Handshake Problem

Number Theory Level 1

There are 10 people shaking hands, if everyone had handshakes, then how many handshakes occured?

45 10 40 300

Anuj Kumar Gupta by Anuj Kumar Gupta , 26, India

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3 solutions

This is a AP's 1 to 9, because the first person salutes 9 people, the second 8, until the last that salutes 1 person only. Thus the sum of 1 til 9 is ((1+9)x9)/2 = 45.

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I did the same way!! AP

Khushwant Singh - 6 years, 2 months ago
Sisay Terefe
Jun 27, 2017

The first person salutes 9person and the next 8...the next 7...you continue withthat simply sum the to 0....Then 9+8+7+6+5+4+3+2+1=45

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Tarun Singh
Mar 4, 2015

For 1 handshake we need any 2 people. Therefore for 10 people, we have
10C2 = 10*9/2 = 45
as the total number of handshakes.

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