# Check out the past discussion problems below. See the question board for the discussion of these problems.

The meeting syllabus for each meeting is also attached below.

Also, make sure to check out our past meetings on our Youtube Channel.

Our activities are based on public resources provided by JRMF.org.

Week 1: Tower of Hanoi

In class, we talked about how the Tower of Hanoi is based on recursive relations. We also found the recursive relation for the Tower of Hanoi with three pegs. We then explored the Tower of Hanoi with two rings of each color, four pegs, and five pegs. We ended by exploring the Tower of Hanoi with colored pegs. In particular, we explored the case where A and B are pegs of one color, while C is another color. You can only move rings between pegs of different colors. Can you find the number of moves with four rings and five rings for the Tower of Hanoi with colored pegs?

Week 2: River Crossings

In class, we started with the classic river crossing problem of a wolf, a goat, and a cabbage. We then moved on to a variation in which we need to carry humans and zombies instead. Remember, if there are more zombies than humans on any side of the river, all of the humans on that side will die. How would you solve the case with 4 humans and 4 zombies, along with a boat with two slots? Is it impossible? If so, what is your reasoning?

Week 3: Chameleons

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?

Week 4: Königsberg

In class, we started with the classic Königsberg problem of drawing a shape with one continuous line. The shape is made up of nodes and lines connected to them; you can go over the nodes 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. What is the most efficient way to go through all of the lines? What additional lines do you need to add if the shape is not crossable?

Week 5: Cup Stacking

This week, we talked about the Cup Stacking problem. We can solve the 3x3 problem by stacking all of the cups in the middle. For the 5x5 problem, we can solve it similarly by focusing on the corners first. Can you find a way to apply these methods to the 7x7 and 9x9 problems? (Hint: For the 9x9 problem, solving the corners will leave leftovers. How can you split the leftovers evenly to move to the center?

Week 6: Jumping Julia

This class, we explored the Jumping Julia puzzle. Look at the puzzle attached. Is this puzzle possible? Using the working backwards strategy we used in class, what is the shortest path to the goal? Which squares are impossible to reach? Is there a fast way to find all of them?

Week 8: Domino Dissection

In addition to some interesting AMC 8 problems, we solved some Domino Dissection puzzles. Puzzle 190 is a very hard 8x7 puzzle, see if you can solve it!

Week 9: Colored Loops

This week, we learned about the Pythagorean Theorem and applied it to a variety of interesting problems. We also tried our hands at the Colored Loops puzzle. The puzzle in the picture has three solutions. Can you try to find all of the solutions? (hint: try starting on one color and finding a complete loop.)

Here is the Jamboard where you can access the problems we solved and the class notes: https://jamboard.google.com/d/1prdftFsEDVCOCEWnDnNdJzxaBMut4DMYNR3aczH3cbk/viewer?f=4

Make sure to let us know if you have any questions!

Here is the Jamboard where you can access the problems we solved and the class notes: https://jamboard.google.com/d/1prdftFsEDVCOCEWnDnNdJzxaBMut4DMYNR3aczH3cbk/viewer?f=4

Make sure to let us know if you have any questions!