I've been stumped on this problem all weekend:
A candy factory has an endless supply of red, orange, yellow, green, blue, and violet jelly beans. The factory packages the jelly beans into jars of 100 jelly beans each. One possible color distribution, for example, is a jar of 58 red, 22 yellow, and 20 green jelly beans. As a marketing gimmick, the factory guarantees that no two jars have the same color distribution. What is the maximum number of jars the factory can produce? (Hint: Think of lining up the jelly beans, by first placing the red ones, then the orange ones, etc. You also place 5 dividers to indicate where one color ends and another starts. Note that two dividers can be adjacent if there are no jelly beans of some color.)
What do you think?