MathDB
Stack of Crates

Source: AIME 2008I Problem 9

March 23, 2008
probabilityfunctionalgebrapolynomialnumber theoryrelatively primegeometric series

Problem Statement

Ten identical crates each of dimensions 3 3 ft × \times 4 4 ft × \times 6 6 ft. The first crate is placed flat on the floor. Each of the remaining nine crates is placed, in turn, flat on top of the previous crate, and the orientation of each crate is chosen at random. Let mn \frac{m}{n} be the probability that the stack of crates is exactly 41 41 ft tall, where m m and n n are relatively prime positive integers. Find m m.
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