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

Assume all symbols represent positive numbers.
* = a
% = b
$ = c
@ = d
! = e

rewrite the expressions as...
1. a + b = c
2. 3c = 2d + 2b + a
3. d = e + a

now start removing variables..
a = c - b (from 1 above), therefore
d = e + (c - b) (from 3 above), therefore
3c = 2(e + c - b) + 2b + (c - b) (from 2 above)

continuing...
3c = 2e + 2c - 2b +2b + c - b
3c = 2e + 3c - b
2e = b

Carrying these to the match in question...
rewrite the expression as...
LHS <-> RHS
!@!!@! <-> %$*$

4e + 2d <-> 2c + b + a

Now, remove as many variables as possible by introducing expression ascertained above...
4e + 2d <-> 2c + b + (c - b)
4e + 2d <-> 3c
4e + 2(e + c - b) <-> 3c
4e + 2e + 2c - 2b <-> 3c
6e - 2b <-> c
3b - 2b <->
b <-> c

Back to the original expression of a + b = c ...

a is assumed to be positive, therefore c is greater than b and the RHS wins.

Posted by Daniel Ciguenza on 2003-06-26 15:24:57