S2T2

Jim Randell 3:27 pm on 11 February 2019 Permalink Reply
Tags: by: Graham Smithers ( 50 )   

• 

  Jim Randell 3:53 pm on 11 February 2019 Permalink | Reply

  This puzzle is similar Enigma 1036.

  Here is a Python program that solves it using a similar analysis.

  Run: [ @replit ]

  from enigma import (irange, nsplit, int2base, printf)
   
  # consider multipliers
  for k in irange(2, 9):
    q = 10 * k - 1
   
    # consider n digit numbers
    for n in irange(1, 8):
      p = 10 ** n - k
   
      # consider possible mobile digit d (different from k)
      for d in irange(0, 9):
        if d == k: continue
   
        # the corresponding n digit number x, is...
        (x, r) = divmod(d * p, q)
        if r != 0: continue
        # x has to be n different digits
        s = set(nsplit(x, n))
        if len(s) != n: continue
        # also different from d and k
        if d in s or k in s: continue
   
        printf("{x}{d} x {k} = {d}{x}", x=int2base(x, width=n))
  

  Solution: The original number is 230769.

  So we have:

  230769 × 4 = 923076

  If we allow leading zeros there is a further solution:

  076923 × 4 = 307692

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  • 

    Frits 11:42 am on 29 October 2020 Permalink | Reply

    @Jim,

    Is the phrase “some of the red cards” the reason why “n” cannot be 9?

    from enigma import SubstitutedExpression, seq_all_different, nsplit, div
    
    # the alphametic puzzle
    p = SubstitutedExpression(
      [# solve J * ABCDEFGHI = IABCDEFGH, J is one of the black cards
       
       # the derived formula
       "div(I * (10**N - J), (10 * J - 1)) = ABCDEFGH",
       # all different numbers
       "seq_all_different(nsplit(ABCDEFGH) + (I, J))",
       
       "len(str(ABCDEFGH)) = N"
      ],
      answer="10 * ABCDEFGH + I, J, I * 10**N + ABCDEFGH",
      verbose=0,
      d2i=dict([(k, "IJN") for k in {0,1}]),
      distinct="",   # allow variables with same values
      #reorder=0,
    )
    
    # Print answer
    for (_, ans) in p.solve():
      print(f"{ans[0]} x {ans[1]} = {ans[2]}")
    
    # 230769 x 4 = 923076
    

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