This morning, the CAMPers gathered in the auditorium for a collection of **math puzzles** and the new **problem of the day**: *How many Tower of Hanoi board states are there?* The CAMPers had fun trying to work it out, rewriting the problem on the board – in the Greek alphabet. Right before breaking up into their usual Math groups, Japheth led them all in the **International** **Math Salute**.

Following up on the argument they made yesterday, the **COS **group worked together to prove that there couldn’t be an 8th symbol in a 3-*Spot-It! *deck. They then drew up a graph that brings to mind the** “Deathly Hallows” **from Harry Potter, showing the 7 cards as nodes and the symbol in common between two cards as edges. Next, they broke up into smaller groups to work on designing a **4- Spot-It! **deck –

*What’s the greatest number of cards we can get with 4 symbols on each card?*Some of the CAMPers observed that for the 2- , 3- , and 4-Spot-It! cases, the number of symbols was the same as the number of cards. To look for more patterns, they took the difference between the number of cards in n-

*Spot-It!*and (n-1)-

*Spot-It!*, then took the difference between the differences – getting 2 every time. Leaving this conjecture as a

**cliffhanger**for a later date, the CAMPers embarked on a final investigation – to make one pile for each symbol using existing Spot It! decks.

Meanwhile, the **SINE **group used **tree diagrams **to explore the main concepts of combinatorics. Taking the letters S, T, R, and E, they mapped out all the possibilities of what letter could come after each letter in a word, branches branching off into other branches. They followed different branches to make **different words **like SET, REST, STREET, TEETERS, and – appropriately – TREES. The CAMPers continued their discussion by breaking into two smaller groups to work on these examples: choosing **ice cream **flavors for a multi-scoop cone, and choosing **paths **to take when going from Point A to Point B. *How many combinations are there? How many choices do we have?*

In Computer Science class, the **SEC **group learned about the **random() **function, **void setup() **and **void() **, **variable assignment** – how to turn x into (x+1) in order to move a shape somewhere else on the canvas. Their challenge for today: *Rather than just moving your drawing around, can you make your drawing move in an animation?*

After class, the students joined their elective groups: more **magic tricks**, more **paper puzzles** (AKA the Harry Potter debate club), as well as **origami**.

During lunch, the rain started pouring outside Kline, and the CAMPers had to break out their umbrellas to make it to their next classes – Art and Computer Science.

**CSC **went to Computer Science, where they continued to learn about truth tables. Then they broke into small groups, using logical operators to write out a combination of A and B that was equivalent to the **XOR **(exclusive or) operator. Then they took out **Little Bits **(batteries, cables, and LEDs) to make an XOR statement in real life.

In the Art room, music was blasting while the **SEC **group continued working on their ** Spot It! cards**, then dove into a variety of artistic and mathematical endeavors –

**Fibonacci**challenges, 4×4

**tic-tac-toe**, pink

**paper airplanes**,

**and**

**optical illusions**.

Afterwards, the two groups converged in the auditorium – finally dry and ready for some **math games**.

New ideas, new methods, new questions and answers filled Day 3 with color, excitement, and fun! The CAMPers made so many new discoveries today, leading to even more unanswered questions – perfect to tackle with zeal on Day 4.