"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).
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Puzzle size: |
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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).
End Game SET was "discovered" by Gary Gordon & Liz McMahon; I learned about it from the Set Enterprises Facebook page. I am not receiving any promotional consideration from Set Enterprises; I just really like their games. (If you have never played SET, you should consider buying a set of cards, especially if you like math and/or finding patterns.)
Dec. 9, 2014: First release.
Dec. 24, 2014: Slight revisions (image pre-loading, "flashing" card).
SET card game and images © 1988, 1991 Cannei, LLC. All rights reserved. SET® and all associated logos are registered trademarks of Cannei, LLC. Used with permission from Set Enterprises, Inc.
The card images were copied (with permission) from setgame.com. Other contents of this page are © 2014 Darryl Nester. Please send me an email if you have found it to be useful, or if you have suggestions.