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arXiv · 2504.19911

Pick-up Sticks and the Fibonacci Factorial

Aidan Sudbury·Arthur Sun·David Treeby·Edward Wang
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Abstract

We present a variation of the broken stick problem in which $n$ stick lengths are sampled uniformly at random. We prove that the probability that no three sticks can form a triangle is the reciprocal of the product of the first $n$ Fibonacci numbers. Extensions to quadrilaterals and general $k$-gons are also discussed.

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Aidan Sudbury, Arthur Sun, David Treeby, Edward Wang. 2025-04-28. Pick-up Sticks and the Fibonacci Factorial. https://doi.org/10.1080/00150517.2026.2663981

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