Discrete Mathematics Warmups

Enumeration can be a tricky process. With every restriction put in place, the counting problem we wish to solve quickly becomes much more complex and can take hours or even days to solve. Enter combinatorics, the branch of mathematics that endows us with the clever techniques used to count endless possibilities.

As you begin to learn the essential techniques that apply to Combinatorics, you'll start by learning how to rearrange and group objects to create symmetrical arrangements that are easier to count. The more combinatorics problems you work on, the more your toolbox of counting techniques will expand!

Here are some tips to get you started:

• Experiment! Don’t be afraid to try many different things, to move objects around and to group or combine them in different ways.
• Symmetry is at the heart of many combinatorics puzzles. Look for a symmetrical way to rearrange or group objects that you're counting.
• Use smaller cases! If you're stuck, try to think of a simpler version of the problem and see if it helps give you an idea of how to solve your trickier one.