Question 80
Two players alternate placing $2 \times 1$ tiles, with no overlap, on a $5 \times 5$ chessboard until no player can place a tile.
A number of $1 \times 1$ squares remain empty.
a) Prove that there must be an odd number of empty squares remaining.
b) Of the empty squares remaining, are more coloured black or white?
c) What is the maximum number of remaining squares?
A number of $1 \times 1$ squares remain empty.
a) Prove that there must be an odd number of empty squares remaining.
b) Of the empty squares remaining, are more coloured black or white?
c) What is the maximum number of remaining squares?