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 Score Squares Crossed Two Squares Settlement (Posted on 2023-04-27)
Angela and Brad play a game where they commence with a row of 20 squares. The two players remove a square each turn. The game concludes when there are precisely two squares left.

Angela wins if the two remaining squares are next to each other, and Brad wins if they are NOT next to each other.

1. If Angela goes first, who has a winning strategy?
2. Who has a winning strategy if Brad goes first?

 See The Solution Submitted by K Sengupta Rating: 5.0000 (1 votes)

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Whoever goes second can force a win with a parity strategy.

If Angela goes second she then creates 10 dominoes, each consisting of two adjacent squares.  Whatever square Brad removes then Angela removes the other half of that domino.

If Brad goes second he then creates 10 disjoint pairs, one such way is to choose squares that are 10 apart (1,11; 2,12; etc).  Whatever square Angela removes then Brad removes the other half of that disjoint pair.

 Posted by Brian Smith on 2023-04-27 13:39:24

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