The Math Behind Spot it! 

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.

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?

There was massive time put into this great video

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

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.

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.

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

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

You guys just blew my mind

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!

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.

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

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.

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

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.

Thanks for sharing this!!

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!

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.

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

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

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

Only 6 snowmen for us as well, thanks for the great explanation!

love this! unveiling the math and patterns behind an awesome game 👌🏾

In the image @ 4:40 where are all cards in the deck are shown, there are 8 YinYang symbols. There is one YinYang in each column -- the right-most column has it hidden under the sky blue line in the 5th one from the top. Having a symbol repeated 8 times appears to break the rule for a 7X7 grid.

My kids pulled out our spot it game, sorted through for all the snowmen, found only 6. I think they skipped a few steps. We are ready to build our own deck now!

Thank you for helping to explain this game. I had created my own spreadsheet to begin the process of figuring it out, but wasn't able to complete the task. p.s., I too only have 6 snowmen.

great video!

Six snowmen here as well and missing the same cards! Must be standard issue.

On the part of the manufacturer an interesting aside would have been to have a different two cards missing, eventually you could build a complete deck from the missing cards of the other decks!

i have slightly different version of the game and the two cards that i miss are almost identical cards to yours, but not exactly the same: on the left card (the one with the cactus) i do not have a flower, but instead a stop sign (red). and on the right (the one with the dog) i have a hammer (orange) instead of the word "stop". it took me a while to build the matrix...

Great video with detailed, concise and visually appealing information. I think I understood most of it except for how you determined the angle at which the lines intersect the dots And How you determined the density of these lines; Diagram 1 (top left) at 3:28 shows all the 7 lines spread over 7 dots whereas diagram 3 and diagram 7 show all the 7 lines crammed in the space roughly three dots everytime it wraps around Please tell me if I have misunderstood something here

After a lot of counting, and recounting, we too have only six snowmen. Another 14 cards have a count of 7. Then I worked out the two cards identical to yours. NB Our packs have ART, BALLOON, OK and STOP. I have seen on the internet TORTOISE, HAMMER, NO-ENTRY and BIRD, especially regarding PYTHON programming. IMHO The same symbols, in a different order, will produce a totally different pack of cards. I think you can even see this when N=2.

We had 6 snowmen also...

I'm not sure if this relates to the explanation provided, but I just finished a Linear Algebra course and so want to understand via vectors If we consider each card to be a vector in 7-D, and they are not parallel or the same vector, can we think of the matching icon on each card as in fact the point at which these vectors intersect? It's kind of inverse to what you explained here but it's how I understood it.

The 8 spots you've taken around the matrix, could they also be on a different place or do they have to be like this? (compare minute 3:47 to 3:58) Would be nice to know the secret of determing the slope :)

I have Dobble, and have 6 snowman too

Awesome, thanks!

I've played Spot It quite a bit and am pretty surprised to learn that there are 57 images. It feels like we all shout the same 10 most of the time. I wonder why they excluded two cards.

Hi! Just wondering how to work out which two cards are missing? I am lost😂xx

Intresting... I've got the concept behind the game..but a question came on mind, which is: if two cards were got rid of, then there are at least 5 more symbols that aren't repeated 7 times, the same as the snowman symbol right? @science mom

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...

Can you make a video about six images and 31 cards?

Sedryn says that he also is missing two snowmen!!!

we found six snowmen too!

I also only have 6 snowman cards!!

only 6 snowman for us too!

The subscribers and views are same 36k!!

I think the game is called dobble

I made it with 6 images and it totally failed. :( Quite a few cards are not matching

We only had 5 snowmen☃️💀

Join our Kickstarter and get a fantastic 2020 Science Calendar! www.kickstarter.com/projects/sciencemom/science-mom-explains-the-atmosphere?ref=22gpz7

The pack I use with my students has 6 snowman

Yes we had 6 snowman.

Mind blown. I only got six snowmen!!!

Yes. We only have 6 snowmen

I made a Spot It clone using images of Hot Wheels cars.

I only have 6 snowman on my deck.

We call it Dobble.

Missing 2 snowmen

Only 6 snowman here.

Actually, I watch this video three times and coundn't understand the principle. So sad.

6 snowman

Hi, I’ve been looking at the maths behind dobble recently and it’s so interesting how it was achieved! Just wondering how did you manage to create the two additional cards whilst also ensuring that they didn’t have more than one picture the same as an other card?

I don't understand why they would not just provide all the 57 cards, if they had printed them?