## Saturday, September 26, 2009

### The Secret Meeting

At the recent UN meeting, president Obama decided to invite a number of other party leaders for a private meeting. No one knows who exactly and how many people were invited to this secret meeting, but rumor says it that a lot of handshaking was going on there. Every leader entering the meeting was approaching everyone already present in the room and shaking hands. Obama mused that something around 78 handshaking moments have happened at this meeting. How many people were invited?

Submit your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

naama said...

13

Maria said...

That is right.
First shakes 1 hand, second 2, third 3 etc till the last person comes and shakes hands with everyone present. If there are N people, last person does N-1 handshakes.

This puzzle could be solved by slowly adding up numbers 1+2+3+ .... till the sum is 78. The last number will be 12, meaning that the last person will shake 12 hands. So, we have 13 people total.

Alternatively, you can write an arithmetical progression:
1+2+3+...+ (N-1)
the sum of it is:
1 + (N-1) * (N-1) /2 = 78
and the you solve this quadratic equation and find N=13.

Whatever Naama did, she is right and she get her first point in our Marathon.