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# 6x6 game with 9 coins

## Question

Note: I actively sought if this was posted before but found no such posting

Two players are playing a game. There is a 6x6 square board. Player A must place 9 coins on the board. Player B will remove three columns and three rows and collect all coins within those rows or columns that they select. Player B watches Player A make their moves so Player A needs to find the best squares to place their coins so that they can keep as many of them as possible. Where can A play their pieces?

## Recommended Posts

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No matter how 9 coins are placed on 6x6 board, according to pigeonhole principle, there have to be three columns containing 6 or more coins total. After removing such three columns (a greedy approach works here for Player B, he chooses best columns one by one), there will be no more than three coins left on the board. Obviously Player B can choose three rows to collect all remaining coins. There is nothing Player A can do about it.

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