Miscellaneous fun stuff about SET®

How many sets can you have in 12 cards?

We thought about this one day after doing a SET® puzzle, where we were presented with 12 cards and asked to find the 6 Sets that were present. (We did.) This was in the early days of the official SET® home page, when their nifty interactive SET puzzle was nifty, but not yet interactive.

Our first thought was that this would make a nice CGI script -- just hit "reload" on your browser and get a new and different SET® puzzle every time. So we did that, too. (Now, of course, the folks at the official SET® home page have made theirs interactive, so it's more fun than ours.)

Along the way, we started wondering, if you pick 12 SET® cards at random, how many Sets will you usually get? So we made a little program that would pick 12 cards and count the Sets, over and over again. We ran it for a million trials. The most it ever got was 12 Sets. Here are the full results.

We briefly wondered if 12 was best possible, but it isn't. After a little more thought (by our own brains this time, instead of the computer's), we figured out you can get at least 14. But we haven't proved that this is maximal.

Can you find 12 cards with 15 or more Sets, or prove that it can't be done?

By the way, perhaps you noticed how "regular" the 12 cards that yield 14 sets look. The same is true for these 12 cards with 12 sets. But look how remarkably random-looking these 12 cards with 11 sets are!

By the other way, up above you may have noticed the link for the random SET® puzzle. If randomness is not to your taste, or if you'd like to be able to specify the number of sets that will be there, here's a customizable SET® puzzle.

Other stuff

Here's another SET® probability factoid.

It's possible to have a draw in Set Quarto.

mag and judd