Question

at a party 136 handshakes took place. each person shook hands exactly once with each of the others present. how many people were at the party?

Answer 1

9514 1404 393

Answer:

17

Explanation:

The number of handshakes among n people is n(n -1)/2. Then ...

n(n -1)/2 = 136

n(n -1) = 272 = 17×16*

n = 17

There were 17 people at the party.

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* This factoring can be facilitated by recognition that √272 ≈ 16.5, the number midway between the consecutive factors.