### Brain Teasers

# Chess Matches

In my class there are 60 students. We decided to hold a chess tournament.

In the first phase, every one plays 6 matches each, each match with a different player.

What is the minimum number of people that will have to back out if all participants play 6 matches ONLY? Also how many matches will be played in the first phase?

In the first phase, every one plays 6 matches each, each match with a different player.

What is the minimum number of people that will have to back out if all participants play 6 matches ONLY? Also how many matches will be played in the first phase?

### Answer

The number of players that need to back out is 4. Number of matches is 168.For 6 people to play each other, a minimum of 7 people are required. So the total number of players is a multiple of 7. The nearest is therefore 56 (7x8).

Number, of matches = 7 students per group x 6 matches per student / 2 students per match x 8 groups = 7 x 6 / 2 x 8 = 168

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