S2T2

Jim Randell 11:18 am on 11 June 2020 Permalink Reply
Tags: by: Ann Kindersley   

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  Jim Randell 11:20 am on 11 June 2020 Permalink | Reply

  Assuming the ages cannot have a leading zero (which means the phone numbers can’t either) gives us a unique solution to the puzzle.

  This Python program uses the [[ SubstitutedExpression() ]] solver from the enigma.py library to try 3-, 4- and 5-digit numbers satisfying the required conditions. It runs in 54ms.

  from enigma import (sprintf as f, join, SubstitutedExpression, subsets, all_different, printf)
  
  # alphametic forms for possible palindromic phone numbers
  numbers = [ 'ABA', 'ABBA', 'ABCBA' ]
  
  # collect possible (number, age) solutions
  ss = list()
  
  # consider possible phone numbers
  for n in numbers:
    # age is 1st and 3rd digit
    a = n[0] + n[2]
    
    exprs = [
      # sum of digits is the same as age
      f("{s} = {a}", s=join(n, sep=" + ")),
      # the number itself is divisible by the age
      f("{n} % {a} = 0"),
    ]
  
    # solve the alphametic expressions
    p = SubstitutedExpression(exprs, distinct="", answer=f("({n}, {a})"))
    ss.extend(p.answers(verbose=0))
  
  # choose three solutions with different ages
  for (A, B, C) in subsets(ss, size=3):
    if not all_different(A[1], B[1], C[1]): continue
    printf("A={A} B={B} C={C}")
  

  Solution: The ages are: 21, 23, 27.

  The corresponding phone numbers are: 28182, 28382, 28782.

  These are the only three solutions for 5-digit phone numbers, and there are no solutions for 3- or 4-digit phone numbers.

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• 

  GeoffR 4:48 pm on 16 July 2021 Permalink | Reply

  % A Solution in MiniZinc 
  % assumes 5-digit tel. no. is ABCBA
  include "globals.mzn";
  
  var 1..9:A; var 0..9:B; var 0..9:C; 
  
  var 10..100: age1;
  
  var 10000..99999: ABCBA = 10001*A + 1010*B + 100*C; 
  
  constraint age1 == 10*A + C /\ age1 == 2*A + 2*B + C
  /\ ABCBA mod age1 == 0;
  
  solve satisfy;
  
  output ["Age = " ++ show(age1) ++ ", Tel. No. = " ++ show(ABCBA) ];
  
  % Age = 21, Tel. No. = 28182
  % ----------
  % Age = 23, Tel. No. = 28382
  % ----------
  % Age = 27, Tel. No. = 28782
  % ----------
  % ==========
  
  
  

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