Consider two opposing armies of knights armed only with swords. The sizes of these armies are 500 and 300 knights.

When locked in combat with an enemy each knight has even odds of winning or losing. Knights, being chivalrous, prefer single combat and will not double up on their enemies. The extra knights in the larger army will wait until there is a free enemy to fight.

[Essentially the killing power of the larger army is proportional to the size of the smaller army.]

When the dust settles the smaller army is eliminated. How many knights (are expected to) remain in the larger army?

Generalize for two armies of size A and B where A>B.

okay, so i haven't really thought this through, but my first inclination is that there would be 200 knights left in a battle of opposing forces of 300 and 500 knights. Because each knight has an equal chance of winning and losing you assume that half of the smaller knights win and half of them lose. Thats all good and dandy, but eventually all of the smaller knights have to die, so i just assumed that each one of the smaller knights would take one larger knight with them, allowing one victory and one defeat for each of the smaller knights... Wouldnt that make sense? But now that i think about it I dont quite agree with myself, but oh well....

Edited on August 23, 2005, 2:31 am

Posted by sean on 2005-08-23 02:28:50