Question

You have just arrived at summer camp. And your cabin, the counselor has each camper perform the super secret handshake with every other person in the cabin. You and another person or in the cabin, so there is one handshake. Another person arrives, and another, until there are 14 people in the cabin. How many handshakes will there be an all?

Answer 1

Just try to follow my description. When two persons are in the cabin, there is only 1 handshake. When a third person comes, he will have to handshake the two people who came before him. So, there will be 2 handshakes. When a fourth person comes, he would make 3 handshakes with the 3 people who came before him. When the fifth person comes, he would make 4 handshakes with the 4 people who came before him. So, you see there is a pattern. The number of handshakes is 1 less than the total number of people inside the cabin. So, if there are 14 people in the cabin, the last person to come in would have to make 13 handshakes with the 13 people who came in first. Obtaining the sum of all the handshakes starting from the 2 handshakes initially to the 13 handshakes, the sum would be

Total handshakes = 2+3+4+5+6+7+8+9+10+11+12+13
Total handshakes = 90

Therefore, there will be a total of 90 handshakes made within the cabin of 14 people.