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Twelve Sum and Digit Substitution Puzzle

  1. Aug 5, 2009 #1
    Substitute each of the capital letters in the figure given below by a different digit from 0 to 7 such that:

    A+B+C = A+D+F = C+E+H = F+G+H = 12.

    Code (Text):
    A    B    C
    D         E
    F    G    H
    Note: The rotations and reflections of a valid arrangement are deemed as the same solution.
     
  2. jcsd
  3. Aug 5, 2009 #2
    a=2 b=3 c=7 d=4 e=0 f=6 g=1 h=5 (solution 1)
    a=2 b=4 c=6 d=3 e=1 f=7 g=0 h=5 (solution 2)
    a=5 b=0 c=7 d=1 e=3 f=6 g=4 h=2 (solution 3)
    a=5 b=1 c=6 d=0 e=4 f=7 g=3 h=2 (solution 4)
    a=6 b=1 c=5 d=4 e=0 f=2 g=3 h=7 (solution 5)
    a=6 b=4 c=2 d=1 e=3 f=5 g=0 h=7 (solution 6)
    a=7 b=0 c=5 d=3 e=1 f=2 g=4 h=6 (solution 7)
    a=7 b=3 c=2 d=0 e=4 f=5 g=1 h=6 (solution 8)

    However, solutions 2-8 are reflections or rotations of solution 1.

    (solution 1): a=2 b=3 c=7 d=4 e=0 f=6 g=1 h=5
    2 3 7
    4 _ 0
    6 1 5

    (solution 2): a=2 b=4 c=6 d=3 e=1 f=7 g=0 h=5
    2 4 6
    3 _ 1
    7 0 5
    (This is a reflection of (solution 1) along the AH-line)

    (solution 3): a=5 b=0 c=7 d=1 e=3 f=6 g=4 h=2
    5 0 7
    1 _ 3
    6 4 2
    (This is a reflection of (solution 1) along the CF-line)

    (solution 4): a=5 b=1 c=6 d=0 e=4 f=7 g=3 h=2
    5 1 6
    0 _ 4
    7 3 2
    (This is a rotation of (solution 1) by 180°)

    (solution 5): a=6 b=1 c=5 d=4 e=0 f=2 g=3 h=7
    6 1 5
    4 _ 0
    2 3 7
    (This is a reflection of (solution 1) along the DE-line)

    (solution 6): a=6 b=4 c=2 d=1 e=3 f=5 g=0 h=7
    6 4 2
    1 _ 3
    5 0 7
    (This is a rotation of (solution 1) by 90° to the right)

    (solution 7): a=7 b=0 c=5 d=3 e=1 f=2 g=4 h=6
    7 0 5
    3 _ 1
    2 4 6
    (This is a rotation of (solution 1) by 90° to the left)


    (solution 8): a=7 b=3 c=2 d=0 e=4 f=5 g=1 h=6
    7 3 2
    0 _ 4
    5 1 6
    (This is a reflection of (solution 1) along the BG-line)
     
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