We can solve the 3x3 problem by stacking all of the cups in the middle. On the 5x5 problem, we can solve it similarly by focusing on the corners than the center lines. Can you find a way to apply this to the 7x7 and 9x9 problems? (Hint: on the 9x9 problem, solving the corners will leave leftovers. How can you split the leftovers evenly to move to the center?

Last class we learned about the conditions we need to make all three colors of chameleons into one color, which was having the same amount of two colors of chameleons. Can you figure out the pattern needed to make this condition happen, and in turn, the conditions for being able to turn all fifteen chameleons into a single color?

In class, we started with the classic Königsberg problem of drawing a shape with 1 continuous line. The shape is made up of nods and lines connected to them, you could go over the nods multiple times but only once for the lines. We practiced numerous questions before explaining how to identify whether a shape is crossable or not. Lastly, we provided real-world problems that use the same application as the Königsberg problem. How do you go through all roads of a street in the fastest way? What additional roads do we need to add if the shape is not crossable? The app is linked below: https://www.jrmf.org/activities/konigsberg Here are the real-world problems: