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| Tug-o-war (Posted on 2003-06-21) |
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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?
!@!!@!-------%$*$
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Submitted by Jon
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Rating: 3.4545 (11 votes)
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Solution:
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(Hide)
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%$*$ would win.
Suppose each symbol has its own numerical value. Using system of equations, you can find out there relations to eachother. Here is my step by step answer. Anything marked by parenthesis is used later.
Match 1: *+%=$
Match 2: 3$=2@+2%+*
--> $+*+%+*+%=2@+2%+*
--> $=2@-*
Match 3: @=!+*
--> $=@+!+*-*
--> ($=@+!)
--> *+%=2!+*
--> (%=2!)
Now we use the two parenthesised equations to substitute in the final match.
Final match: 4!+2@ --- 2$+%+*
--> 4!+2@ --- 2(@+!)+(2!)+*
--> 4!+2@ --- 4!+2@+*
The right side is the victor by one *. |
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