Question

You have just arrived at summer camp in your cabin the counselor has each camper perform the super secret handshake with every other person in the cabin you want another person or in the cabin so there is one handshake another person arrives in another until they’re 14 people in the cabin how many handshakes will tThere be an all

Answer 1

Initially there is Counselor in the room when the first person arrives.

the person shakes hand with the counselor.

So there is 1 hand shake.

Now the second person arrives and he shakes hands with two persons already in the cabin.

So there are 2 handshakes

So the number of handshakes depends on the number of the person entering.

Now as Counselor was already present and we want 14 persons to be present in the cabin, so only 13 persons shall be entering the cabin.

Hence the total number of handshakes = 1 + 2 + 3 + .....+ 13

The formula to find the sum of n natural numbers is $\frac{n(n+1)}{2}  $

hence the sum of 13 numbers shall be $\frac{13(13+1)}{2} =91$ handshakes.

There shall be 91 handshakes in all.