There is a tug-o-war competition consisting of rounds upon round that all end in a draw meaning both sides end in equal strength. There are several people of exactly equal strength and are represented by the same symbol. (i.e. all * pull the same, but a * and a @ must be different) Each team is representeed by a series of symbols followed by a dashed line being the rope. On the other side of the rope is the team that was equally matched in strength. Here are some of those rounds:
*%-----$
$$$-------@%*%@
@-------!*
Again remembering that ll of the above are ties, and assume that position on the rope doesn't matter, who will win the following match?
!@!!@!-------%$*$

(In reply to solution by Chii)

MAthematically, this works, but why must we assume that * and % are equal? Couldn't they be say, * = 70 and % = 30?

If so, then we can figure out that @ = 85 and ! = 15.
It still works, since 230 < 300, but number substitution isn't a valid proof, because we haven't demonstrated that our solution works for all number sets. In fact, your solution brings up an interesting point. If we continually make the % higher, we get closer and closer to equality. For instance, if % = 99, we get 299 , 300, and if we use 99.9 for % we get 299.9 < 300. This seems to indicate that as * approaches 0, (where % would then equal $ and @ = ! = $/2), the sides approach equality. You could argue that since someone on a side must have some mass or strength, and so a value can never reach zero, that this equality is an impossibility, and I would agree--except for maybe my daughter =-)

Posted by Jim C on 2003-07-03 07:33:42