If we have $5$ coins, each of them tails up, and flip $3$ coins at time (any $3$ coins), then is it possible to get all coins heads up in $2$ moves?
Flipping coins in 2 moves
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combinatorics
1 Answers
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No. Each flip changes the parity of the number of tails up. After two flips you will have an odd number of tails up, so will not have zero.