Wednesday, January 20, 2016

Spot It: a matching game leading to interesting mathematical questions

Spot It! (amazon affiliate link here) is a matching game. On each card, there are 8 symbols (with varying size and orientation) out of a possible 57 (I think? I haven't counted and the internet does not have a consensus), and each pair of cards has exactly 1 symbol in common.  You're goal is to find that common symbol as quickly as possible.  The interesting thing about this game is understanding how they were able to design the game so that each pair has exactly one symbol in common.

There are a lot of blog posts explaining the mathematics behind Spot It! and how it could be used as a math circle topic, for example this, this, and this. There are also a few StackExchange questions, such as this and this. I've asked students: If you have S total symbols with C on each card, what's the largest deck of cards you can make so that each pair has exactly 1 symbol in common? With smaller values of S and C, this problem is more manageable, and students can even use their solutions to design their own (easier) versions of the game!

Also, it's interesting to note that with C = 8 and S = 57, you can make 57 cards, while the Spot It! game only has 55.  Can you figure out which two cards are missing?

There are a bunch of different versions of Spot It! aimed at various demographics, as you can see below (images lead to Amazon affiliate links).

 

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