# Spot It! is a fun game where you try to match the most pictures

Our 4yo and 8yo both love these cards. There are a bunch of other games you can play with them, too. And weâ€™ve started getting them as birthday presents for the 4yoâ€™s friends.

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Agree - Spot It is a fantastic game.

Itâ€™s also a really good game to play with younger children who are having speech difficulties. Instead of speed matching, we take turns saying, 'I see two green treesâ€¦" (or whatever is the match) and there are a lot of good sounds there for kids to work with.

Mathy bits: itâ€™s about the fact that two great circles on a sphere always intersect in two antipodal points. If you imagine drawing the symbols on a sphere (twice each, antipodally), then the cards correspond to the great circles.

Of course, if you did that with a sphere in R^3, thereâ€™d be infinitely many symbols and cards. Spot It! is a corresponding version where the real numbers are replaced with integers mod 7. There are 7+1 symbols per card, 7+1 cards with a given symbol, and there should be 7^2+7+1 cards and symbolsâ€¦

â€¦but there are only 55 cards!

Apparently the piece of paper that they cut the cards out of (and the size of cards they want) only lets them fit 55, not 57. Too bad! Otherwise you could play the Spot It! variant â€śgiven two symbols, find the card that contains bothâ€ť.

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This is a pretty fantastic game, of the sort that 5-year-olds and adults are more or less on equal footing. Itâ€™s harder than it looks, but practice helps.

Thanks for this. Iâ€™d wondered about the algo while playing, and it bothered me that I couldnâ€™t map it out, conceptually. I was thinking rows and columns, not spheres. Such is life.

Rows and columns is okay too. Make a 7x7 grid of symbols and consider all rows (slope 0 lines), all columns (slope=infinity lines), and lines of all other slopes (e.g. knight moves up right right, up right right, â€¦); these will be the cards. There are 7+1 slopes and 7 lines with each slope, so thatâ€™s 7^2+7 lines. Unfortunately two lines of the same slope wonâ€™t share a point in common.

So fix this by making one new symbol for each slope. Put that symbol on each card with that slope (now that will be the symbol in common), so now they all have 7+1 symbols, and make a new card containing only slope-symbols.

The amazing bit, when youâ€™re done, is that itâ€™s mathematically impossible to tell which card was the â€śslopesâ€ť card; theyâ€™re all on an equal footing.

To connect to the sphere picture: imagine if you didnâ€™t have the equator on the sphere, just delete all those points/symbols. Now two great circles might miss each other (i.e. their intersection might be on the equator). Putting in the slopes card is like adding the equator back, getting a nice rotationally-symmetric sphere.

Puzzle: how does this construction break if you replace 7 by 6 (or some other composite number)?

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Too much overlap, right? Iâ€™ll speculate that it only works with primes?

I once tried to make this game for ESL students, but I couldnâ€™t figure out how to do it mathematically. (The idea was to be able to change the pictures to suit our current vocabulary set, so each picture would be a link to a picture in a folder that could be updated later on). I think in the end I just assigned numbers to each picture and reproduced each card (e.g. card 1 has pictures 1-8, card 2 has 8-15, 3 has 2, 15-21 etc.).

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