How to play the triangle game. Issue 550 (3rd February 2017)

• Record Type: Journal Article
• Authors: Crilly, Tony
• Is Part Of: Mathematical gazette. Volume 101:Issue 550(2017)
• Page Start: 1
• Page End: 10
• Publication Date: 2017-02-03
• Subjects: Mathematics -- Periodicals; Mathématique; Mathematik; Mathematics; Periodicals; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); Zeitschrift; Online-Publikation; 510
• DOI: 10.1017/mag.2017.1
• Languages: English
• ISSNs: 0025-5572

Abstract

Abstract : 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 ℕ n = {1, 2, 3, …, n }, and see there are two variants of the game: From ℕ n draw at random three numbers sequentially. At each stage do not replace the drawn number. From ℕ n a number is drawn at random and is recorded. In three stages three numbers are drawn. Replace the number at each stage.