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Counting game where the first to reach 50 wins

Question

Two players take turns calling out whole numbers. The opening call must be from 11 to 1010, and every later call must be larger than the previous one by between 11 and 1010. The player who calls 5050 wins. Would you choose to go first, and how would you play?

Short answer

Go first and say 6. Winning positions are 50,39,28,17,650,39,28,17,6 (stepping down by 1111). After the opponent adds any k∈{1,…,10}k\in\{1,\dots,10\}, you add 11−k11-k to land on the next of these, so you eventually call 5050.

Adapted from Crack, Heard on the Street, Q1.16, p.12; question and answer rewritten by SelfMadeQuant.com.

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