Winning a coin-placing game on a round table
Question
Two players take turns placing identical coins flat on a round table so that no coin overlaps another or the edge. The first player who cannot place a coin loses. Would you go first or second, and how would you win?
Short answer
Go first and put your first coin exactly at the centre. After that, answer every coin your opponent places with one at the point reflected through the centre. By symmetry that spot is always free, so you always have a move and the opponent runs out first.
Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q8.24, p.278; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- Counting and Combinatorics
- Sample Spaces, Events, and the Probability Axioms
- Conditional Probability, Total Probability, and Bayes' Rule
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