The Math Behind SpotIt

[tigeravatar]

Over Thanksgiving weekend I was introduced to a new game: SpotIt. The object of the game is to find a matching symbol between two cards. Each card has 8 symbols and there is only 1 match between any two cards.

The game was a lot of fun, but I got to thinking afterwards, "How can there be only 1 match between any two cards?" So I brought up my trusty friend Excel and started looking for patterns (starting with small patterns like 2 symbols/card, 3 symbols/card, etc). It wasn't long before I had discerned what I needed to translate the pattern into math.

Attached is the result. You can set the # of symbols/card and see what picture # is in symbol spot A, symbol spot B, etc for any given card. And yes, there is only 1 match between any two cards. To keep the file size low I limited the # of symbols/card to a maximum of 10, though it could have gone much higher since its all formulas.

Enjoy!

[darkyam]

It's interesting, but I have two observations:
1. B3 could simply be =B2, couldn't it?
2. There is the distinct possibility you have too much free time on your hands. (Join the club. I've developed spreadsheets, or at least started to, that analyze the odds of various hands for different poker games).

[davegugg]

darkyam, if you're playing poker for $, I'd call that financial analysis.

We have a similar game called Set:
http://grandkidsgiftguide.com/age/5-...-for-all-ages/

It's an interesting game, you put down twelve cards face up, and each card has one, two, or three shapes, there are three different shapes, three different shading patterns, and three different colors. You have to find a set of three cards that each of the four categories (number of shapes, shape type, shading, and color) are the same or different.

For example, you could find a set of three cards that each have a different shape, all have the same color, each have a different number of shapes and all have the same shading. It's a very challenging game in that you have to think about matching four different things, but also think about the possibility of all things being different.

[anaskye]

Hi,
I am actually doing a high school math investigation on the mathematics of the game, Spot It! I was looking at your table (super helpful, must have taken some time), but because I am not to great with excel, I don't understand the equations you used to make the data. I was hoping that you could explain them for me?
So far for my investigation, I've found an equation that tells me how many unique images I will need if I have x images per card (P^2 - P + 1). I'm now trying to understand the relationship between the number of cards and the number of images.
Also, interestingly enough, when I counted the images on the cards, I found that the frequencies of each unique image varied from 6-10 times, and I'm wondering if you would have an explanation for how that is possible?

Thanks a lot!

[bsacheri]

Nice work! Thanks for sharing the Excel file. Sorry for coming to the party so late. I just discovered the Spot It game while on a family vacation and it kept me up at night trying to figure out the algorithm. I'd like to find a card generator algorithm that I could implement in VBA with some nested loops. Has anyone has seen code for this in any programming language?