A friend of mine was speculating this afternoon that the world may well be in the midst of some sort of cosmic electoral weirdness oneupsmanship. It goes something like this:
USA: We have an undecidable election going before the Supreme Court!And now, for you mathematical whizzes out there, a story problem, brought to you by the letters 'o', 'my', and 'god':
Ukraine: Oh, yeah, well, one of our candidates poisoned the other with Dioxin!
Canada: Oh, YEAH? Well...we're all switching sides! It's musical parties! And--GO!
Five kids want to play a game of marbles. They need at least fifty marbles to play, and the game allows for an unlimited number of participants. Nobody's allowed to loan their marbles to anyone else.
Angie Black has 35 marbles.
George Red has 34 marbles.
Guido Yellow has 10 marbles.
The twins, Oscar and Greg Crimson, have 9 marbles between them.
Josh Green has 8 marbles.
Angie would most like to play with Guido, and utterly refuses to play with the twins. She would prefer not to play with Josh or with George, but she'd rather do that than not play at all.
George would most like to play with Josh, and has said he would never play with the twins. He doesn't want to play with Guido or Angie, either, but again, would rather do that than not play at all.
Guido used to play very nicely with both Angie and with George, but at different times. Recently he's been hoping to play with Angie and promising never again to play with George, but he's a fickle sort and would probably break that promise if he absolutely had to. He's also willing not to play at all, if it comes to that. He would never dream of playing with the twins.
The twins don't really want to play with anyone (they're happy just to stand on the sidelines taunting Angie, Guido, and George), but they would probably entertain a quick little game with Josh or maybe even George (especially if nobody was looking).
Josh would most like to play alone with George, but he knows that's hopeless. He hasn't promised not to play with anybody else, but he doesn't really get along very well with anyone but George and would prefer to sit this one out if he can't play with him. But in a pinch, he could probably be talked into a game with at least some of the others.
What combination of children (and marbles) would make the largest number of them happy?