Asked by sandra
At the first meeting of the chess club, the 10 members decided that everyone in the club should play everyone else one time to determine the best players for the inter-school competitions. How many games had to be played?
Answers
Answered by
Reiny
Same as the standard "hand-shake" problem
number of games = 10 choose 2
= C(10,2) = 45
In the hand-shake problem, we have 10 people and they all shake hands on meeting.
so each of the 10 people can shake hands with 9 others for 90 shakes
but that would include A shaking with D and D shaking with A, the same handshake, so we divide our 90 by 2 to eliminate all duplicate pairs.
The same argument applies to your players
Player A vs B is the same game as B vs A
number of games = 10 choose 2
= C(10,2) = 45
In the hand-shake problem, we have 10 people and they all shake hands on meeting.
so each of the 10 people can shake hands with 9 others for 90 shakes
but that would include A shaking with D and D shaking with A, the same handshake, so we divide our 90 by 2 to eliminate all duplicate pairs.
The same argument applies to your players
Player A vs B is the same game as B vs A
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