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Q: What fair dice can be simulated by adding up other dice?
However, if you renumber the dice using nonnegative whole numbers you can create other pseudo-N-sided dice. Doing the same to the weirdly labeled dice you can simulate any fair d(xn), where x is any D number. The D numbers now include D = {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 20, 25, 27, 32, ….} So, every divisor of a D number is a D number, and every product of D numbers is a D number. But very technically, it’s impossible to simulate a fair d7 using fair polyhedral dice (same is true for an non-D-number).
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