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The handshaking problem.

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In this assignment you are going to find outhow many handshakes there are in a group of people.

To do this you need a ball of wool.One thread of wool going from one person to another standsfor the handshake the two of them make.Make sure to sit as much in a circle as you can(especially when there are a lot of people in a group).

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1. Make groups of two people. How many threads of wool are there? So how many handshakes if there are two people?

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2. Make groups of three people.How many threads of wool are there?So how many handshakes if there are three people?

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3. Make groups of four people. How many threads of wool are there? So how many handshakes if there are four people?

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4. Make groups of five people. How many threads of wool are there? So how many handshakes if there are five people?

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5. Make groups of six people. How many threads of wool are there? So how many handshakes if there are six people?

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6. Make a group of nine people. How many threads of wool are there? So how many handshakes if there are nine people?

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7. Fill in the table below:

Number of people 2 3 4 5 6 7 8 9 10handshakes

8. Do you see a pattern in the table?

9. Find a formula to calculate the number of handshakes if you know how many people there are.

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10. Use the formula to calculate how many handshakes there would have to be given in Spain in November (probably there will be 16 teachers and 36 students) if everyone shakes hands with all other people.

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11. You can see this process also as an arithmetic progression (rekenkundige rij in Dutch). Start with the first person: how many handshakes does this person have to give if there are 10 people in total? Now look at the person standing to the right: how many handshakes does this person have to give? Continue this process for all people in the circle. Now add all these numbers. What is the result?

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12. You should have found the same result as in the table of exercise 7. Now going back to the handshaking problem in Spain. It would be a bit difficult to calculate it in the same way as exercise 11. Can you find an easier way to add up all numbers from 1 to 51?

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