Pigeonhole Principle: A professor tells 3 jokes each year...

G

Guest

Guest
Can't figure this one out:

A professor tells three jokes in her ethics course each year. How large a set of jokes does the professor need in order to never repeat the exact same triple of jokes over a period of 12 years?

Any help is appreciated
 
We must assume that she teaches only one ethics section per year.
The number of subsets of three from five is \(\displaystyle {5 \choose 3} = 10\) so five jokes are not enough. So what is?
 
Suppose that she has 4 jokes, {A,B,C,D}.
She can use: {A,B,C}, {A,C,D}, {A,B,D}, or {B,C,D}.
That is, she can tell four different sets of three jokes from the same four jokes.
If she adds one more joke, five in all, she has 10 sets of three jokes from five.
So in 12 years she must repeat at least one of the set, RIGHT?
Thus, what is the least number of jokes does she need?
 
You must log in or register to reply here.
Top