Wednesday, December 22, 2004
Math puzzles for the holidays
I've always been a fan of clever math puzzles, so here's one for the holidays (after which I'll get back to slagging President Smirky and his band of idiots.)
There's an old story of two pirates who chance upon a cache of mixed valuables (gems, gold, that sort of thing) and want to divide it evenly, so that no one's feelings get hurt. The puzzle is, of course, how to divide the goodies so that both pirates feel that the division was equitable. Note the careful wording here -- the division doesn't have to be exactly in half; it simply needs to leave each pirate feeling satisfied that it was fair. The solution isn't hard to figure out -- one of the pirates divides the swag into two piles, after which the other gets to pick which pile he prefers. If you think about it, it's the obvious answer -- neither pirate can cheat the other or bend the rules to his advantage.
But what if you add more people to the mix? Say you have (God help us all) a Christmas fruitcake, and an arbitrary number of people. With just a sharp knife, how can you slice the fruitcake so, once again, every single person in the group is satisfied with their slice and doesn't feel cheated compared to anyone else?
Now it's not so easy, is it?