# A Simple Logic Problem

#### Hessakia

##### Senior member
3 people pair up and play chess together (A, B, C). Each pair plays the same number of games. For each win, a player gets 1 point and for each tie the player gets 1/2 point. No points are rewarded for a loss.

how is it possible for the following three statements to be correct?

Player A: "I'm the best because I have the most wins"
Player B: "I'm the best because I have the least amount of losses"
Player C" "I'm the best because I have the most points"

#### calbear2000

##### Golden Member
Smells a little like college homework

9 variables, 9 equations. Just plug it into a matrix solver or a linear programming application like Lindo/Lingo.

#### MAME

##### Banned
they only play against eachother?

#### Omegachi

##### Diamond Member
uh... is this for your probablity class?

#### Hessakia

##### Senior member
In all honesty, its not for any of my classes--i seen the problem posted on the wall--and i've been thinking about it all day.

#### Kyteland

##### Diamond Member
Start by picking a nice round number. Say everyone plays 100 games, 50 against each opponent.

a plays b: a wins 20, b wins 27, a and b tie 3
a plays c: a wins 21, c wins 29, a and c tie 0
b plays c: b wins 0, c wins 0, b and c tie 50

overall this gives a 41 wins, 56 losses, 3 ties, and a score of 42.5
overall this gives b 27 wins, 20 losses, 53 ties, and a score of 53.5
overall this gives c 29 wins, 21 losses, 50 ties, and a score of 54

#### marquee

##### Banned
And the school bully comes around, kicks the crap out of the chess club dorks, and claims he's the best.