This is yet another handshake puzzle, and again from one of the Martin Gardner collections. This one is from Second Book of Mathematical Diversions and Puzzles…Martin Garder, Page 55
Here is the puzzle:
Prove that a t a recent convention of biophysicists the number of scientists in attendance who shook hands an odd number of times is even. The same problem can be expressed graphically as follows. Put as many dots (biophysicists) as you wish on a sheet of paper. Draw as many lines (handshakes) as you wish from any dot to any other dot. A dot can “shake hands” as often as you please, or not at all. Prove that the number of dots with an odd number of lines joining them is even.
Note: A good way for children to try this puzzle will be to try out within your family, and let them figure out why this is happening.
As always, please send your answers directly to me at firstname.lastname@example.org and if you like the puzzle, please share with others.