Resisting the pull of cynicism since 1969.

Sunday, September 18, 2005

A story problem

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!

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!

Germany: Amateurs.
And now, for you mathematical whizzes out there, a story problem, brought to you by the letters 'o', 'my', and 'god':

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?

4 comments:

Matt said...

I strongly suspect that Angie and George are going to end up having to play together. The big question is which one of them gets to shoot their marble first (i.e. which one claims the title of Chancellor). I think that Josh will be along for the ride as well. Talk about a nightmare governance situation, even with proportional representation!

gnackwatschn said...

George is never going to play with Oscar.

I also suspect that Angie and George are not going to play with each other, simply because George has much more to gain in the long run if he sits this one out and plays a different game for the next few years, rather than play with Angie. He'd really be stupid to play with Angie, actually.

Guido has much more to win with George: he can claim that he's influenced the mighty George, and George in turn can defend himself against his supporters by arguing that whatever nasty tricks they are going to play are all Guido's fault. It's a perfect match, strategy-wise. With Angie, on the other hand, Guido would drown. They're just not different enough so that he could distinguish himself as a player.

Josh, who might be replaced by a different team leader, will more likely play with George than with Angie, so my guess is that they're going to form a nice marble streetlight - George, Guido and Josh (or his replacement).

Idealistic Pragmatist said...

Matt,

I'm with you -- either George and Angie are going to have to be forced to play together (which means deciding which one of them makes the rules; never a good prospect when you're dealing with control-freak kiddies), or else they're going to have to call for a new, erm, distribution of marbles.

gnackwatschn,

You're right, George would never play with Oscar. George would probably play with Greg before he'd play with Oscar. I think he'd be willing to play with Angie, though, as long as she shuts up and plays by his rules. Which doesn't seem terribly likely.

You have a good point about Guido, too. Hmm.

I think Josh should consider playing with Angie. Not that I actually think it would be a decent outcome, of course; I just think the world needs to hear the word 'Schwampel' a few more times. ;-)

tom said...

Thank you, very interesting!