1. Compute the number of ways to divide a $20 \times 24$ rectangle into $4 \times 5$ rectangles. (Rotations and reflections are considered distinct.)
Answer: 6
Solution: For convenience, say the edge of length 20 is vertical.
Consider some vertical line inside the rectangle. It must pass through rectangles of some heights adding to 20. In particular, these heights correspond to ways to add up to 20 with fours and fives, which is either $4+4+4+4+4$ or $5+5+5+5$. These options correspond to columns of rectangles with width 5 or 4 , respectively. In particular, we need to span the width of the original $20 \times 24$ rectangle using these columns, meaning that we can just count the number of ways to add to 24 with fours and fives.

There are two ways to do this: either $4+4+4+4+4+4$ or $4+5+5+5+5$. Considering the orders in which the second sum can be written, we get an answer of $1+5=6$.