Sunday, January 01, 2006
13:42
More about Set theory.
Suppose you have a collection of cards which do not contain any Sets, and you want to know the probability of randomly adding one more card and getting at least one Set. For any two cards in your collection, there is exactly one third card that, when combined with them, will form a Set. At first glance it might appear that for N cards, there would be (N choose 2) different cards that could be added which would make at least one Set. The trouble is that it's possible to have two (or more) different pairs of cards in your collection, all of which need the same card to complete them. If there are four cards, for instance, there can be either five or six new cards, each of which would form a set if added. It's possible to do all the calculations by brute force on four or five cards, but then it gets really really complicated.
Suppose you have a collection of cards which do not contain any Sets, and you want to know the probability of randomly adding one more card and getting at least one Set. For any two cards in your collection, there is exactly one third card that, when combined with them, will form a Set. At first glance it might appear that for N cards, there would be (N choose 2) different cards that could be added which would make at least one Set. The trouble is that it's possible to have two (or more) different pairs of cards in your collection, all of which need the same card to complete them. If there are four cards, for instance, there can be either five or six new cards, each of which would form a set if added. It's possible to do all the calculations by brute force on four or five cards, but then it gets really really complicated.
# posted by Fibonacci @ 1.1.06 
