The Game of Set (and some variations) - Numberphile

Mathematicians love the game of Set - and here are some variations on the classic. Featuring Catherine Hsu. More links & stuff in full description below ↓↓↓
Catherine Hsu is Assistant Professor at Swarthmore College - chsu.domains.swarthmore.edu
Projective and Non-Abelian SET Decks - chsu.domains.swarthmore.edu/s...
Conventional Set on Amazon - amzn.to/3K7forn
SET with a Twist (paper by Cathy Hsu, Jonah Ostroff & Lucas Van Meter) - doi.org/10.1080/10724117.2021...
Online non-abelian SET games written by Gabriel Dorfsman-Hopkins - www.gabrieldorfsmanhopkins.com...
Numberphile is supported by the Simons Laufer Mathematical Sciences Institute (formerly MSRI): bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. www.simonsfoundation.org/outr...
And support from The Akamai Foundation - dedicated to encouraging the next generation of technology innovators and equitable access to STEM education - www.akamai.com/company/corpor...
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[@boRegah]

I once taught this game to some strangers and two of them were so incredibly quick that it wasn't even a game for them.

[@emilwandel]

Let them find supersets. Two sets which overlap in one card, so five cards

[@wobblysauce]

Yep… done the same and was more then humbled

[@denishclarke4470]

May be they were the mathematicians

[@rewrittenperspective547]

Which one do u mean?? The wooden extremely hard one?

[@vigilantcosmicpenguin8721]

It's an easy game to pick up on. You just need to learn it once, and you're all Set!

[@nowen1233]

In undergrad, I brought a copy of Set to the math-major's lounge for lunch. More than half the people there missed at least one afternoon class that day. The next day, there were three more copies of Set being played at lunch.

[@KimMilvang]

We had the problem of finding sets too fast for the game to be fun. To extend the game we added a 5th property. This can easily be done by buying 3 copies of the game and adding a different value of the property to each copy (this would be the F(3,5) version of the game). We added a border: no border on one copy of the game, corners on the 2nd, and a full border on the 3rd. If you still want to to play the original, you just use all the cards with no border. This version of the game plays very well for us.

[@obiwanpez]

The developers thank you for your patronage. ;)

[@precumming]

How many cards are on the table? Any change from 12?

[@KimMilvang]

@@precumming 12 were too few, we experimented with 15 or 18, and both worked. 15 is of course slower since you sometimes spend a few minutes searching before adding more cards. I can't see a mathematical reason it has to be a multiple of 3, but it seems right. I thought about doing the math, but I skipped it, so I do not have the probability for there being at least one set.

[@tristantillij8425]

@@KimMilvang I like the idea of adding a fifth property, I might give the game another try this way :) Some fun facts: You'd need 46 cards on the table to guarantee a set. Set-free collections are called 'cap sets', Wikipedia can tell you plenty about them. In the regular Set game, given 12 random cards the probability of them containing a set is about 0.968. To get a similar probability in your expanded Set game, you'd need either 17 or 18 cards on the table, with probabilities of roughly 0.954 and 0.976, respectively. I guess 18 cards seems more right.

[@coopergates9680]

This is what I did back in the days of Adobe PageMaker - the fifth variable is slant. Straight, clockwise, or counterclockwise rotated shapes. I still have the 243 cards I printed out. You could also try 4 or 5 cards to a set, in which case 3 variables is already 64 or 125 cards, and of course it gets drastically tougher to find a set as more cards are necessary.

[@davidconnell1959]

I use a straightforward technique to introduce Set to new players efficiently. Shuffle the deck and turn over the top two cards. There is only and always one card that makes it a set. Name it. Keep working through the deck, naming the unique card that completes a set. Game learned.

[@theadamabrams]

I’ve played this “What’s the third card?” puzzle myself just to practice (didn’t help much-I’m still pretty slow), but I never considered using it as a teaching method. I like this idea!

[@goldenalt3166]

I use the "never two" rule. For any set there can't be two of something.

[@limzhixing2658]

since they say the order matters, the sets are g * g^-1 and g^-1 * g, where g^-1 is the inverse of g. That's a pretty nice way to introduce the uniqueness of inverse for elements in the group.

[@sachs6]

With the non abelian groups there may be up to six cards that complete the set in some order.

[@tomaszadamowski]

yeah, I just saw this game in this video here for the first time and my first thought 3 or so minutes into video was: "don't two cards already define the unique set of three"?

[@chrisschwanekamp1583]

My partner and I play Set every single day. I wrote a python simulation to answer some questions we had about it. I simulated hundreds of millions of hands. Some of that data: The odds are 1 in 10 million to get to 21 cards on the table before there is a set. About 1.5% of the time the game will end with what we call a "complete set" which is no cards left on the table (we've done this 3 times naturally). About 1 in 10,000 hands you will get either all the same color, all the same #, all the same shading, or all the same shape. The most sets that can be made out of 12 cards is is 14 and that is incredibly rare to happen in the course of play, about one in every 5 million hands.

[@paulpinecone2464]

We deduce that you and your partner have been together for 100/1.5*3 = 200 days.

[@jujdj6214]

couple goal

[@-Milo]

It’s possible to get to 21 cards without a set!?

[@paulpinecone2464]

@@-Milo Pay attention! It is possible to reach *20* cards without a set. This message and the information that it conveys are entirely pointless.

[@chrisdooph5092]

In the set of 12 from the beginning, there was also the set of "1 solid red diamond, 2 purple striped squiggles and 3 green open ovals" :D

[@reformCopyright]

I beat you by about four minutes, though. ;-)

[@boRegah]

You two do great work. Keep it up! Hopefully you will still love yourselves once you're old

[@lswcs]

Regarding the original game of Set, I found the following property using a program: Assume there are 20 cards that contain no Set. Then, there exists precisely one card X in the remaining 61 cards so that you can partition the 20 cards into 10 pairs s.t. each pair forms a Set with X.

[@josephgraff8671]

My favorite extra rule to play Set with is that the last card in the deck gets dealt face down. If nobody has made a mistake by picking up 3 cards that are not actually a set, its characteristics are deducible by looking at the rest of the cards on the board; you isolate characteristics and make sets with them one by one, and the last card is going to be the card that solves single-characteristic sets for all 4 separate characteristics. Making a set that includes the face-down last card counts for 3 points, and solving for its characteristics and announcing them first counts for 1 point. It makes for an interesting gamble: do you try finding a set with it for 3 points once you figure out what it is, or just announce it for the 1 point? It is also interesting to mentally model the game as a 3x3x3x3 matrix in which sets are straight lines. This helps you understand how you can determine the characteristics of the last card without looking at it, just by looking at the other 11 (or 8, or 14, or maybe even 5) cards remaining.

[@mezzomatics]

There is another card game similar to Set called "Swish" that uses reflections and rotations. The game is about filling each "hoop" on the card with a "ball" on another card. The cards are translucent so that they can be rotated and flipped in order to make sifferent sets. It's fun and great practice for visualizing rotations and reflections!

[@WaynaPicchu05]

I played Swish at a table top gaming convention about 4 years ago. I am horrible at Set, yet was very fast at Swish. It feels as if we have neural nets that are by coincidence "tuned" to finding different types of combinations.

[@JM-us3fr]

I think the hardest sets are the ones where there are no properties in common. It's often indistinguishable from random noise.

[@Sam_on_YouTube]

I got this game to being to summer camp on 1992. Still have the cards. I taught my kids to play recently and they love the game. Only missing 2 cards. We laid them out once to figure out which 2 we're missing.

[@zzzaphod8507]

Interesting variations! And nice how neatly the arrow crossings are done at 13:59

[@johannesh7610]

I immediately had to think about which group the last one is. Namely: the semidirect product of S(3) and F_2^3, where S(3) acts on F_2^3 by permuting the elements of the vector. This gave me the same excitement as finding a SET :) Very cool generalization of one of my favorite games!

[@Apophlegmatis]

The 4-line tile game would make an excellent solitaire game

[@honeypygmypuff]

(obligatory english is not my first language) I was introduced to set from the korean gameshow The Genius. From what I remember, the contestants were only required to say whether there was a set in the 12 given cards or not. The idea of set was so interesting to me that I had to try it out for myself. I’m still not that great at it but it makes me feel so proud of myself when I find a set that I cant stop playing it, no matter how much it hurts my brain 😂

[@GordonHugenay]

and in The Genius the set cards only had 3 properties, so it was a much easier game.

[@stevengigrich6264]

perfect english

[@RubixB0y]

Absolutely fantastic English, better than many Natives. -If you're looking for constructive feedback, I would personally move the comma after "playing it," back to after "find a set," but seriously perfect otherwise and clear regardless.- Edit: I have a hard time with runons myself, my writer's voice tends to be conversational. People tend to communicate by telling stories, so I didn't want to lose the meaning. Your version is actually better than mine but here's my final version! "I'm still not that great at it, but it makes me feel so proud of myself when I find a set that I can't stop playing it. No matter how much it hurts my brain otherwise." Sorry for the initially incorrect advice!

[@TheZotmeister]

@@RubixB0y That comma wouldn't belong there. OP has it right. (Apart from a missing apostrophe.) Reduce the sentence to just what's needed for validity: by removing everything up to and including "but" (this is a compound sentence and that could be its own; there could be a comma before "but" but it's optional), the phrase "when I find a set" (which is a prepositional phrase and isn't needed to make the sentence valid), and "no matter" and everything after (which is also not needed for validity and as such is correctly separated out with a comma), you're left with "it makes me feel so proud of myself that I cant stop playing it". There's no room for a comma in there. Someone _saying_ that aloud might put a dramatic pause after "myself", but that doesn't equate to a comma in writing.

[@aaron6627]

Gyul hap! Also how I got introduced to it :)

[@nataliekanakova9496]

My friends made a "4-set" and even a "5-set" versions (with more colours, shapes, shadings...) since the original Set wasn't really a challenge for them. I enjoy the 4-set much more since it usually takes a few minutes to find a set. I haven't played the 5-set yet, but I've heard that it took group of people about 1,5 hour to find even one set (so now no one wants to play it...).

[@benjaminpedersen9548]

I guess a set then consists of 4/5 cards, right?

[@rewrittenperspective547]

🤣🤣🤣🤣 No one wanting to play it was the best ending i could ever ask

[@coopergates9680]

Did they use 64 cards (3 variables) or 256 cards (4 variables) for the version with 4 cards to a set?

[@user-bv5gd5mh8u]

Is it possible to make it lesser, like 2x

[@juliestevens6931]

OMG!! I LOVE SET!! I hardly ever hear anyone talk about it. I have had my deck for like 30 years!

[@BenjaminLu]

My game group played another F(3,5) variation that we called "3D Set". We used a standard deck, but instead of playing on a 3x4 grid, deal 3 separate 3x3 grids (think 3D tic-tac-toe). Now each card in a set must come from the same 3x3 grid, or all cards must come from different grids.

[@ragnkja]

How do you deal with the “no set” case where, in the normal game you just deal three more cards? Or is that mathematically impossible?

[@CraigGidney]

The 3-wire beaded permutation is isomorphic to the rotation group of a cube, plus mirroring (because a rotation permutes the XYZ axes and mirrors an even number of them). You could redraw each tile to be some object rotated by that rotation. You could remove the mirror degree of freedom by using a mirror-symmetric object like a teacup or a plane (equivalent to adding the rule that beads always appear in pairs). I wonder if that version of the game is easier or harder; it strikes me as probably easier to memorize but harder to visualize.

[@RobertMilesAI]

You can also play Quarto with 16 cards from a Set deck

[@bitti1975]

18:56 "We automatically get our third line for free if we have the right number of wedges". If you confirmed the first two lines work, you don't even need to count the wedges, since you already get the third line for free. In fact, to my understanding, it's enough to confirm that one line works and that you have an even number of wedges, with an even number of swaps the other two have to be the identity permutation.

[@LoganKearsley]

Permutation set feels very similar to a game I invented on the elements of the braid group B4, in which not only ordering but the chirality of the line crossings matters.

[@belg4mit]

iota is a tiny palm-sized version of Qwirkle with cards that you can also use to play a version of Set. In it, rather than four attributes with three values, there are three attributes with four values.

[@norm58inator]

Whenever I'm explaining this game I've always just said "The sets are just lines in F3^4". Unfortunately that is yet to work.

[@ChrisBreederveld]

I love this variation! I was expecting non-set or super-set, but this one I've not seen before! ETA: you may know non-set also as anti-set

[@davidanoble]

What does ETA stand for? All I can think of is "Estimated Time of Arrival" but somehow I think it means something else in this context

[@columbus8myhw]

@@davidanobleEdited to add

[@eta2321]

@@davidanoblenah they were just referring to me

[@bobknip]

​@@eta2321I was wondering when you would appear here.

[@ender5312]

@@eta2321eta2321

[@drskelebone]

"There's at least two sets on the board." is 100% "find one, please!" and also 100% "I have two, but I'll let you take one if you have one now." I have used both strategies in the past. Kid Set is cool too, because you can tank yourself all you need to there.

[@JM-us3fr]

I discovered the x+y+z=0 thing by myself, and my mind was totally blown when I discovered it! I showed my friends in my graduate program, and we were all pretty hyped.

[@benjaminpedersen9548]

Cool. I had not thought of that before, but I had thought about the straight lines in 4D-space.

[@rewrittenperspective547]

QED😂😂

[@kylepekosh3136]

Set has been my favorite game since I was five years old! I'm chuffed to see it featured on one of the best channels on KZbin :)

[@crueI]

I find the hardest sets are the ones that have the shading go in a different order than the numbering. For example in 4:26 the set of a full red diamond, two half full purple squiggles and 3 empty green ovals is easier because the fill is decreasing as the count increases. But this notion is not necessary and it’s possible to switch any property between 2 cards in a set to get a new valid set.

[@benjaminpedersen9548]

I like to think of sets as grouped by the number of varying characteristics. It seems to me that most people have an easier time finding "1-sets", meaning only one characteristic varies. They especially find sets within one color. I tend to find 4-sets faster than most.

[@JG-zs8tr]

There are at least 5 sets in the first 12 cards, though several of them overlap.

[@SeanCMonahan]

I love this game! I'd play it with my dad all the time growing up.

[@russellchido]

lol, love that permutation of "remap it unto" into "permutation"

[@stechuskaktus8318]

Oh yeah, I remember that game. Haven't played it in years. So I glance to the side, see it sitting in the shelve, and come walking into the living room grinning ear to ear. It's Set time!

[@nemoyatpeace]

I'd love some sort of file for those permutation tiles so I can laser cut or 3d print them myself. Would be great for my classroom!

[@Dodo-ur7cq]

finally some set content online

[@shreyanshupanda1219]

This is the first time i have geard of this game. Sounds interesting, though i suspect it would hurt my brain initially.

[@benedictdaleggy]

I love Set so much! It was lovely to be able to hear more about the backstory of the original game and see the new permutations Dr. Hsu & co came up with

[@leoquesto9183]

Absolutely love Set. It’s not just a beach house game. Been playing it for about 15 years and have found it to be a great way to relax. It’s also a blast to play with kids. This video is just fantastic and I will now employ some of this zaniness.

[@rubiks6]

I loved this game when my children were growing up. One of the beauties of this game is that even 6, 7, 8-year-old kids get it and do as well, with practice, as the adults.

[@Impatient_Ape]

The Temperley-Lieb algebra was the first thing that popped into my head when I saw the wooden tiles.

[@Chazulu2]

So cool. I drew all of those 3 permutation tiles so many times when I was finding the functions to define all of the balanced ternary unary operations. It was basically just finding a set of tiles from a limited selection that's equivalent to each tile, tho I needed to consider all non-injective surjections as well but could only use 1 of them. Was excited to see them as cards and tiles, lol.

[@TheErichill]

Electronic tiles that can change the colors of the lines to match the tile to the left would be neat.

[@you_just]

i love set!! i played it all the time in high school and i was so fast at it... i work at a university physics department now--I should buy a copy and bring it!

[@Ashebrethafe]

4:37 That was actually the first set I noticed. There's also a set with the maximum amount of variance: one solid red diamond, two shaded purple squiggles, and three empty green ovals.

[@YoungGandalf2325]

How can these games be combined with elements of Twister and/or strip poker, with alcohol involved?

[@mickeyrube6623]

Make the cards much larger and put them on the ground. Then use your hands and feet to find sets.

[@woutertrieling4182]

Just came up with a strip and alcohol variant: You play Set with a limited deck of between 12 (so one full table) and say 20 cards (based on the group size and desired speed of escalation), which you play till there are no more sets to be found. Now compare the amount of sets everyone found. The worst player needs to strip 1 garment and the best player needs to take a sip (to make the game more balanced). Based on desired speed of escalation, make the strip and drink rules apply to all best and worst players, or only if there is exactly 1 worst and/or best player.

[@fantisamir]

That was amazing! I greatly enjoyed this video. This is the kind of game I hope my kids would like playing

[@JonathonV]

I love this game so much that I made a digital implementation of it! I never considered using modular arithmetic to check whether a group of three is a set, but I love modular arithmetic so this video was right up my alley! Now I want to borrow my school’s Glowforge and print me some tiles!

[@dav1dsm1th]

Those last sets of cards look like they would translate into an electronic game really well - where the tiles connected internal conductors that matched the traces - and you could test your "solution" with some LEDs or a multimeter in diode test mode - or a rig that the cards clipped into...

[@altan3850]

Hi! Thanks for the video. Is there a blueprint for the laser cut set? Couldn't find on the website

[@seanm7445]

Oh, love the Claddagh ring.

[@sidgurjar]

I don't how yet, but I see great value in these games in helping young children develop mathematical thinking if the rules are tweaked in such a way so as to simplify them enough for children.

[@0LoneTech]

Lots of inverses (reciprocals?) here. E.g. at 19:05, the upper path is two swap upper, one identity, rotate both up and down, and two swap outers. That's 4 identities no larger than a pair. In the lower one, the outer tiles are a swap upper pair, and one of the rotate downs is wrapped in a swap outer pair, turning it into a rotate up to pair with the first rotate down. Neat game.

[@zmaj12321]

Oh, interesting way to show off some group theory! I think those laser-cut pieces look super satisfying too.

[@reformCopyright]

Set! One red solid diamond, two striped purple squiggles and three green empty ovals.

[@R2debo_]

n my moment! I love SET! ❤️

[@RubixB0y]

So you copied my comment, including the typo and added a heart because the word "love" appears. What a bot! Disgusting

[@annevanderbijl3510]

12:25 is the coolest edit i’ve seen in a while

[@drskelebone]

There's also a "symmetric offset" away from the centers of the tiles for intersections. If you have a (+1, +1) intersection, it must be matched by a (-1, -1) intersection along the tile chain. Right? That seems like an obvious thing.

[@rogerwitte]

This is my first exposure to the game SET, It looks like a cool game (although I always hesitate to play games based on speed because I am not good at moving or reacting quickly). It looks really cool and I want to thank Dr Hsu for a great presentation. That said, it kind of bugged me when she suggested labelling with F3 (the finite field) when she was not using multiplication. I would have prefered her to refer to the cyclic group of order 3.

[@curtiswfranks]

I partially analyzed this game in undergrad. It is a great topic!

[@dewaard3301]

This is the kind of game you buy as a father, hoping your kids will be interested in playing it when the time comes.

[@fakjbf3129]

3:00 I found a set where every category has three different options! One solid red diamond, two purple striped squiggles and three open green ovals.

[@Reconsiderate]

one of the best card games 🔥 need a deck at home, also one to carry around for on the fly games

[@hard4hardware]

Just a suggestion for your game. Make the traces electrically conductive and either add rgb leds to the right side of the tilea or just have a start and end piece that lights up 4 different colors so you can see the order of your first and last tiles (maybe even on every tile) and you have a turn based game where you kind of look for a tile you think you need. Add a time for the turn ti increase difficulty (might nit be needed😂)

[@TheScarvig]

for the variant with the negations you can actually just include NOT gates in the tiles. it makes the tiles a tiny bit more complicated as they now need to have a common power bus, but in theory you could just have them manufactured by a pcb manufacturer with a two layer pcb , edge contacts and surface mount components for quite cheap the signal path is on the silk screen and the evaluation can be done either by simply having two connected endcaps with leds and a button for each signal, or by having a microcontroller that checks each line one by one and only gives you the number of successful paths to make it a bit more challenging to figure out which line is not ok. the micro could even have a switch to set the mode where it uses a number of leds to either give you the total of correct signals or lights them up in order so you see which lines are correct. if a deck of valid tiles is given one could prolly whip up a gerber in less than a day...

[@SaveSoilSaveSoil]

So very creative!

[@ronald3836]

I always think of a set as a line. Take any two points/cards and the line through those points/cards will go through a unique other point/card.

[@johnchessant3012]

The underlying group in the last game is the semidirect product (Z_2)^3 ⋊ S_3, where S_3 acts on (Z_2)^3 in the natural way. Is there an easy way to see that S_4 is a subgroup of this?

[@jonahostroff]

I don't think I would call it "easy", but you can try to convince yourself that (Z_2)^3 ⋊ S_3 is the group of symmetries of the cube (think of S_3 as permuting the three pairs of parallel faces, while (Z_2)^3 flips-or-doesn't-flip each of those pairs). On the other hand, S_4 is the group of symmetries of a cube without reflection: each such rotation corresponds to a unique permutation of the 4 diagonals of the cube.

[@graduator14]

Looks fun!

[@YingwuUsagiri]

Ooh I loved set, many bruises and purple hands have been slapped for hours on end when there was time to fill

[@paulbuchinger4585]

Great video! That means playing "Set" is essentially the same as solving the rubik's cube.

[@jonathanjacobson7012]

One of my favorite games! Although my brain starts hurting after a few rounds :)

[@Angi_Mathochist]

My kid, Storm (now in their mid 20's -- no longer such a kid!) has always been SO fast at Set that nobody else can really play with them. We have to give them a handicap: they have to close their eyes every time cards are added and count to 10 before looking. That's the only way anyone else has any chance of competing (or even finding any sets at all before Storm does). And Storm is far from the only mathemagician in our community. I'm a mathochist, myself, in fact. I have an MS in Math (set theory, coincidentally) and BS Math and BA in Physics. Storm just happens to have a VERY set-oriented brain. The easiest way for me to think of sets is that any 2 cards determine a set. For any characteristic, if the 2 cards match, the third card must also match; if the 2 cards don't match, the third card must also not match (must be the third, missing element). Another thing the Set game was AWESOME for when Storm was young was teaching, very well and very intuitively, the concept of proof. She was quick to grasp that it's one thing for someone to say they THINK there aren't any more sets in the layout -- even for all the players to agree that there aren't any more -- and quite a different thing for there to ACTUALLY NOT BE any more sets. To be SURE there are no more sets, you HAVE TO **PROVE** IT. So when WE were playing (at least among family), we would never add more cards until we had actually PROVEN there were no more sets. Proof requires exhausting all the possibilities. But the cards generally help you by providing some handy categories. For example, there might be only 2 or 3 cards with blue on, so you start by checking whether there can be any sets with blue. Once you've eliminated the possibility of blue in any sets, you can ignore the cards with blue on, AND you also know that there are no sets with mixed colors (any set would have to be all one color, and not blue). You go from there. Maybe there's only one squiggle, so you check for any sets with the squiggle. If you can eliminate that, then you can ignore the cards with blue and the one with the squiggle, and you know that any sets will be all the same color and all the same shape (since no blue and no squiggle). And so on, until you've actually conclusively proven there are no sets. Not all proofs have to exhaust long lists of possibilities, but all proofs have to consider all possible cases (even if there's only really one possible case, you still have to make sure you've considered whether or not there could be other cases, really). So this was a pretty damn good introduction to the whole concept of what a mathematical proof *is*.

[@LesCish]

I played this with my son when he was growing up. He wound up majoring in math years later.

[@curtiswfranks]

I would love to see an introductory course to wreath products (or even just more basic algebra) taught with these tiles.

[@walkermenkus104]

It's cool how the last card in the permutations is the inverse of the product of all of the cards preceding it, i wonder if there's some linear algebra representation there?

[@SaberTail]

Unless I'm misunderstanding what you're asking, yes. A square matrix with exactly one 1 per row and per column and 0s everywhere else will permute the elements of a vector. These matrices form a group, and you can multiply and invert them accordingly.

[@fakezpred]

this quickly follows from some group theory actually

[@viliml2763]

That's literally the definition of set. Their total product is the identity, therefore obviously the last one is the inverse of the product of the previous ones, because the thing that multiplies something to give the identity is the inverse.

[@Silas_MN]

I grew up with set! I think something of it sank into my brain haha

[@moshecallen]

We have and play this game at home. The only caveat is that I and one of my daughters has an eye condition which means that my eyes take longer to focus and to look around at the cards. So when racing, we're at a distinct disadvantage. We just make sure everyone can see them before people grab sets.

[@mathmethman]

There is a magic trick on 'Fool Us' with Penn and Teller in which the pair are fooled by something involving simple maths very like the paths described here. Frustratingly I can't track it down to provide the link. But the magician basically used five cards similar to the wooden tiles in this video (though more complicated to disguise their nature) to trace a link between Penn and Teller showing how they met. A closer analysis of the cards revealed a) that the permutations were the same either way up and b) that each permutation shifted all five tracks by the same number (e.g. 1 to 3, 2 to 4, 3 to 5, 4 to 1, 5 to 2) so that no matter what order the cards were placed the outcome was the same.

[@davidkaiser7206]

You can deal the cards face down to remove the speed element and make it more memory based.

[@ingiford175]

Wish she took the formula and 2 cards and 'determined' what the 3rd card is, as for each set of 2 cards, there is only one card that 'complements' them into a set.

[@caeonosphere]

Cool video, cool game!

[@triangledefinition]

Wow! this was really cool, I've always liked making little games and stuff but I'm not so good with the math

[@MsSamareh]

Iota has all the cards for an F(4,3) version of the game, but played with different rules. I'm totally going to try playing this way!

[@Craznar]

This is like the board game called Quarto ... it is noughts and crosses but with sets.

[@RobertMilesAI]

You can play it with a Set deck! Just pick your least favourite type of each of the properties and discard them, you end up with a 16 card deck that corresponds to a Quarto set

[@lanceraltria]

Equivalently, the parity of each permutation tile is the parity of number of crossings on each tile (counting n lines crossing at 1 point as n-choose-2 crossings). The proof is straightforward enough too, each crossing just corresponds naturally to a swap.

[@reformCopyright]

Set is a favourite in Mensa!

[@SuviTuuliAllan]

Aww!! Isn't it a bit too advanced for them, though?

[@ryanwellence]

Oh man, I haven't seen a numberphile video in a bit now and got so lost when Catherine said 1+1+1=0. OK. At least I understand Set.

[@fakezpred]

since in F^3 (field of order 3) the operation is mod 3, we have 1+1+1 mod 3 = 3 mod 3 = 0

[@TheZotmeister]

Modular arithmetic is one of those concepts in math that is almost _always_ glossed over FAR too quickly every single time it comes up. You're lucky if you even get "like a clock" out of whoever mentions it. You're stupendously lucky if you get "we only care about the remainder".

[@DogBehaviorGuy]

What I learned in the initial presentation is that apparently I'm wired to notice differences, because the ones that immediately jumped out at me where the ones with variance in every category (ie - a set that has one of each in every category)

[@DogBehaviorGuy]

and i think it's because i think about it as an analogy to qcd and I want to build baryons

[@jonathanjacobson7012]

"All the same or all different" = "No exception"

[@Zeraevous]

Equivalent explanation I've had success with when the "all unique or all the same" explanation doesn't land: A set can't have only 2 of anything. Shapes? Can't be 2 squiggles. Color? Can't be only 2 greens.

[@Zeraevous]

Also, any 2 cards have exactly 1 unique card that completes the set.

[@aankwenti]

that does sound like the best way to explain it imo

[@ianmohlie]

My game! I play it all the time!

[@rdbasha5184]

VERY COOL!!

[@gcewing]

The one with the dots on the lines makes me think of Petri nets. Now I'm going to lie awake all night trying to think how to make a game about Petri nets.

[@tyleringram7883]

I wonder if there is like a way to strategize with these games mathematically like a calculation or something. Cause if some college students can do faster than you can or I, how do they do it

[@MrRyanroberson1]

3:45 made me realize: you don't always have to check all four qualities. you can check three, and if those three are satisfied as the SAME then the fourth one will correctly be all different

[@FrostMonolith]

The set that I love is the set that all four vectors are different.

[@Matsersuperkul]

At the conference "FUN with algorithms 2018" I got introduced to the variant SUPER-SET by one of the papers presented there. I think that was a fun one. Basically, you have to point out 4 cards, that together with exactly one fifth imaginary card would make two sets. Or said in another way: you will need to look for two sets that share a card, but that card doesn't have to be on the board. So using the system in the video: (0,0,0,0),(1,1,1,1) & (2,2,2,0),(2,2,2,1) would be a SUPERSET, since both groups of cards would be a set using the card (2,2,2,2) See "Fabio Botler, Andres Cristi, Ruben Hoeksma, Kevin Schewior and Andreas Tonnis: SUPERSET: A (super)natural variant of the card game SET"

[@DavidGuild]

You said the shared card doesn't have to be on the board - do you mean it has to be not on the board? Because if I'm allowed to "share" a card on the board then any normal set is trivially a super-set.

[@MeriaDuck]

TIL that "remap it unto" is an anagram of the word "permutation".

[@edawgroe]

Non-Abelian Set is something I hope I never have the misfortune of playing lol

[@AndrewTaylorPhD]

This implies the existence of a game where instead of dealing out cards you tip a billion scrambled Rubik's cubes onto the table and wish the players luck

[@vigilantcosmicpenguin8721]

I would play that.

[@myrmatta1]

Yoooo someone made the Among Us Wires task into a real game!