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Problem 1. I am placing pieces on a 3 × 3 square board such that pieces are placed on non-adjacent squares (squares that are not directly above, below, left, or right of another square). How many ways are there for me to place 4 pieces on his 3 × 3 board?

 

Problem 2. How many ways are there to place 3 pieces on this 3 × 3 board?

 

Problem 3. I decide to change to a 5 × 5 board, keeping the same piece placement rules as before. How many ways are there for me to place 11 pieces on this 5 × 5 board?

 Apr 11, 2024

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