CSMC 2024 Part A - Question 6, CEMC UWaterloo

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Difficulty: 8

This problem is tagged with csmc, csmc24, highschool.

(Canadian Senior Mathematics Contest 2024, Part A, Question 6, CEMC - UWaterloo)

A Gleeson list is an increasing list of distinct positive integers with a sum of $2024$. For example, $70, 700, 1254$ is a Gleeson list of length $3$ and $2, 4, 6, 10, 15, 987, 1000$ is a Gleeson list of length $7$.

Let $M$ be the maximum possible length of a Gleeson list. How many Gleeson lists of length $M$ are there?

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