"End Game SET" is a puzzle based on the card game SET from Set Enterprises. You are presented with the final collection of cards left on the table at the end of a game of SET, with one card face down. Your job is to determine what is on the hidden card. To learn how to play, you can watch this YouTube video, or read more at the End Game SET page.

Once you have specified the hidden card, click "Submit answer" to see if you got it right (and see how long it took you to solve it).

Puzzle size:

 NUMBER: one two three FILL: empty striped solid COLOR: red purple green SHAPE: squiggle diamond oval ____ ____ ____ ____
Technical notes

The puzzle size selection determines roughly how complicated the problem is. If you choose "Any size," there is a slim chance that you might see a 3-card puzzle, as well as a tiny chance you might have 15 cards, and minuscule chances of seeing 18 or 21 cards. How slim are these chances? Based on the outcomes of 3,000,000 simulated games:

Puzzle size
(cards on table)
Probability Prob. that hidden
card makes a set
3 1.45% 100%
6 26.91% 0%
9 55.52% 39.56%
12 15.65% 59.05%
15 0.47% 85.57%
18 0.0003% 88.89%
21 0.0000% 100%

If there are three cards on the table, the hidden card always makes a set with the two visible cards; if there are six cards, the hidden card will never make a set.

For the bottom two lines of the table, even 3,000,000 simulated games produced only 9 cases with 18 cards (with a set formed in 8 of those cases), and no instances of 21 cards. For 21 cards, theory tells us that there is always a set (see, for example, this paper by Davis and McLagan, or this one by Jim Vinci).