As you do more and more trials, you will find that the number approaches 14.7. This number is given by:
6/1 + 6/2 + 6/3 + 6/4 + 6/5 + 6/6 = 14.7

Similarly, it can be shown that for an eight sided die, the theoretical number (expected value) of rolls needed to get all eight sides is:
8/1 + 8/2 + 8/3 + 8/4 + 8/5 + 8/6 + 8/7 + 8/8 = 21.7

Use this pattern to find the expected number of rolls of a 12-sided die to get all 12 sides. Then use a 12-sided die, a spinner, or some other appropriate model and conduct 50 trials. Compare your estimated number of rolls of the die with the theoretical value given by this formula"*

Now that you have modelled the problem with a die and seen the theoretical expected value, try this online demonstration of the problem.

For a full analytic explanation of the mathematics behind this problem, see "The Cereal Box Problem" by Jay Wilkins (PDF file).

*From Using Statistics, by Travers, Stout, Swift, and Sextro. Addison-Wesley Publishing Company. 1985.

Interested in the mathematics of the cereal box problem?
Check out the following article by Jesse "Jay" Wilkins, Wilkins, J. L. M. (1999).
. School Science and Mathematics, 99(3), 117-123.
Click on the title to download the article in Adobe Acrobat format.

Special thanks to School Science and Mathematics, for allowing us to distrubute the article in this manner.