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Math Prize 2022 Problem 10

Source:

October 12, 2022

Problem Statement

An algal cell population is found to have aka_k cells on day kk. Each day, the number of cells at least doubles. If a0≥1a_0 \ge 1 and a3≤60a_3 \le 60, how many quadruples of integers (a0,a1,a2,a3)(a_0, a_1, a_2, a_3) could represent the algal cell population size on the first 44 days?
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