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Math Help - More 6-sided dice

  1. #1
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    More 6-sided dice

    I was inspired by Wilmer's 6-sided dice problem, so I created one that is slightly more complex.

    4 six-sided dice have numbers on each face such that:

    When the dice are rolled, every sum on the faces of the dice from 1 to 1296 is possible.

    The greatest numerical value of a face, positive or negative, is 436.

    Only one die has any negative values on it.

    Challenge: Give one possible solution to the problem. I will post the solutions I have found later as a spoiler.
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  2. #2
    MHF Contributor
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    Here are the solutions (there may be more):

    Spoiler:

    Die 1:
    (436, 428, 4, -4, -428, -436)

    Die 2:
    (x, x+4, x+144, x+148, x+288, x+292)

    Die 3:
    (y, y+2, y+48, y+50, y+96, y+98)

    Die 4:
    (z, z+1, z+16, z+17, z+32, z+33)

    where
    x+y+z = 437

    0 \leq x \leq 144, 0 \leq y \leq 338, 0 \leq z \leq 403
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