A variant by Wei-Hwa Huang. The following is taken pretty much verbatim from his email; it could use a little cleaning up. One of these days...

What's a SuperSet?

A "SuperSet" is four cards such that there exists a fifth card, the "joint," that forms two intersecting Sets with those four cards. The intersection is always the fifth card. Example:

  1. One Green Shaded Squiggle
  2. One Red Solid Diamond
  3. Three Purple Shaded Diamonds
  4. Three Red Hollow Squiggles

This is a SuperSet; the joint is E. Two Red Shaded Ovals. ACE is a Set, as well as BDE.

A few useful properties of SuperSets that may or may not be immediately obvious, and are similar to existing properties of Sets:

  1. A SuperSet NEVER contains three cards that are a Set. (In other words, a SuperSet never has a Set as a subset. Maybe I should have called them "NonSuperSet"s! :-) )
  2. Given any three cards that do not form a Set, there are EXACTLY three other cards that will form a SuperSet with those three. In the example above, D might have been: D2. Two Purple Solid Squiggles D3. Three Green Solid Ovals (As practice, work out the two corresponding joints for yourself.)
  3. If there are three of one and one of another, then it's not a SuperSet. (E.g., if three cards are purple and the fourth one isn't, then it's not a SuperSet.) Unlike the corresponding rule for Sets, The converse is NOT true.
  4. Given any SuperSet, the joint is unique.
  5. There are 63180 SuperSets in the deck (as opposed to a mere 1080 Sets).
  6. Let X be any three cards that do not form a Set. Let Y be the three cards that each create a SuperSet with X. Let Z be the three cards that are the joints of those three SuperSets. Then any card in Z creates a SuperSet when joined with the three cards in Y (and the joint is in X), and any card in X creates a SuperSet when joined with the three cards in Z (and the joint is in Y). Also, those nine cards form a "plane" (aka a "magic square" on the official website).

The rules

Play just like regular SET, except use only NINE cards, and look for SuperSets. (Nine cards is sufficient to have a good chance of a SuperSet existing.) Say whatever you want; in experience the players tend to stare at those cards a veeery long time before anyone makes any progress.

Warning: This variant is tough!

mag and judd