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## Question

The World Champion Chess Match of 1921 was held at a resort in the US Virgin Islands and pitted against each other those two masters, Yeti and Zugzwang.

The winner won seven games and lost six. They took turns playing white, with Yeti having white in the final game which decided the match. The black pieces won five times.

Who won the match?

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ZUGZWANG

Hint: it only works if black won the first game.

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No matter what the order of winning, for black to win 5 games either at the end of 12th game black has won 5 times and white wins the 13th game or black has won 4 times and black wins the 13th game.

Also, by the end of 12th game, both players have won 6 games each. For this condition to be true, an even number of games should have been won by both black and white pieces. This implies that the 13th game is won by black piece

Hence, Zugzwang is the winner

@ CrayolaSunset: This condition would be true even if white wins first 8 games and black wins the last 4 games. Black does not necessarily have to win the first game

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Let:

wyw = number of games Won by Yeti playing White

lyw = number of games Lost by Yeti playing White

wyb = number of games Won by Yeti playing Black

lyb = number of games Lost by Yeti playing Black

We have:

lyw + wyb = 5

and

wyw + lyw = 7

Adding above equations gives:

wyw + wyb + 2*lyw = 12

or

wyw + wyb = 2*(6-lyw)

This shows that Yeti won even number of games, so the winner is his opponent.

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