# SuperSet

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:

- One Green Shaded Squiggle
- One Red Solid Diamond
- Three Purple Shaded Diamonds
- 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:

- 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! :-) )
- 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.)
- 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.
- Given any SuperSet, the joint is unique.
- There are 63180 SuperSets in the deck (as opposed to a mere 1080
Sets).
- 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