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Imagine a chessboard – with your usual 8 by 8 = 64 squares. Say the squares are one inch by one inch each. Now imagine rectangular blocks that are one inch by two inches each. So, any rectangular block can cover 2 adjacent squares on the chessboard.
You have to fill up the chessboard with the rectangular blocks without any rectangle spilling outside the board. They are allowed to overlap on each other though.
What is the minimum number of rectangular blocks required to fill up the whole chessboard? That is 32 of course.
Okay, now imagine that I tore off one of the corner squares on that chessboard. And I went ahead and tore off the corner square that is diagonally on the other end of the board. So, now I have a chessboard with two farthest corner squares missing.
Now, tell me how many minimum rectangular blocks are required to cover the whole board (that has only 62 squares now). You are allowed to overlap but cannot spill outside the board.
Even trickier – what is the minimum number of blocks required if you CANNOT overlap or spill outside either?