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?
!@!!@!-------%$*$

Start with equations based on the matches listed as ties:

* + % = $
3$ = 2@ + 2% + *
@ = ! + *

From these, derive a few simple forms:

2* + 2% = 2$
3* + 3% = 3$
2@ = 2! + 2*

Combine these with the second given equation:

3$ = 2@ + 2% + *
3* + 3% = 2!+ 2* + 2% + *
% = 2!

Finally, compare the final match:

4! + 2@ (?) 2$ + % + *
4! + 2! + 2* (?) 2* + 2% + % + *
6! + 2* < 6! + 3*

Therefore, the right-hand side wins by a *.

There are any number of numerical values that can be assigned to the characters. ! and * can be assigned any arbitrary values, including zero, with no regard to which is greater.
% is then twice !, @ is the sum of ! and *, and $ is the sum of % and *.

It should be noted that while negative values also fit the system algebraically, if * is assigned a negative value, then naturally the left-hand side wins instead of the right (the right has an extra person).

Posted by DJ on 2003-06-22 23:34:56