The Cookie Problem

Here’s a problem that was presented to me in Math Enrichment. It’s main purpose is to guide an investigation of infinite series.

Part 1:

The cookie monster sneaks into the kitchen and eats half a cookie; on the second day he comes in and eats half of what remains of the cookie from the first day; on the third day he comes in and eats half of what remains from the second day. If the cookie monster continues this process for seven days, how much of the cookie has he eaten? How much is left?

Part 2:

Problem: Share 6 cookies among 7 people. Restrictions: You cannot use 6/7 or any non-reduced form of that fraction. Find a way to use the sum of an infinite series.

(Obviously, the cookies must be divided equally.)

Here is my 9-page, illustrated solution in PDF format.