Math Poster: Handshakes
Date: 08/11/97 at 19:50:52 From: Ralph Vitale Subject: Math poster I have to do a poster and figure out the question: if there are 15 people in the room and each person shakes hands with every other person, how many handshakes will there be? I don't have an answer, other than that I can start with 15 and add 7. Thank you.
Date: 08/11/97 at 21:22:01 From: Doctor Scott Subject: Re: Math poster Hi Ralph! Good question. A great way to solve some problems is to look at a much simpler example and then see if you can make a conclusion about the more complicated problem. Working with 15 people is pretty complicated. What if we tried something easier ... maybe two people. Well, let's see. If there are 2 people in the room, there would be one handshake. (Since people don't shake hands with themselves.) Okay, maybe two people was TOO simple and example. Let's try three. With three people (let's call them A, B, and C), A shakes hands with B, A shakes hands with C, and B shakes hands with C. That's it, right? Everyone has shaken hands at this point. (Notice that we don't have to say that C shakes hands with A, because we've already counted that handshake). Making this ordered list helped a lot, I think. So, there are 3 handshakes. How about four people? Well, if we call them A, B, C, and D, we would have: A-B, A-C, A-D, B-C, B-D, and C-D shaking hands. There are then 6 handshakes. Whew. It might be a good idea to start building a little table of our results: number of people number of handshakes 2 1 3 3 4 6 Okay, one more, maybe. With five people (call then A, B, C, D, and E) we get A-B, A-C, A-D, A-E, B-C, B-D, B-E, C-D, C-E, D-E, or 10 handshakes. (We can add this to our table) If you continue like this you can determine the number of shakes with 15 people. You might also continue with the table for a while, maybe for 5, 6, and 7 people, and then see if you notice a PATTERN in the number of handshakes. There seems to be one forming (I'll let you think about what it is). This problem-solving technique of looking at simpler cases and then building a table of your results is VERY important in mathematics and often helps to solve difficult problems. Good luck! Let us know if you need any more help with this problem. -Doctor Scott, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Date: 08/12/97 at 02:41:40 From: Doctor Sarah Subject: Re: Math poster Hi there - In addition to Dr. Scott's answer, you might want to look around in the Dr. Math archives for answers to similar questions. Here are some good places to start: Counting Handshakes http://mathforum.org/library/drmath/view/56513.html Handshakes at a Party http://mathforum.org/library/drmath/view/56139.html Handshake Problem http://mathforum.org/library/drmath/view/56157.html -Doctor Sarah, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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