12 man participate in work Recruitment Service. Each participant saw every other participant and shook his hand.

How many handshakes took place?

  • 1
    $\begingroup$ I have edited your question to make the English clearer. Please check if it still matches your intent. $\endgroup$ Jan 10, 2015 at 10:32
  • $\begingroup$ Please use appropriate tags. There is no need for a question to have a minimum(and maximum) of 5 tags. $\endgroup$
    – Spikatrix
    Jan 10, 2015 at 10:49
  • $\begingroup$ mathsisfun.com/combinatorics/combinations-permutations.html $\endgroup$
    – A E
    Jan 10, 2015 at 16:04
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    $\begingroup$ This is a standard combinatorics question that belongs on Mathematics SE instead. $\endgroup$
    – xnor
    Jan 10, 2015 at 18:52
  • $\begingroup$ @xnor he should still accept an answer. $\endgroup$
    – warspyking
    Jan 11, 2015 at 11:30

2 Answers 2


This is just math...


The numbers each represent a person. When we move on to person 2, he does not shake 11 times. He'll shake 10, due to already shaking with 1 earlier. This will repeat, which makes the equation super simple:


(0 because by the time it's 12's turn he's shaken with everyone already)
Which comes out to be:



66 handshakes will go down between those 12 men. 78 if people shake their own hands (lol)


This one is easy.

Each person needs to shake hands with 11 other participants and the total number of participants are 12. So the total number handshakes that took place would be

11x12=132 handshakes

But then there are some people who have shook their hands twice! So just divide the answer by 2 thus giving us

132/2=66 handshakes

and that is the answer. This is done because the first participant shakes their hand with 11 other participants,the second participant shakes their hand with 10 other participant(-1 because he has already shook hands with the first participant) and so on.. Thus the answer is

11+10+9+8+7+6+5+4+3+2+1+0=66 handshakes

The +0 in the answer is because the last participant has already shook his hands with all the other participant and so he does not have to shake hands with anyone.

  • $\begingroup$ Cool Guy in your method some people shake twice. If person A shakes with everyone and the person B does the same, A and B have shaken twice. See my answer. $\endgroup$
    – warspyking
    Jan 10, 2015 at 10:50
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    $\begingroup$ @warspyking , Your answer includes all the participants shaking his own hand.... $\endgroup$
    – Spikatrix
    Jan 10, 2015 at 11:08
  • $\begingroup$ Snap didn't even see that lol. $\endgroup$
    – warspyking
    Jan 10, 2015 at 11:09
  • $\begingroup$ Thank you, I've fixed my answer (Unless shaking their own hand is part of a trick or something.) $\endgroup$
    – warspyking
    Jan 10, 2015 at 11:10

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