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# A Mathematician at Play Puzzle #1

I’ve been collaborating with the English-language newspaper in India called The Hindu for the past few months, producing puzzles for a column called A Mathematician at Play.

It’s a great collaboration. I produce the puzzles, and they make them look beautiful.

I’m going to start sharing these puzzles on the Math for Love blog. Some of these puzzles are classics, others are original. All of them involve some kind of thinking or insight that strikes me as pretty, or surprising, or delightful.

Puzzles will go out Mondays for the next few months.

The first puzzle, below, is a series of grid puzzles. I hope you have fun trying these out! Share them with your kids or students, or work on them with your friends, and let me know what you think in the comments!

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1. Brandon Hendrickson

I love that I’ve taught math for years, and yet am stumped by even puzzle #1! (Right now I’m toying with the notion that you’ve tricked us, and there is no solution…!)

A question for you: why is a “puzzle” (like these) so much more engaging than a typical math “problem”? What makes a puzzle a puzzle?

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Dan

I got stumped by this one too. A colleague of mine actually actually figured it out after I’d given up. But it’s totally doable! (As long as you don’t give up too soon.)

Very interesting question. I think what makes a “puzzle” so engaging is that it resists a simple solution but has an easy way to begin working or thinking about it. So it’s a mix of inviting—you can try connecting dots right away!—and challenging.

2. Alexis Fineman

Ok, so problem #1 leads into a whole other slew of problems to engage with, having to do with the relationship between concave and convex polygons and # of sides. For example, if I take a pentagon, how do I “dent” it to become a five-pointed star, and how many sides does this star have? In thinking about that relationship, I can figure out the “parent” convex polygon of a 16-sided concave polygon, and then “dent in” and “bulge out” accordingly.

I teach young kids, so I’m more likely to start with a simpler shape and riff off of this pattern, building up to the 16 sides! (Because they’ll still have to figure out the proper orientation of the parent concave polygon to get it right! Unless there are multiple right answers – I only found one.)

Thanks for a great puzzle!

2. Colleen Brajcich

Thanks for the entertainment, especially enjoyed #1. Looking forward to tackling the research questions next.