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Grouping Games

We have thoroughly studied various ways to order elements. In this chapter, we’ll study various ways to group elements. We got a taste of the tasks involved in grouping elements when we studied hybrid games, which both order and group items.

Because grouping games partition elements into sets, the number of elements is often an issue. As mentioned before, counting can be challenging. This tends to make grouping games more difficult than ordering games.

Pay close attention to the maximum or minimum number of elements in a group; this is often the heart of the game.

Grouping games can be classified as those that partition the elements into 2 groups, and those that partition the elements into 3 or more groups. The former are sometimes called selection games because they “select” elements from a pool, dividing the pool into two groups: those selected and those not selected. The example on the next page will illustrate.

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