The Triangle Game

Why I like this problem: It gives students the opportunity to play a game before tackling the critical thinking, which allows them to gradually immerse themselves in the problem of the week. The rules of the game are at first a bit convoluted, but get much clearer once you actually start playing.

Observations from class: At first students got hung up on the rules, so I ended up skipping over the instructions and explaining it to them on the board. I may leave them out altogether next time I use this problem. I used the following diagram to summarize the restrictions on vertex labelling:

Students quickly discovered that color-coding triangles according to which player got the point as they went along made scoring at the end much easier. In addition, some groups chose to use a third color for triangles that did not receive any points.

I found that occasionally reminding students that they could only use two letters on the sides saved us a lot of time because many played the game wrong the first few times, which caused them to have less time to dive into the real thinking.

Follow-up questions I asked: 

1. What attribute about being the first player do you think contributed to them winning all the time?
2. How could you change the game to test your hypothesis?

Required skills / content: Figuring out patterns, counting.

Links: PDF / Google Doc

Source: https://nrich.maths.org/