I have a pair of odd six-sided dice at my house... I don't quite remember where I got them.

Each die has only one number on each side, and each of these numbers is a positive number.

Each pair of opposite faces sums to the same number on each individual die (but not necessarily the same across both dice)

Furthermore, the two dice, when rolled together, have the same probability of coming up a certain number as two six sided dice coming up with the same number.

Here are my drawings of three faces from each die:

enter image description here

(the 6 on the top drawing is actually a 6)

To solve the puzzle, all you have to do is:

Draw a complete cube net of each die.

Good luck and happy puzzling!

  • $\begingroup$ is that a 6 or a 9? or can it be both? thanks! $\endgroup$ Commented Jan 22, 2019 at 13:53
  • $\begingroup$ @OmegaKrypton it's a 6, I completely forgot 9 was 6 upside down, lol! $\endgroup$ Commented Jan 22, 2019 at 13:57
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    $\begingroup$ Now that an answer has been accepted, I'll add that they are called Sicherman dice. $\endgroup$ Commented Jan 22, 2019 at 15:51

1 Answer 1



To get a 2 we need a 1 on the 224 die, and this must be opposite the 4, so 1,2,2,3,3,4, and we also need a 12, which must be 4+8, so the other die is 1,3,4,5,6,8.

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    $\begingroup$ In the absence of the requirement that opposite faces on a given die sum to equal values, would there be any other solutions (beyond the obvious permutations)? $\endgroup$
    – supercat
    Commented Jan 22, 2019 at 16:48
  • $\begingroup$ not according to en.wikipedia.org/wiki/Sicherman_dice#Mathematical_justification; @supercat $\endgroup$
    – JMP
    Commented Jan 22, 2019 at 17:00

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