Enigmatic Code

Programming Enigma Puzzles

Enigma 516: The ABC of division

From New Scientist #1668, 10th June 1989 [link]

In the following division sum each letter stands for a different digit. Rewrite the sum with the letters replaced by digits.

[enigma516]

2 responses to “Enigma 516: The ABC of division

  1. Jim Randell 9 September 2019 at 8:12 am

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

    The following run file executes in 102ms.

    Run: [ @repl.it ]

    #!/usr/bin/env python -m enigma -r
    
    SubstitutedDivision
    
    "qsmcaq / csm = ween"
    
    "qsm - csm = wbb"
    "wbbc - nhn = wea"
    "weaa - nhn = snn"
    "snnq - sqwe = shs"
    

    Solution: The correct sum is: 539465 ÷ 439 = 1228 (remainder 373).

  2. GeoffR 19 September 2019 at 11:22 am
    # this enigma puzzle uses 10 different letters for digits 0..9
    
    from itertools import permutations
    for p in permutations ('1234567890'):
      c, s, m, w, e, n, q, a, b, h = p
    
      # some variables in the division sum cannot start with zero
      if '0' in {q, w, c, s, n}: continue
    
      # find variables in overall sum, including remainder
      csm = int(c + s + m)
      ween = int(w + e + e + n)
      qsmcaq = int(q + s + m + c + a + q)
      shs = int(s + h + s) # remainder
    
      if int(e) * csm == int(n + h + n):
        if csm * ween + shs == qsmcaq :
          print(f"Sum is {csm} * {ween} = {qsmcaq}, remainder {shs}")
    
    # Sum is 439 * 1228 = 539465, remainder 373
    

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