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Given d dice each with n sides, find the probability that when they are rolled at once, there are no two consecutive numbers.

This task may be quite difficult. For a warm-up, try finding the numerators for fixed d such as {1,2,3} or for fixed n such as {2,3,4}.

Note 1: I don't have a formula so much as an algorithm.
Note 2: This problem arose as an attempt to solve http://perplexus.info/show.php?pid=12342 by Larry which uses non-independent cards instead of dice.

(No Solution Yet, 2 Comments) Submitted on 2021-01-26 by Jer    

Prove that 333 + 433 + 533 < 633
(No Solution Yet, 5 Comments) Submitted on 2021-01-25 by Danish Ahmed Khan    

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