Thanks for your patience! (We'll also get to all your number theory questions when we have a chance.)

For 2.25, there isn't really a formula for there squares, but there is a pattern. The idea is to start by counting the 1x1 squares, then the 2x2 squares, etc.

The 1x1 squares should be fairly easy, this is all the squares, so there are 6*5 = 30 in total. For the 2x2 squares we can do a similar idea. Moving horizontally we can create five 2x2 squares and moving vertically we can create four different 2x2 squares. This is how we get 5*4 = 20 in total. This pattern can continue for the 3x3, 4x4, and 5x5 squares.

For 2.29, I'm confused where the 9 is coming from, as there are only 6 classes in a day. You can calculate the answer as$$\binom{6}{4}\cdot 4!\cdot 8\cdot 7$$where you choose 4 time periods for the math classes, then order the math classes, and then pick the 2 additional classes.