Search this site
Another Round of Handshakes
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?
Some useful links for
- 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