1 Alfred, Ben, Charles and David meet, and some handshaking takes place.
- Alfred shakes hands with David.
- Ben shakes hands with Charles and David.
- Charles shakes hands with Ben and David.
- Complete the bipartite graph in your answer book showing A (Alfred), B (Ben), C (Charles) and D (David), and the number of people each shakes hands with.
- Explain why, whatever handshaking takes place, the resulting bipartite graph cannot contain both an arc terminating at 0 and another arc terminating at 3 .
- Explain why, whatever number of people meet, and whatever handshaking takes place, there must always be two people who shake hands with the same number of people.