The Math Behind Spot it!

How did the creators of the game Spot It design the cards so that any two cards will always share one image in common? Find out in this video, then check out more fano plane math (and a printable "expansion set" of the missing two cards) at:

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[ScienceMom]

A quick announcement about comments: When I first started visiting schools I would get a lot of comments saying things like: "Remember me? I'm John Doe from Mitchell Elementary! My teacher is Ms. Smith!" For a while I replied to these comments and then deleted them to protect the student's privacy--but then I came up with a better idea: Now when I do school visits I have the class name some part of the demonstration - then I let them know that if they want to leave a comment, they can reference the name that they chose and is unique to their class. Naming a ball or balloon is a fun exercise and also a good opportunity to talk about internet safety. So if you see things like #Bob or #teamShocky or "Michael the balloon!" and are wondering what in the world is going on? That is what's going on. Also, since many of my viewers and fans are kids, any comments with vulgar language or curse words will be deleted.

[alexdavis]

Has anyone else ever felt so triumphant when they think that they have found two cards that don't have a match... and then found a match between the cards and felt incredibly stupid?

[zachalsup]

There was massive time put into this great video

[kiiimberlyy]

Also had six snowmen! Yes, it is 12:22am and my boyfriend and I decided to watch this video.

[AnExPor]

Kind of crazy. I found this video by watching Mathologer videos, looking at his merch, searching a topic of one of the shirts (Fano plane), and found this video. The crazy thing is, I have wondered for more than a few years how this game was made. Thank you for the explanation and Mathologer for leading me here. I should probably also go check my deck for snowmen.

[RestingKitten]

After extensive research, we also found only 6 snowmen. We spent maybe 1/3 of the time playing the game and 2/3 trying to work out the mathematics behind it.

[itempool]

Someone should sell the missing two cards as an "expansion".

[isaacsumner]

You have answered a question that has dogged me. Thank you.

[vancerivervillage]

Thank you so much for this explanation, I'm no good at math and I surely didn't understand the terminology used but the diagrams were very easy to follow, at first the blue gradient was difficult to see, but with the PDF I was able to assign the shade of blue with the colors of the rainbow and construct my own diagrams. I was able to make my own spot it game, though it took a long time to complete, but it works perfectly, Thank you again

[wjhb]

I suspect that all games have identical cards. Probably the reason they print 55 has to do with fitting efficiently on a print sheet. Maybe 11 wide & 5 tall, etc.

[yimeng]

If I hadn't been curious and counted the number of icons, I really wouldn't have expected it to have so many icons. I also wouldn't have thought that there was such an interesting mathematical principle behind it. Thank you for your insightful explanation. You made me understand better. Thanks for your clear explanation! Amazing!

[TimeWarpKing]

Such an amazing video. The more I learn about this game the more I come to love it. For me, the maths behind it is what makes it so special. It's a fun game for kids and adults alike to play, sure. But it's ease of play, non-reliance on culture or language, and of course the intelligent design that can open up some fantastic conversations with kids about maths and how we can use it to make sense of our world in a practical way, is what makes it one of the best games ever made.

[wendysolomon]

Just did a full sort of the cards with my Calculus students. SO FUN!! Our two missing cards are almost identical to your two, but our version has a few substituted symbols. Thanks for the fun.

[anarurua]

I checked this out and we’re also missing a snowman ⛄️ Thank you for the video!

[chezpaiz]

Thanks for the break down. I was trying to figure this out in terms of combination complexity. I figured that 57 images represents about 5 bits of complexity with a little room to grow ( 2^5 == 64). Then each card has 40 bits of complexity which means that you could make over 1 trillion cards each containing 8 images. Of course you’d throw away most of them, but since 8 snowmen left to right is the same as 8 snowman right to left. Regardless, of 1 trillion possible cards, you only need 55. What you showed me was how they chose the right 55 cards.

[emilygoosman]

My Spot it! deck only had 6 snowmen as well!

[gnohymmij]

My daughter just I just looked thru the deck, we are missing the same ones!

[vittorio]

After 2 years Stand-up Maths made a video about this game

[chrisl]

Really nice video, thanks for doing this! I play spot it with my kids a lot and really was puzzled... I spent quite a while trying to make a python implementation to create a deck and actually had a 'brute force' method that basically populated card N with images, then added images from card N to cards {N+1, deck_size}, and then had a filtering step to then delete invalid cards. I got it to create a deck with 15 cards that each had 1 match with each other, but couldn't get it to work higher... and now I know why! Will be using this as an example for my daughter as to why learning math is important 🙂. Thank you!

[התאומיםגרפיקה]

Hi, im a graphic desinger and need to make this game, unfortunately, im bad in math... i followed the video, and whats not understood with the scimatics, is that you use blue color gradient to show the lines between the dots, its very hard to distinguish between the colors...