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.

If the smaller army has n knights, then given even odds, n knights in the opposing army will die to defeat them (-1 for the last knight)

So the remaining number of knights seems like it should be A-B+1

In the proposed example

500 300

350 150

275 75

238 38 (rounding up)

219 19

210 10

205 5

203 3

202 2

201 1

201 0

Posted by Bob Smith on 2005-08-23 03:15:02