The eccentric professor has an odd habit He only buys red gr

The eccentric professor has an odd habit: He only buys red, green, and blue books, and he keeps them in completely unordered stacks. However, he does keep track of the total number of books he owns. One day he decides to get a bookshelf so that he can put all books of one of the colors onto it. Unfortunately, when he is at the shelf store, he only knows that he has a total of 271 books, but he does not know how many books of each color he owns. What is the minimum number of books that the new shelf must be able to hold so that the eccentric professor can be sure he can put all his books of one of the colors onto it? He does not care which color it will be.

Solution

The number of red, green and blue books add up to 271.

R+G+B = 271

Now, the best case scenario would be

R = 269, G = 1 , B=1, so he would need only a space of 1 book to accomodate all books of green color, or all books of blue color.

However, this might not be the case always.

The worst case is :

R = 91, G = 90 and B = 90

So he will need space for at least 90 books to accomodate all books of one color (green or blue).

Any other combination: say R = 100, G = 86 , B = 85, will require less than 90 books\' space (in this case 85) to accomodate all books of one color (in this case Blue).

So a safe number of book space that the shelf should contain is that of 90 books, so that the eccentric professor can be sure he can put all his books of one of the colors onto it.

Answer: 90