Alternating balls

Alternating balls

Postby harry.petrone » Wed Oct 25, 2017 7:35 am

Anne and Bob have an infinite number of red and green balls and play the following game: Anne plays first putting two balls, one red and one green, next to each other but at any order. At each of his following moves she places to the right of the existing balls either a red one or a green one. At his turn, Bob chooses any two balls of the existing sequence and flips them. The game ends when a total of 1999 balls have been placed and it is Bob’s turn to play. If the resulting sequence of balls is symmetric in respect to its middle ball, Bob wins, otherwise Alice wins. Is there any winning strategy for any of the two players?
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