# Math Help - More 6-sided dice

1. ## 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.

2. 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
$x+y+z = 437$

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