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

Since $ = * + % (eq. a)
Then $ + $ + $ = @ + % + * + % + @ (eq b)
can be converted to $ + $ = @ + % + @
by subtracting equal terms from both sides
gathering like figures we get:
2 ($) = 2(@) + % (eq. d)

Devide both sides by 2 you get
$ = @ + %/2

since eq (a) tell us $ = * + %
we can combine to get
@ + %/2 = * + %
which simplifies to
@ = * + %/2
eq. c tells un @ = ! + *
therefore
* + %/2 = ! + *
simplifies to
%/2 = ! or 2(!) = % (eq. e)

so when !+ @ +! + ! + @ +! faces % + $ + * + $
using equation e we can say

% + % + @ + @ is facing % + $ + * + $

equation d lets us then say that

% + % + @ + @ is facing % + % + @ + @ + *

since % + % + @ + @ cancels form both sides we can see that the right side wouls win

sorry if this is not elegant but it is how my brain worked it out

Posted by FatBoy on 2003-08-14 08:43:26