Pick-up Sticks and the Fibonacci Factorial

2025/04/28 by Aidan Sudbury, Sudbury, Aidan, Arthur Sun +5 · 1 voice · 1 citation
#Quasicrystal Structures and Properties #Advanced Mathematical Theories and Applications #Advanced Combinatorial Mathematics

paper · pdf · doi:10.1080/00150517.2026.2663981

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.

Cited by

• Computer-aided solution to the k-bonacci pick-up sticks problem

Discussions

• not a long paper and the results for a quadrilateral are also very cool!! plus, i appreciate the clear statement of an open question at the end for the general case of a k-gon: arxiv.org/abs/2504.1991 [bsky, 4 points, 1 comments]

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