You can play the game on any rectangle using the board below.

This is just one example of a discrete mathematics puzzle, but it can demonstrate a lot of important themes in this course.

Here are some questions to ponder:

What are the rules of this game?  When can you move a tile?

Can you move any individual tile anywhere on the board?

Can you describe a method or process to solve a row? 

Can you describe a method or process to solve a column?  If the grid has n columns, what numbers appear in column 1?

Can you think of a method to reduce the problem to a smaller or simpler subproblem?

How many different configurations are possible on a 9 by 9 board?    

Is every configuration solvable?

Other mathematics problems that are discrete that we will learn how to solve in this course: 

If you roll two di, what is the probability of getting 2 sixes?

You are going on errands and you have to visit 5 different stores. What is the shortest path to visiting all 5 stores?

I have a YouTube channel that has never made any money.  But if I ever start making money on it, I will donate half to charity.  Am I telling the truth?

If every one of you like and subscribe to my channel and then share the channel with 2 people on Day 1, and every of your friends that you share it with do the same on Day 2, how long will it take for the YouTube Channel to be liked and subscribed by every human on earth?

Chances are your answer to the last question did not take into consideration the true structure of most Social Networks. We will learn the channel is not likely to take off because social networks typically have small cliques of friends with just a few social butterflies.

This is also a first course on proof-writing.  Proof are a lot of like traditional jigsaw puzzles to.