A Pair of Pretty Perimeter Puzzles

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Here are two puzzles from Alex Bellos’s Monday puzzles.

“Ring it.  Each region has a perimeter given by its enclosed number. What is the length just along the edge of the entire figure?

Round the block.  Assuming all corners are right angles, what is the perimeter?

Today’s puzzles all come from … the Hyde Park Math Zine!  This delightful publication is written in pen on a single folded sheet of paper, has a print run of 30 copies, and is distributed in the neighbourhood of Hyde Park in Austin, Texas.

Fanzine culture is well established in sports and music. Math educator Kevin Gately thought the format would work for puzzles too. “It dawned on me that there might be people in my community who find the novelty of a hyper-local math zine to be amusing and/or curious,” he said. And it seems there are.

Each issue of HPMZ presents three problems, with easily understandable answers, and let’s not forget the cover artwork!  Gately’s puzzles are mostly taken from other sources, and tweaked. Here are [two] that took my fancy.”

Answer 1 ________  Answer 2

See A Pair of Pretty Perimeter Puzzles for solutions.

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Language Students Problem

This is a problem from the 2001 American Invitational Mathematics Exam (AIME).

“Each of the 2000 students at a high school studies either Spanish or French, and some study both. The number who study Spanish is between 80 percent and 85 percent of the school population, and the number who study French is between 30 percent and 40 percent. Let m be the smallest number of students who could study both languages, and let M be the largest number of students who could study both languages. Find M – m.”

Answer.

See Language Students Problem for a solution.

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Smart Money

This is a simple puzzle from Futility Closet.

“Mr. Smith goes to Atlantic City to gamble for a weekend. To guard against bad luck, he sets a policy at the start: In every game he plays, he’ll bet exactly half the money he has at the time, and he’ll make all his bets at even odds, so he’ll have an equal chance of winning and of losing this amount. In the end he wins the same number of games that he loses. Does he break even?”

Answer.

See Smart Money for solutions.

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Maximizing Love

This is a Valentine’s Day puzzle from BL’s (Barry Leung) Math Games.

“Happy Valentine’s Day everyone, I hope you are having a euphoric moment, but if not, you can try this algebra puzzle about maximizing the expression LUV + LU + UV + LV given L + U + V = 12, where L, U, V are non-negative integers.”

Answer.

See Maximizing Love for a solution.

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