I was surprised this time to see only one correct answer from Alok Kuchlous, one of the best puzzle solvers I have known since my IIT days. I also got a very good attempt from Shruti Mittal (from Mumbai), but was not a completely correct answer.

I liked the question as it can explain some very basic concepts about “odd” and “even” to children. Here is the solution:

If you add up the number of handshakes by each person, then the final number has to be even – this is because each handshake results in a count of 2. If the number of people with odd number of handshakes is odd, then the final number of handshakes will be:

odd * odd + even * whatever = an odd number + an even number = an odd number, which cannot be true.

Hope you enjoyed the puzzle!