*Calling all CAMPers, parents, and curious readers – CAMP math instructors Japheth and Frances have a few fun problems for you to think about for the rest of the summer: *

**Cookies and Kids:** Kids A, B, C share a certain number of cookies (some might get zero). Find a systematic way to represent each way to share. Then arrange all the ways to share in a triangle. **Hint:** This problem has a hidden relationship involving the numbers 2 and 5. Can you find it? **Bonus Question:** Can you find a pattern for different numbers of kids, and/or different numbers of cookies?

**Grid Paths:** Point B is two blocks East and some number of blocks South from point A. How many paths are there from point A to point B that are of the shortest possible length? Find a systematic way to represent each possible path. Then arrange all the paths in a triangle. **Bonus Question:** We also looked at shortest walking paths in a square grid with walks North and East. Is there a pattern to the number of possible shortest walking paths when walking 2 blocks North and *b* blocks East? What about when walking 3 blocks North and *b* blocks East?

** Spot It! :** Seven was the largest number of symbols and cards we found if there are 3 symbols per card. Is 7 the largest possible number of cards that could be made with 3 symbols per card? Prove (or disprove) this statement.

**Hint:**

*How can we know when something is impossible or possible but not yet figured out?*

* Spot It!* –

**Bonus Question 1:**Is the largest number of cards that can be made always equal to the number of symbols?

**Bonus Question 2:**Can decks of Spot It! Cards be made for any number of symbols per card or are there numbers for which cards cannot be created?

**Bonus Question 3:**The decks sold have missing cards. Are there efficient ways to find which cards were omitted?

**Bonus Question 4:**How many cards and symbols are there in a deck of 7 Spot It? Then design a deck of 7-Spot It, which some people claim does not exist.

**Fractions:** 2/3 x 5/7 can be thought of as “2/3 of 5/7”. If we use a circle to represent the number one, what can be drawn in the circle to demonstrate the meaning of and answer to 2 ⁄ 3 x 5/7 ?

**Pascal’s Triangle: ** Pascal’s Triangle is full of interesting relationships. Keep looking at it and write the ones you discover. What other questions do you have about these topics?

*Have fun, and keep exploring! *