Alice Posted November 20, 2012 Share Posted November 20, 2012 This is a problem from the 4A IP book, the end of year review challenging problems. (US Edition if that matters) A number of tennis clubs are taking part in a competition. Every team in the competition has to play every other team just once. How many games will there be altogether if 80 teams take part in the competition? The way my son and I did it is to say 80 x 79 and then divide by 2. The answer key in the book has 80 x 78 and then divide by 2. I can’t figure out why they multiple by 78 so I’m thinking it must be an error, but I’m not confident enough to be sure. I looked on the Singapore website and it is not listed as a known error. A similar problem right above this one is: There were 25 people at a birthday party. Each person shook hands exactly once with each of the others. How many handshakes were exchanged at the party? We said 25 x 24 and divided by 2. The book had the same answer, which makes me think even more that the problem with the teams is an error since they are the same principle. I’m just wondering if there is some other detail I’m missing. Thanks! Quote Link to comment Share on other sites More sharing options...
boscopup Posted November 20, 2012 Share Posted November 20, 2012 I think you're right. Each team plays 79 teams, since you don't play against yourself. So that's 80x79. And then you only count a game once, so it's 80x79/2. We've had similar problems in CWP5, and it was done the same way. I think it's an error. Quote Link to comment Share on other sites More sharing options...
Alice Posted November 20, 2012 Author Share Posted November 20, 2012 Thanks for answering. I went back and looked at it again and am also convinced it’s an error. Quote Link to comment Share on other sites More sharing options...
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