Pick-up Sticks and the Fibonacci Factorial
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.
Fields of Study & Subjects
Quasicrystal Structures and Properties
Advanced Mathematical Theories and Applications
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- The Fibonacci Quarterly
- Publisher
- Informa UK Limited
- Pages
- 1–7
- Publication date
- 16 July 2026
- Language
- EN