CAMP 2023 Day 4, Bard Math Circle

The sun is shining over RKC – setting the stage for lots of summer fun at CAMP! This morning, CAMPers got together in the auditorium to solve more math puzzles – the Towers of Hanoi, Rush Hour, and shape-matching challenges. The problem of the day: Completely fill a 3×3 grid with X’s and O’s. How many of these configurations have three X’s or O’s in a row?

In math class today, SINE broke into four smaller groups to work on four different but similar problems: finding the number of possible handshakes between 5 people, then taking 3-way handshakes into account; finding the number of 2-scoop ice cream bowls you can make with 5 different flavors, then doing the same for 3-scoop bowls; figuring out the shortest path out of all the different ways to move by 2 blocks north and 3 blocks east, then generalizing to b blocks in any direction; and finally, determining the number of ways for 3 kids to share 3 cookies – or more than 3 cookies.

“The ice cream bowls are shaking hands!”

Meanwhile, the COS group started analyzing 8-Spot-It! – the classic version. They started with existing Spot It! decks, putting cards in piles based on the symbols they found on a randomly-drawn card C. Next, they chose one pile (A) to put back in the box, laying out the remaining cards in columns and rows that matched the top card of the pile, and discussed the observations and questions they had.

After that, they switched gears to solving the same ice cream bowl problem that the SINE group was working on – How many unique 3-scoop ice cream bowls can we get with 5 different flavors of ice cream? The first scoop gave them 5 choices, the second 4 choices, and the third 3 choices, which multiplied together to give 60 choices. However, the CAMPers found that in counting combinations they had actually over-counted by a factor of 6, since there were 6 ways to get the same ice cream bowl with each combination of 3 flavors.

After math class, CAMPers in the CSC group walked over to the art room, where they worked on origami, highly ambitious 7-symbol Spot It! decks, and beaded Fibonacci necklaces.

In Computer Science, the SEC group learned about using booleans (true or false) and comparators (>, <, greater than or equal to, less than or equal to) to write conditionals: “if” statements with conditions on variables x and y. They also learned about “if else” statements, which tell the computer what to do if the variable does not satisfy the condition. Breaking off into their usual groups, the CAMPers used these concepts to make their drawings bounce in different directions – up and down, side to side, and diagonally.

The CAMPers had lots of fun outdoor electives to choose from – a hike to the Sawkill waterfall, more magic tricks with Frances, variations on tic-tac-toe with sidewalk chalk outside the building, and, drumroll please: Break-Your-Brain Rhythm Games!

After lunch, the CSC group learned about bits and bytes, which are used to store data in a computer – a bit takes a value of 1 or 0, while a byte is an 8-bit (binary) number. The instructors explained why kilobytes, megabytes, gigabytes, and terabytes aren’t “clean” numbers ending in a bunch of 0’s: All of them are powers of 2.

The CAMPers were treated to a special investigation – opening up an actual computer and taking it apart! This allowed them to search for the basic parts of the computer and answer questions: Where does it hold its power? Where does the memory live?

The CAMPers were able to find….

The Central Processing Unit (CPU) …
The transistors, little switches that flip between 0 and 1 …
The motherboard, the most important circuit board, which basically holds everything together …
The RAM (Random Access Memory) chips, which store the computer’s volatile memory …
The capacitors, which are like little battery tanks that hold small amounts of energy …
The hard drive, which is made up of spinning magnetic disks that encode 0’s and 1’s …
… and the fans (to keep the CPU from overheating).