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How to play the triangle game

Published online by Cambridge University Press:  03 February 2017

Tony Crilly
Tony Crilly*
Affiliation:
10 Lemsford Road, St Albans AL1 3PB e-mail: [email protected]
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Extract

We are given n sticks of lengths 1, 2, 3, …, n and three are selected at random. Which selections enable a triangle to be formed?

This question can be written in the form of a game: you win if a triangle can be formed from the three numbers interpreted as side lengths, you lose if they do not.

We let ℕn = {1, 2, 3, …, n}, and see there are two variants of the game:

  • • From ℕn draw at random three numbers sequentially. At each stage do not replace the drawn number.

  • • From ℕn a number is drawn at random and is recorded. In three stages three numbers are drawn. Replace the number at each stage.

Type
Articles
Information
The Mathematical Gazette , Volume 101 , Issue 550 , March 2017 , pp. 1 - 10
Copyright
Copyright © Mathematical Association 2017 

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References

1. Subramanian, K. B., Proof without words: , Math. Gaz. 99 (March 2015), pp. 153–154.Google Scholar
2. Bruckstein, Alfred M., A puzzle, a sequence and some consequences, Technion (Haifa, Israel) Computer Science Department Technical Report CIS9817 (1998).Google Scholar
3. Goodman, G. S., The problem of the broken stick reconsidered, Mathematical Intelligencer, 30 (June 2008) pp. 43–49.Google Scholar
4. Schupp, Hans, The broken stick reconsidered again. Mathematical Intelligencer, 32 (March 2010) pp. 8–9.Google Scholar