BARD MATH CIRCLE

CAMP 2023 – Questions to Ponder

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by

Kateri Doran
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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!

Japheth Wood

I’m Japheth Wood (he/him), the Bard Math CAMP co-director, and a math professor at Bard College. CAMP (which is an acronym for Creative and Analytical Math Program) is a very special week of the year for our young math community. It's inspiring to see our students return year after year. This is our 11th summer of CAMP! We're back once again on the idyllic Bard College campus in Annandale-on-Hudson, and thankful to the CAMP students, parents, and staff, for making this mathemagical week happen. Notably, we've (finally) had our first CAMP reunion this past June, an event that I know will grow to be an integral part of what we do.

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Frances Stern

My name is Frances Stern (she/her/hers)! I’ve been teaching math at CAMP since the first year, making sure our math theme has a connection to art and computer. It’s fun to show students math that they don’t see in school. I've retired from daily teaching but continue to teach for the New York Math Circle & students who are seeking more math in their lives. My hobbies include learning to draw, paint, & juggle, reading, walking & folk dancing. I’ve written 2 books for teachers and parents called “Adding Math, Subtracting Tension” (for different age-ranges of children). They pay as much attention to how to keep out of a fight (what many parents told me is a problem) as they do to math.

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