13 pm on 4 May 2019 Permalink Reply
Tags: by: S G Worthington   

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  Jim Randell 2:14 pm on 4 May 2019 Permalink | Reply

  Once we have the solved the alphametic sum the value of ROBERT is determined.

  We can use the [[ SubstitutedExpression() ]] solver from the enigma.py library to solve this puzzle.

  The following run file executes in 1.24s.

  #!/usr/bin/env python -m enigma -r
  
  SubstitutedExpression
  
  "BRIAN + BETTY = MOIRA"
  
  "is_square(M + O + I + R + A + R + O + B + E + R + T)"
  
  --answer="R + O + B + E + R + T"
  

  But it is faster to write a short program that uses the [[ SubstitutedSum() ]] solver.

  This Python program runs in 101ms.

  Run: [ @repl.it ]

  from enigma import SubstitutedSum, is_square, printf
  
  # make the alphametic sum
  p = SubstitutedSum(['BRIAN', 'BETTY'], 'MOIRA')
  
  # solve it
  for s in p.solve():
    # compute the ages
    (m, r) = (sum(s[x] for x in w) for w in ('MOIRA', 'ROBERT'))
    # check they sum to a square
    if not is_square(m + r): continue
    # output solution
    printf("r = {r} [m = {m}] [{s}]", s=p.substitute(s, "BRIAN + BETTY = MOIRA"))
  

  Solution: Robert is 23.

  Moira is 26. Together the ages sum to 49 (= 7²).

  There are 2 possible sums as the values of N and Y (in the units column of the sum) are interchangeable.

  So the sum is one of:

  14836 + 15007 = 29843
  14837 + 15006 = 29843

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  GeoffR 3:10 pm on 6 May 2019 Permalink | Reply

  % A solution in MinZinc 
  include "globals.mzn";
  
  var 0..9: B; var 0..9: R; var 0..9:I; var 0..9: A; var 0..9: N;
  var 0..9: E; var 0..9: T; var 0..9:Y; var 0..9: M; var 0..9: O;
  
  constraint B > 0 /\ M > 0 /\ R > 0;
  constraint all_different ([B, R, I, A, N, E, T, Y, M, O]);
  
  var 10000..99999: BRIAN = 10000*B + 1000*R + 100*I + 10*A + N;
  var 10000..99999: BETTY = 10000*B + 1000*E + 100*T + 10*T + Y;
  var 10000..99999: MOIRA = 10000*M + 1000*O + 100*I + 10*R + A;
  
  constraint BRIAN + BETTY == MOIRA;
  
  % The sum of the children’s ages is a perfect square
  set of int: sq = {9, 16, 25, 36, 49, 64, 81, 100};
  constraint  (M + O + I + R + A + R + O + B + E + R + T) in sq;
  
  solve satisfy;
  
  % The sum of the individual digit values gives each child's age
  output [ "ROBERT = " ++ show(R+O+B+E+R+T)] ++  
  [", MOIRA = " ++ show(M+O+I+R+A) ]
  ++ ["\nSum is " ++ show(BRIAN) ++ " + " ++ show(BETTY) ++ 
  " = " ++ show(MOIRA) ] ;
  
  % ROBERT = 23, MOIRA = 26
  % Sum is 14837 + 15006 = 29843
  % % time elapsed: 0.03 s
  % ----------
  % ROBERT = 23, MOIRA = 26
  % Sum is 14836 + 15007 = 29843
  % % time elapsed: 0.03 s
  % ----------
  % ==========
  % Finished in 254msec
  
  
  

  The parents ages (22 and 13) or (23 and 12) don’t seem to make much sense in relation to the children’s ages! ie Robert (23) and Moira(26)

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