Question

Solve the problem. An average library contains at least 50 and at most 250 books. How many library owners must be polled to be certain that at least two owners have the same number of books in their libraries?

A. 203 owners

B. 202 owners

C. 200 owners

D. 201 owners

Answer 1

Let's do a smaller example. Say there are a bunch of libraries. Each library has between 1 and 10 books.

Now say you want to poll each one and figure out how many books each library has. You also want to draw a poll where you're guaranteed to get a sample of libraries where at least 2 of them have the same number of books.

The worst case scenario is that the first ten libraries you poll will have a different amount of books than the others and that eleventh library will have some amount of books equal to another previously polled library.

Answer 2

So to summarize:

if each library has between 1 and 10 books, then you need to poll 11 libraries to guarantee that at least 2 of them have the same number of books

Answer 3

Does this example make sense?

Answer 4

so is the answer 203?

Answer 5

no, if each library has between 1 and 30 books, how many do we have to sample to guarantee that at least 2 of them have the same number of books

Answer 6

202?

Answer 7

say we have the 7 libraries A through G

library A has 1 book
library B has 2 books
library C has 3 books

etc etc