Graph Theory: The same 5 people as last week decide to shake
hands with a different number of people, that is, one with 4
people (you can't shake with 5 - that would include shaking hands with
yourself), one with 3 people, etc. Is this possible?
Math Factor podcast
Answer available
June 29,
next
puzzle
Answer to math puzzle of
June 15:
Graph Theory: There are 5 people at a party. Is it possible for each
person to shake hands with 3 other people?
Math Factor podcast
Solution: this is equivalent to placing 5 dots on a paper and
connecting each with 3 other dots. If this were possible, then there
would be 15 ends to the lines connecting the dots, each end at a dot.
But each line has 2 ends, so there should be an even number of ends of
the lines. Therefore, it is NOT possible for each person to shake hands
with exactly 3 other people. In general it is not possible for each
person in a finite group of an odd number of people to shake hands with
an odd number of others in the group.
For
more math puzzles, check out
http://www.mathpuzzle.com/,
http://mathschallenge.net/,
http://www.princeton.edu/~mathclub/puzzles4.html
and
http://mathforum.org/k12/k12puzzles/
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