But our shape after removing a corner has: Color 0: 9 Color 1: 8 Color 2: 7

Why? Color the 5×5 board in a clever way — not like a chessboard (alternating black-white), but in three colors repeating diagonally:

Try to visualize: the 5×5 board has 25 squares. Remove one corner → 24 squares. Each tromino covers 3 squares. 24 ÷ 3 = 8 trominoes needed. So numerically it’s possible.

Now remove the top-left corner (1,1). Its color is (1+1) mod 3 = 2 mod 3 = Color 2? Wait — careful: (1+1)=2, so 2 mod 3 = 2 — yes, Color 2. So after removal: Color 0: 9 Color 1: 8 Color 2: 7 (since we removed one from Color 2) Each 1×3 tromino, no matter how you place it (horizontal or vertical), covers exactly one square of each color .