S2T2

Jim Randell 9:07 am on 21 October 2021 Permalink Reply
Tags: by: Alfred Moritz   

• 

  Jim Randell 9:08 am on 21 October 2021 Permalink | Reply

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

  The following run file executes in 73ms.

  Run: [ @replit ]

  #! python3 -m enigma -rr
  
  SubstitutedExpression
  
  # values are 0 to 25, so let's use base 26
  --base=26
  
  # X is the unused value, so: k = (tri(25) - X) / 5, tri(25) = 325
  # so X is a multiple of 5
  "X % 5 == 0"
  
  # each row/column/diagonal sums to the magic constant
  "5 * (A + B + C + D + E) + X == 325"
  "5 * (F + G + H + I + J) + X == 325"
  "5 * (K + L + M + N + O) + X == 325"
  "5 * (P + Q + R + S + T) + X == 325"
  "5 * (U + V + W + Y + Z) + X == 325"
  
  "5 * (A + F + K + P + U) + X == 325"
  "5 * (B + G + L + Q + V) + X == 325"
  "5 * (C + H + M + R + W) + X == 325"
  "5 * (D + I + N + S + Y) + X == 325"
  "5 * (E + J + O + T + Z) + X == 325"
  
  "5 * (A + G + M + S + Z) + X == 325"
  "5 * (E + I + M + Q + U) + X == 325"
  
  # Y is the highest mark
  "(25 if X != 25 else 24) = Y"
  
  # H is the second highest mark
  "(Y - 1 if X != Y - 1 else Y - 2) = H"
  
  # J is the third highest mark
  "(H - 1 if X != H - 1 else H - 2) = J"
  
  # Y beat W by the same margin that W beat V
  "Y - W == W - V"
  
  # and this is the same margin that S beat M and M beat G
  "S - M == Y - W"
  "M - G == Y - W"
  
  # V = 2G, G's score was odd
  "2 * G = V"
  "G % 2 == 1"
  
  # I = 4F
  "4 * F = I"
  
  # U beat Z, C beat R, K beat O
  "U > Z"
  "C > R"
  "K > O"
  
  # [optional]
  --template=""
  --denest
  

  Solution: Kenneth beat Olga by 16 marks.

  The complete layout is:

  [A 21] [B 14] [C  7] [D  0] [E 18]
  [F  2] [G  5] [H 23] [I  8] [J 22]
  [K 20] [L 15] [M 12] [N  9] [O  4]
  [P 11] [Q 16] [R  1] [S 19] [T 13]
  [U  6] [V 10] [W 17] [Y 24] [Z  3]
  [X 25]

  So the marks awarded were 0-24, no-one scored 25.

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• 

  Frits 12:54 pm on 22 October 2021 Permalink | Reply

   
  # Y + V = 2 * W  \
  # Y = 24 or 25    > V is even so Y is also even
  # V = 2G         /
  #
  # (X, Y, H, J) = (25, 24, 23, 22)
  # W = 17
  #
  # F + G + I = 15 \   G + 5 * F = 15
  # G is odd        >  so G = 5, F = 2, I = 8
  # 4 * F = I      /
  #
  # V = 10 (2 * G)
  # center M = 60 / 12
  # S = 19 (S - M == Y - W)
  #
  # C + H + M + R + W = 60 \  C + R = 8
  #                         >
  # C > R                  /  so only option R = 1, C = 7
  #
  # A + G + M + S + Z = 60 \  A + Z = 24  so Z > 2
  # U > Z                   >
  # U + V + W + Y + Z = 60 /  U + Z = 9 only option Z = 3, U = 6, A = 21
  #
  # D + I + N + S + Y = 60 --> D + N = 9, only options (D, N): (0, 9) or (9, 0)
  #
  # only candidates for 4 are O and T -- > O + T = y + 4  (y is O or T)
  # E + J + O + T + Z = 60 --> E + O + T = 35 --> E + y = 31 --> E > 10
  #
  # B + G + L + Q + V = 60 \  B + L + Q = 45 so B > 6 and also B > 10
  #                         >
  # A + B + C + D + E = 60 /  B + D + E = 32
  #
  # minimal(B + E) = 24 --> D <= 8 --> D = 0 and N = 9
  #
  # E + O + T = 35 \
  #                 > Q = O + T - 1 = y + 3
  # E + Q = 34     /
  #
  # B + E = 32, only options (B, E, Q): (14, 18, 16) or (18, 14, 20)
  # last option implies y = 17 which is not possible
  # so B = 14, E = 18, Q = 16, L = 15
  #
  # A + F + K + P + U = 60 --> K + P = 31
  # only options (K, P): (20, 11) or (11, 20)
  #
  # K + L + M + N + O = 60 --> K + O = 24 with K > O
  # only option (K, O): (20, 4)
  # K = 20, O = 4, T = 13, P = 11 
  

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