I do not know if there is a correct solution to this puzzle, but I can't stop thinking about it, so here goes: is it possible to accurately simulate a single, fair, six-sided die using three custom six-sided dice?
Here are the more specific stipulations:
- The only possible roll totals between the three dice must be one through six.
- These six numbers must be rolled with equal probability.
- No negative numbers are allowed.
- The dice do not have to be identical.
- When a six is rolled, all three dice must contribute some number greater than zero to the total (to avoid the trivial solution).
I feel like I'm getting closer but I'm not there yet. I know that you can't simplify the dice down to two- or three-sided dice (as in, having each die have only two different numbers, equally represented), because then the number of combinations possible isn't divisible by six.