Problems and Solutions for Kingston Math Circle 3/10/12

Solutions

1. In the correctly worked out addition problem below, different letters represent different digits. What digit does A represent?

A4+4A=BCB

First, look at how big the sum can be, and deduce that B must be 1, since the sum of two 2-digit numbers can’t be more than 198 (which is 99+99). Second, consider the units digits. Since A + 4 ends with B = 1, A must be 7.

Check: 47 + 74 = 121.

2. What is the first year in the 21st century (2001 through 2100) that is divisible by 11?

Divide: 2000 ÷ 11 = 181 with remainder 9. Add 2 years to get the next multiple of 11, which is 2002.

Alternate solution: Find a nearby multiple of 11, for example 2200, and count back by 99. Counting backwards, 2200, 2200 – 99 and 2200 – 99 – 99 are all multiples of 11. The last one is 2200 – 99 – 99 = 2002.

3. 9 apes weigh as much as 4 bears. 8 bears weigh as much as 15 cougars. 10 cougars weigh as much as 27 deer. How many deer weigh the same as 4 apes?

Let’s scale up! If 9 apes weigh as much as 4 bears, then doubling, 18 apes weigh as much as 8 bears, and so 18 apes weigh as much as 15 cougars. Let’s double that to find that 36 apes weigh as much as 30 cougars, and so 36 apes weigh as much as 3 times 27, or 81 deer. Now scale down by a factor of 9 to find that 4 apes weigh as much as 9 deer.

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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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