Two people are playing a game with a row of 10 coins, all showing heads. On a turn, a player can flip either one coin or two adjacent coins, provided the rightmost coin in their selection changes from tails to heads (or stays heads? No: provided the rightmost coin flipped goes from heads to tails). The player who makes the last move wins. If both players play perfectly, who wins?
The first player
This is a classic combinatorial game analyzed via symmetry or Nim-values (Sprague-Grundy theorem). By mirroring the second player's moves on the opposite side of the 10-coin row, the first player can always guarantee a winning strategy.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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