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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.19911 |
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| _version_ | 1866908783980052480 |
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| author | Sudbury, Aidan Sun, Arthur Treeby, David Wang, Edward |
| author_facet | Sudbury, Aidan Sun, Arthur Treeby, David Wang, Edward |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19911 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pick-up Sticks and the Fibonacci Factorial Sudbury, Aidan Sun, Arthur Treeby, David Wang, Edward Probability 60D05 (Primary) 05D99 (Secondary) 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. |
| title | Pick-up Sticks and the Fibonacci Factorial |
| topic | Probability 60D05 (Primary) 05D99 (Secondary) |
| url | https://arxiv.org/abs/2504.19911 |