You are given an $8 \times 8$ chessboard and a large supply of $\text{T}$-shaped tiles and square-shaped tiles of the kind shown below.
Note that the squares in these two shaped tiles are of the same size as the black/white squares on the chessboard.
We wish to cover the squares of the chess board using these tiles. Each square of the chessboard must be occupied by exactly one square from a tile; we are not allowed to break the tiles.
- Is it possible to cover the chessboard with $16 \; \text{T}$ shaped tiles? Why?
- Is it possible to cover the chessboard with $15 \; \text{T}$ shaped tiles and one square tile? Why?
