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Learning about graphs, formulas with movement

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- 1. The handshaking problem. 28-10-2014
- 2. In this assignment you are going to find out how 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 stands for 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). 28-10-2014
- 3. 28-10-2014
- 4. 1. Make groups of two people. 28-10-2014 How many threads of wool are there? So how many handshakes if there are two people?
- 5. 2. Make groups of three people. 28-10-2014 How many threads of wool are there? So how many handshakes if there are three people?
- 6. 3. Make groups of four people. 28-10-2014 How many threads of wool are there? So how many handshakes if there are four people?
- 7. 4. Make groups of five people. 28-10-2014 How many threads of wool are there? So how many handshakes if there are five people?
- 8. 5. Make groups of six people. 28-10-2014 How many threads of wool are there? So how many handshakes if there are six people?
- 9. 6. Make a group of nine people. 28-10-2014 How many threads of wool are there? So how many handshakes if there are nine people?
- 10. 28-10-2014
- 11. 7. Fill in the table below: 28-10-2014 Number of people 2 3 4 5 6 7 8 9 10 handshakes 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.
- 12. 10. Use the formula to calculate how many handshakes there 28-10-2014 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.
- 13. 28-10-2014
- 14. 11. You can see this process also as an arithmetic progression 28-10-2014 (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?
- 15. 12. You should have found the same result as 28-10-2014 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?
- 16. 28-10-2014
- 17. 28-10-2014

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