Using Wolfram-Cloud/Mathematica to look at the Monkey and the Coconuts Problem

Published: 18 July 2024
on channel: Thomas Blum

In this video we use Mathematica/Wolfram-Cloud to find a solution to a simplified version of the Monkey and the Coconuts problem (fewer people/fewer divisions). We adapt the nomenclature used in the Numberphile video on the problem. We start with four equations which through a series of Solve, Substitute, and Simplify reduces to a single linear Diophantine equation. ("Diophantine" means we only want integer solutions.) First we follow a technique for solving the equation by using Euclid's algorithm for finding the GCD (greatest common divisor) of the two coefficients. Reversing the steps of the Euclid algorithm leads to a particular solution. (Linear Diophantine equations have either no solutions or infinitely many.) The solution to the equation that we find first does not solve the problem because the numbers are negative. After finding the solution "by hand" we show how Mathematica's FindInstance method could do the same. We show how to get multiple instance out of Mathematica and in addition how to place some conditions on the instances generated.

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