How many Dice Rolls Would It Take to Reach Your Favorite Kind of Number?

By Lucy Martinez and Doron Zeilberger

.pdf    .tex   

published in Maple Transactions, Vol. 3 No. 3 (2023).

Inspired by a recent beautiful paper [arxiv version] by Noga Alon and Yaakov Malinovsky, we extend it in several directions. First we consider dice with other number of faces, rather than the usual 6, and second consider what happens if you don't start at 0, but further on, and third consider many other properties that a natural number can have, not just that of being a prime.

In the process we show the great power of symbolic computation (i.e. "symbol-crunching") as opposed to mere numerical computation (i.e. "number-crunching") to efficiently get both symbolic and numeric output. We conclude with some philosophical remarks that often so-called "rigorous" error-analysis as done brilliantly in the Alon-Malinowsky paper (that was the inspiration to our paper) is only of theoretical interest, since it tacitly assumes that we live for ever, that unfortunately we don't.

Written: Jan. 31,2023

Maple packages

Sample Input and Output for HIT1.txt

Sample Input and Output for HIT2.txt

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