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.

(In reply to Intuitive Solution by Bob)

The catch which required the over complication is the problem parameter that the larger army wins.  In the case where the outcome is not known, you are exactly correct (if you consider that when the smaller army wins, the larger amry ends up with ~negative~ knights equal to the number of actual smaller army knights left).  When you remove the (unlikely) possibility that the smaller army wins, the ending numbers are affected.

Posted by Cory Taylor on 2005-08-24 16:17:25