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Cocktail Party

You are observing a cocktail party that has seven guests. You notice that each guest shakes hands with one another once they meet, but never again. How many handshakes occurred during the cocktail party?

Many people quickly rush to the answer of 42 since 7(7-1) = 42. However, you must remember that once person A shakes hands with person B, person B does not re-shake hands with person A again. Therefore, the solution become (7(7-1))/2 = 21, or 1+2+3+4+5+6 = 21.


surya prakash singh

7c2 = 21

Majeed Siddiqui



I think the answer shall be 8 * (8 - 1) / 2 = 28. Since the question says 'YOU are observing ... has seven guests' therefore there should be 8 people in total...

Sounds like trolling...


A fun way to solve this, since it's only 7 guests, is to construct a complete graph (k7). Then all you need to do is count up the edges.



Interesting approach. Combinatorics also works nicely.


Simple combination: 7! / ( 2! * (7-2)! )

Anand Kumar




Anubhv Yup Pii Moon's

1-6 2-5 3-4 4-3 5-2 6-1 count the right side numbers ( 6+5+4+3+2+1)=21


the answer is probably something like 21




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Submitted by
over 5 years ago
Difficulty 2.4 ?

mathematics number theory