Ten people have entered a chess tournament. Each person is scheduled to play every other person once. How many games are scheduled for the tournament?

Question

I do not get this. how do i figure it out 

Answer 1

This is a question to determine the possible outcomes of a scenario.

 

If there are 10 people, and each person plays every other player once, then the each player is playing 9 matches, but since there are 2 players, you have to divide this total by two, or 45 matches in total.

 

You could lay it out in a grid format as well.  Just remember, it doesn't matter if it is player 1 playing 2 or player 2 playing 1, it is the same combination:

 

Player  1  2  3  4  5  6  7  8  9  10 (Number of games not listed under another player)

         1    x  x  x  x  x  x  x  x  x   (9)

         2        x  x  x  x  x  x  x  x  (8)

         3           x  x  x  x  x  x  x   (7)

         4               x  x  x  x  x  x   (6)

         5                   x  x  x  x  x   (5)

         6                       x  x  x  x   (4)

         7                           x  x  x   (3)

         8                               x  x   (2)

         9                                  x    (1)

        10

                                                  (Total=9+8+7+6+5+4+3+2+1=45)

 

Hope this helps

Answer 2

Start with the Player 1.  He plays against every one of the other players.  That's 9 games.

 

Now take the Player 2.  He also plays against every one of the other 9 players.   You already counted the game he plays against Player 1, so how many games does he play against the other 8 players.  That's 8 games to add.

 

Take Player 3.  He also plays against every one of the other 9 players.  But again, you already counted his games against Players 1 and 2.  So this step only adds 7 games.

 

Follow this to the end and you will see that the number of games is 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45.

 

Another way to look at it is:  Each of the 10 player plays against 9 other players.  That's 90.  But if you counted this way, you'd be counting each game twice -- one for each player in the game.  So divide 90 by 2 to get the actual number of games -- 45.

 

Answer 3

I think your supposed to use this equation: (N*(N-1)) and since you play every other person once it would by (N*(N-1))/2

 

so (10*(10-1))/2 = 45 games

 

 

Answer 4

Hi Tymon,

 

We need to know how many ways you can combine 10 things taken 2 at a time

 

so,

 

we can pick the 1st person 10 ways

 

we can then pick the 2nd person 9 ways

 

and we get 10*9 or 90

 

but order is not important in this problem because if the same two people are playing each other it does not matter what order they are picked.

 

therefore we need to divide by 2

 

90/2 = 45  and this is the number of games played in the tournament.

 

Hope this helps