Challenge Level

It is possible to dissect any square drawn on a grid into smaller squares, by cutting along grid lines.

For example a 3 by 3 square can be dissected into either 9 smaller squares or 6 squares:

- What is the minimum number of squares a 13 by 13 square can be dissected into?

- What is the smallest size square which can be dissected into squares which are all different sizes?