Math Stinger # 131
by Steve Edwards, Professor of Mathematics
Six boys live in a neighborhood, and two
of them have been stealing cars.
When asked, Allen said "Bosco and Chase".
Bosco said "Allen and Chase".
Chase said "Donald and Freddy".
Donald said "Chase and Eddie".
Freddy said "Donald and Eddie".
For some reason, Eddie couldn't be found to make a statement. In fact,
four of the boys correctly named one thief, and each of these four had
also slandered another boy. One of the boys just plain lied.
Who has been stealing cars?
This problem can be solved very simply with a little application of
graph theory. Let the boys be the vertices, and let the edges be the
determined by the boys that are paired together by an accuser.
Consider how many vertices are thieves, and how many edges these
vertices must have in total.