Discrete Mathematics
# Discrete Mathematics Warmups

The figure above consists of 19 unit squares. How many rectangles are there in the figure?

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**Note:** Squares are also considered as rectangles.

$\large \displaystyle S = \{{1,2,3,\ldots, 19,20}\}$

How many subsets of three numbers each can be formed from the set above so that no two consecutive numbers are in the set?

In the $4 \times 4$ grid, how many squares have all 4 vertices on these dots?

**Bonus**: Generalize this for $n \times n$ grid.