Game of SET

Here are 5 ps/jpg files which you can print out, cut and perhaps mount on cardboard.
page1 (ps)   page1 (jpg)
page2 (ps)   page2 (jpg)
page3 (ps)   page3 (jpg)
page4 (ps)   page4 (jpg)
page5 (ps)   page5 (jpg) (has the last piece and some examples.).

There are a total of 81 distinct cards in this game.

Each card has four properties:
either squares, circles or triangles; (shapes)
The shapes are either 1, 2 or 3 in number;
The shapes are either unfilled, lightly filled or full i.e. solid;
The shapes are either red, green or blue.
Thus there are total of 3x3x3x3=81 cards, with no card repeated.

The game has to do with triplets. A triplet is a set of 3 cards such that for each of the four properties above, all cards should have the property identical or all should have it different thus the following are examples of triplets:
solid red sq; solid blue sq. ; solid green sq;
1 B open circle, 2 blue open circles, 3 blue open circles
1 G open circle, 2 R hashed circles, 3 B solid circles
1 G open circle, 2 R hashed sq., 3 B solid triangles

The following is not a triplet:
1 solid B sq, 2 solid B triangles 3 solid G circles

There are 1080 different triplets possible. Each piece participates in 40 different triplets. Given any two pieces, there is a unique piece that completes the triplet.

The game is played between two (or more) players by placing 12 pieces and looking for triplets in it. Once you find one, replace those three cards with another set of 3. If there isn't any (make sure first) add three more and then look for triplets.

A harder problem (which you may enjoy solving) is to find out a set of 20 pieces such that there are no triplets in that set.


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