Book by

William Gasarch, Erik Metz, Jacob Prinz, Daniel Smolyak

Consider the following problem:

You have 5 muffins and 3 students.

You want to divide the muffins evenly so that everyone gets 5/3 muffins.

You can clearly divide each muffin in 3 pieces and give each person 5/3.

NOTE- the smallest piece is of size 1/3.

Is there a procedure where the smallest piece is BIGGER than 1/3?

Can we get exact bounds?

(Spoiler Alert: Yes and Yes)

What about 3 muffins and 5 students?

You want to divide the muffins evenly so that everyone gets 3/5 muffins.

You can clearly divide each muffin in 5 pieces and give each person 3/5.

NOTE- the smallest piece is of size 1/5.

Is there a procedure where the smallest piece is BIGGER than 1/5?

Can we get exact bounds?

(Spoiler Alert: Yes and Yes)

The two problems above are easy in that I suspect you could solve them.

They lead to a technique called The Floor Ceiling Method.

Does the Floor Ceiling Method solve all cases?  No.

The first case it fails on is 11 muffins, 5 students. That lead to The Half Method.

The first case that neither the Floor-Ceiling Method, nor the Half method worked on is....

        COME AND FIND OUT!

In our book, and in this talk, we discuss many techniques to solve

such problem for the general case of m muffins and s student.