Pick-up Sticks and the Fibonacci Factorial
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.
Authors
- David Treeby (ORCID: https://orcid.org/0000-0002-2397-3177)
- Edward Wang
- Aidan Sudbury
Institutions
- The University of Melbourne (AU)
- University of Cambridge (GB)
- Monash University (AU)
Publication Details
- Journal
- The Fibonacci Quarterly
- Published
- 2026-07-16
- DOI
- https://doi.org/10.1080/00150517.2026.2663981
- Primary Topic
- Quasicrystal Structures and Properties
- Type
- article
- Field-Weighted Citation Impact
- 0.00