A professor has a repertoire of 7 jokes He will tell exactly

A professor has a repertoire of 7 jokes. He will tell exactly 3 jokes every year. He is allowed to repeat 1 or 2 of the jokes every year, but he is not allowed to repeat the same set of 3 jokes.

a. How many years will he last with his repertoire of 7 jokes?

Solution

For first year he will use 3 unique jokes out of 7.

He will left with 4 unique jokes and 3 used jokes. Now for second year, if he picks one from 3 used jokes and 2 from 4 unique jokes, he will left with 2 unique jokes and 5 used jokes but if he picks 2 from 3 used jokes and 1 from 4 unique jokes he will left with 3 unique jokes and 4 used jokes.Therefore he must go for the second option as large number of unique jokes remaining in hand will last for more years.Therefore now onwards(that is after 1 year) 1 joke decreases from unique numbers of jokes remaining every year. After 1 year he will left with 4 unique jokes which will last for 4 more years.

Therefore total number of years that jokes will last = 4 +1 = 5 years