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Another Round of Handshakes

Arm extended to shake hands

In the May 2013 teaser I had recounted the handshaking tale of the class of '80 at a reunion. On that occasion everyone had shaken hands with everyone else exactly once and there were 1225 handshakes in all. At that time I was left tearing my hair out while trying to figure out how many people were present from the number of handshakes.

Recently I had to pull out my remaining hairs while trying to figure out how many people were present at a party from the number of handshakes. In fact, I would have been happy if everyone in this party too had shaken hands with everybody else because I knew how to work that out. But here, each person shook hands with exactly three others.

That was only some unncessary background. Here is the actual question:

A certain number of people meet at a party. Each of them shakes hands with exactly three others (not a handshake more and not a handshake less). There were 24 handshakes in all. Can you tell me how many people were there at the party?






Click here for the solution


Some useful links for
your career:


  • Union Public Service Commission - www.upsc.gov.in
  • IIT-Kharagpur - www.iitkgp.ac.in
  • Indian Statistical Institute - www.isical.ac.in
  • Indian Institute of Technology Madras - www.iitm.ac.in
  • Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
  • Indian Institute of Mass Commission - www.iimc.nic.in
  • IIT Bombay - www.iitb.ac.in
  • Indian School of Mines, Dhanbad - www.ismdhanbad.ac.in
  • Birla Institute of Technology, Ranchi - www.bitmesra.ac.in
  • Central Institute of Fisheries Nautical and Engineering Training - www.cifnet.nic.in
  • Indian Institute of Information Technology, Allahabad (Deemed University) - www.iiita.ac.in
  • Central Marine Fisheries Research Institute, Kochi - www.cmfri.com
  • Tata Institute of Social Sciences, Mumbai - www.tiss.edu