Enigmatic Code

Programming Enigma Puzzles

Enigma 331: All change please

From New Scientist #1479, 24th October 1985 [link]

In the following long division sum the figures given have this is common — they are all wrong. The sum comes out exactly.

Enigma 331

Write out the correct long division sum.



One response to “Enigma 331: All change please

  1. Jim Randell 5 February 2016 at 7:53 am

    This Python program uses the SubstitutedDivision() solver from the enigma.py library to find division sums with the right “shape”, and then checks them to see if all the digits giving in the diagram are wrong. It runs in 979ms.

    from enigma import SubstitutedDivision
    # check specified digits are wrong
    def check(n, s):
      return all(b == '?' or b != a for (a, b) in zip(str(n), s))
    # look for solutions with the right shape
    p = SubstitutedDivision(
      '?????', '??', '????',
      [('??', '??', '??'), ('???', '???', '??'), ('???', '???', '?'), ('??', '??', '')]
    for s in p.solve():
      # check given digits are wrong
      if not check(s.a, '????8'): continue
      if not check(s.b, '41'): continue
      if not check(s.c, '???1'): continue
      i = p.solution_intermediates(s)
      if not(check(i[0][1], '?5') and check(i[0][2], '2?')): continue
      if not(check(i[1][1], '1?8') and check(i[1][2], '3?')): continue
      if not(check(i[2][1], '118') and check(i[2][2], '9')): continue
      if not(check(i[3][0], '96') and check(i[3][1], '?4')): continue

    Solution: The correct sum is 70992 ÷ 36 = 1972.

    Enigma 331 - Solution

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