Challenge #1: How many different squares are on an 8 x 8 checkerboard?

Challenge #2: Find a way to place all 12 pentominoes on an 8 x 8 checkerboard.

Challenge #3: Find a way to place 6 pentominoes on an 8 x 8 checkerboard so that none of the remaining 6 pentominoes will fit on the board without an overlap.

Click on a color and then click on squares to change their colors.