S2T2

Jim Randell 6:45 am on 24 April 2025 Permalink Reply
Tags: by: Bob Walker ( 10 )   

• 

  Jim Randell 6:46 am on 24 April 2025 Permalink | Reply

  Here is a solution using the [[ SubstitutedExpression ]] solver from the enigma.py library.

  The following run file executes in 78ms. (Internal runtime of the generated code is 331µs).

  #! python3 -m enigma -rr
  
  SubstitutedExpression
  
  # numbers range from 1 to 10
  --base=11
  --digits="1-10"
  
  "abs(U - N) = S"
  "abs(D - A) = U"
  "abs(A - Y) = N"
  "abs(T - I) = D"
  "abs(I - M) = A"
  "abs(M - E) = Y"
  
  --assign="U,1"
  --answer="(D, A, Y)"
  
  --template=""
  

  Solution: DAY = 672.

  

  At least the digits have values: D = 6, A = 7, Y = 2.

  But since the digits go from 1 to 10, you could argue that the result is expressed in base 11, so:

  DAY = 672 [base 11] = 805 [base 10]

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  • 

    Ruud 6:14 am on 28 April 2025 Permalink | Reply

    Brute force one liner:

    import itertools
    
    print(
        *(
            f"{d}{a}{y}"
            for s, n, d, a, y, t, i, m, e in itertools.permutations(range(2, 11), 9)
            if s == abs(1 - n) and 1 == abs(d - a) and n == abs(a - y) and d == abs(t - i) and a == abs(i - m) and y == abs(m - e)
        )
    )
    

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• 

  Frits 10:51 am on 26 April 2025 Permalink | Reply

  #    S
  #   U N                            U = 1
  #  D A Y
  # T I M E
  
  sols = set()
  U, mx = 1, 10
  r0 = set(range(2, mx + 1)) # remaining digits to use
  
  for N in range(2, mx - 1):  # no using <mx - 1> and <mx> on this level
    S = N - U
    r1 = r0 - {N, S}
    if len(r1) != len(r0) - 2: continue
    for A in r1 - {mx}:       
      r2 = r1 - {A}
      for D in (A - U, A + U):
        if D not in r2 or D == mx: continue
        r3 = r2 - {D}
        for Y in (A - N, A + N):
          if Y not in r3 or Y == mx: continue
          r4 = r3 - {Y}
          if max(r4) - min(r4) < max(D, A, Y): continue
          for I in r4:
            for M in (I - A, I + A):
              if M not in r4: continue
              for T in (I - D, I + D):
                if T not in r4: continue
                for E in (M - Y, M + Y):
                  if {T, I, M, E} != r4: continue
                  sols.add(100 * D + 10 * A + Y)
  
  print("answer(s):", ' or '.join(str(s) for s in sols))
  

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