Hein (fub) wrote,

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Math challenge

OK, here's a mathematical challenge for people who remember more of Discrete Math than I do. It's about the cardgame of Set!, for which I have written a program for single-player puzzles. It'll be released after I've ironed out a few more kinks.

Anyway, Set is played with cards. Each card has four features, and every feature has three values:
- Color (red, green, purple);
- Shape (square, oval and 'wavy thing');
- Filling (empty, full and 'with spots');
- Number of items (one, two or three).
Each card occurs only once, so there are 3^4 = 81 cards.

The purpose of the game is to create sets. A set consists of three cards, with, for each feature, the same values or three different values.
An example set could be:
One green empty square and two red empty ovals and three purple empty waves.
Colors, shapes and numbers are all different, filling is the same for all three cards.

Your mission, should you choose to accept it, is to construct a group of fifteen (15) cards with not a single valid set within that group.

This post will self-destruct in five seconds.

EDIT: It seems that the maximum number of cards without a single set in 'em is 20. Look here for a proof. But don't let that stop you from devising your own proof. ;)

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