+35 Problem 1.
Andy is 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 Andy to place 4 pieces on his 3 × 3 board?
Problem 2.
How many ways are there for Andy to place 3 pieces on his 3 × 3 board?
Problem 3.
Andy decides to change to a 5 × 5 board, keeping the same piece placement rules as before. How many ways are there for Andy to place 11 pieces on this 5 × 5 board?
