You are given blank six-sided dice, with equal weight on each side (fair dice). You're allowed to write on each side of each die a number between 0 and 6. Numbers may repeat themselves on a single die, so for example, one die can have five 4s and one 0.

1) Can you create two such dice which, if they are rolled and their results added, will give equal odds for every number from 1 to 12?

2) Can you create three such dice which, if they are rolled and their results added, will give equal odds for every number from 1 to 18?

(NOTE: Don't get smart and make all the dice all 0s. The probability of getting 0 should be 0)

(In reply to Extension to question 2 by Joel)

Using a technique from Renumbered Dice, I find 6 sets of integer dice:

12*(x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18)

Posted by Brian Smith on 2017-02-27 12:56:16