Question
Hillside has 12 teams. Each team plays each other teams twice. How many games are played?
Answers
Daisy205
I think 24
Reiny
that would be C(12,2) = 66
Sandy
I am getting 264
Reiny
You are wrong.
Think of it this way:
Each of the 12 teams can play against the other 11 teams, that would would be 12x11 = 132
But each of these has a double,
e.g team A plays team B is the same game as team B vs team A
so we have to divide our 132 by 2 to get 66.
Trust me, 66 is the correct answer.
Google "handshake problem"
Think of it this way:
Each of the 12 teams can play against the other 11 teams, that would would be 12x11 = 132
But each of these has a double,
e.g team A plays team B is the same game as team B vs team A
so we have to divide our 132 by 2 to get 66.
Trust me, 66 is the correct answer.
Google "handshake problem"
Damon
but they each play twice so double it
Sandy
132i. Is not the right answer
Sandy
12 x 22= 264
Sandy
11 games x 12 teams doubled, because each team plays the same amount of games twice = a total of 264 games
Bethany
This question can be solved in two ways:
1. 12 X 11. If you make a table, you can see why this works. For the first column, number 1 plays against 11 teams. There should be 12 columns for 1-12. When you organize it this way, each team plays each other twice. Think about if there were two teams who each played each other twice. You would have 2X1. You would not divide by 2 because this would leave you with 1. Now think of three teams. Most people would be easily able to see that this is 6 in their head. It is the same concept.
2. The second method, which is a little trickier, is to divide factorial of 12 by the factorial of 12-2. This gives us the factorial of 12 divided by the factorial of 10.
1. 12 X 11. If you make a table, you can see why this works. For the first column, number 1 plays against 11 teams. There should be 12 columns for 1-12. When you organize it this way, each team plays each other twice. Think about if there were two teams who each played each other twice. You would have 2X1. You would not divide by 2 because this would leave you with 1. Now think of three teams. Most people would be easily able to see that this is 6 in their head. It is the same concept.
2. The second method, which is a little trickier, is to divide factorial of 12 by the factorial of 12-2. This gives us the factorial of 12 divided by the factorial of 10.
Robb
The Answer is 198