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?
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
To determine the number of games that need to be played, we can use a simple formula: the number of games equals the total number of members multiplied by the total number of members minus 1 divided by 2.
In this case, we have 10 members. So, we can substitute that into the formula as follows:
Number of games = 10 * (10 - 1) / 2
= 10 * 9 / 2
= 90 / 2
= 45
Therefore, 45 games need to be played in order for each member to play against every other member once.