You've always got the standard way to get fair random numbers from a fairness-unknown coin. Flip it twice. Restart if you get both heads or both tails. If you get H then T or T then H, those are equally probable, so take the first one of those as the final outcome.
This generalizes to a die of N sides. Roll it N times. If you don't get all N distinct results, restart. If you do, then take the first result as your final outcome.
(That may take a lot of trials for large N. It can be broken down by prime factorization, like roll 2-sided and 3-sided objects separately, and combine them for a d6 result.)
This generalizes to a die of N sides. Roll it N times. If you don't get all N distinct results, restart. If you do, then take the first result as your final outcome.
(That may take a lot of trials for large N. It can be broken down by prime factorization, like roll 2-sided and 3-sided objects separately, and combine them for a d6 result.)