2. Pentagram

2. Pentagram

Highlight 1: 25 Solutions
21 students, 3 math teachers, and 1 assistant principal submitted successful solutions.

Highlight 2: I was one of them.
I first saw this problem in grad school, and after trying it for a while, I got rather frustrated. My classmates were trying it too, and I wasn’t entirely convinced that the problem had a solution. After trying the problem a couple of different times and taking up several sheets of paper, I gave up and forgot the problem. I remembered the problem when we were starting Play With Your Math, and I solved it in about 20 minutes. It was incredibly satisfying to solve it 18 months after failing.

Highlight 3: Amazing Participation
This problem got an even better response than the first one. This problem is magically engaging; all sorts of people are willing to try it and it is great, twisted fun watching people struggle with it. In addition to my students and colleagues, we’ve gotten friends and friends-of-friends to try this problem, and they all get hooked. Some people get hooked and then get angry at us for showing them the problem.Frustrating Triangles

This engagement makes me wonder: Why do so many people like this problem? Can I replicate that engagement elsewhere?

Dan Meyer was asking these questions in April when he brainstormed a list of criteria for Tiny Math Games. His criteria is below in bold, with my reflection unbolded afterward.

  • The point of the game should be concise and intuitive. Check.
  • They require few materials. Just paper and pencil. Check.
  • They’re social, or at least they’re better when people play together. It is not as obvious that this problem would be more fun with other people, but it definitely was. We posted this problem on a Friday, and I had 5-6 students hanging out after-school until around 5:30 PM working on the problem. Two of the students solved it, and their celebration and subsequent trash-talk was priceless.
  • They offer quick, useful feedback. Simply count the triangles, but be wary of the dreaded 4-sided triangle.
  • They benefit from repetition. Check … to some degree. After a while, it can feel like you’ve tried everything.
  • The math should only be incidental to the larger, more fun purpose of the game. meh?


Highlight #4: Persistence
I find this problem to be somewhat paradoxical, in that this problem is:

  1. endlessly frustrating
  2. totally doable

As a result, people never truly give up. I have had people tell me months later that they are still trying. One of my colleagues is one of them (you can do it Ms. Harding!).

I should mention that the “totally doable” part of the paradox is debatable. I was taken aback when I finally solved this problem because it didn’t feel like I had really made a discovery nor had I shifted my thinking in any meaningful way. But one of my colleagues disagrees; she is adamant that the problem requires thinking “outside the box.” So I’ll finish with a follow-up question for anyone who solved the problem: Do you think the solution requires thinking outside the box? How so?


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