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Handshake Problem #2
Transcript of Handshake Problem #2
Loc Bui Handshake Problem #2 Assume there are 10 people in a room, including you. Each person in the room must shake hands one time, and only time with all the other people in the room. How many handshakes will occur? If there are N (where N > 0) people in the room, how many handshakes will occur? Problem If we calculate each number of hands we shake, the problem would look like "9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0". The total will be 45 hands shook in a room of 10 people. We keep going for person 3, 4, 5, 6, 7, 8, 9 and 10. From the 8 handshakes we keep subtracting one handshake for each new person. The 10th person would have no handshakes because the other 9 people have already shook his hand so there would be 0 handshakes by the 10th person. For 20 people we would do the same thing it's just we would start with 19 handshakes from person 1. The next person who shakes hands would shake 18 and the 3rd would be 17 handshakes. This would keep on going until we get to the 20th person who would shake no hands. The equation for this would look like 19 + 18 + 17 + 16 + 15+ 14+ 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0. The total amount of handshakes would lead to For N People:
We would start off the sequence as N-1 + N-2 + N-3 + ongoing until we have the last number equal to 0 (which would only happen when we have N-N). For each term we have to keep subtracting one more than the previous term. Understanding
problem - 10 people in room including self
- Each person in room must shake hands one time
- Try to define how many handshakes for 10 people, 20 people N people Planning the solution So we have 10 people right?
The first person we shake hands with, is one subtracted from the total hands we have to shake so there is now only 9 people left to shake hands with. The second person would shake with 8 people because it has already shook hands with number one and it can't shake with themselves. Reflection The process was easy but explaining it was a challenge.
Next time we would use illustrations for explaining.
The equation for problems like this is N-1 because for each person there is one less person to shake a hand with.