1974 USAMO Problems/Problem 4

Problem

A father, mother and son hold a family tournament, playing a two person board game with no ties. The tournament rules are:

(i) The weakest player chooses the first two contestants.

(ii) The winner of any game plays the next game against the person left out.

(iii) The first person to win two games wins the tournament.

The father is the weakest player, the son the strongest, and it is assumed that any player's probability of winning an individual game from another player does not change during the tournament. Prove that the father's optimal strategy for winning the tournament is to play the first game with his wife.

Solution

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See also

1974 USAMO (Problems • Resources)
Preceded by Problem 3	Followed by Last Question
1 • 2 • 3 • 4 • 5
All USAMO Problems and Solutions