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Unfair Game

Author: mathforces
Problem has been solved: 31 times

Русский язык | English Language

You are playing a game with Lin and Nil. Each of you will choose a number from 0 to 1 and the one whose number is between the numbers of the other two players wins. Lin told you that he would choose a number between $ \frac{1}{2} $ and $ \frac{2}{3} $. Let $ \frac{m} {n} $ be an irreducible fraction - the number that is more likely to bring you victory in this game. What is $ \|m + n\| $ equal to?

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