Technology in Mathematics Education
Winter 2005, Volume 5, Issue 2
Jerry and the Doughnuts
The title almost sounds like a 60s band. Anyway, Jerry's talk was well received.
The costuming was amusing, but I was somewhat taken aback as I expected to get some Krispy Kremes. Jerry always treats us well - he's almost like a father to us. In fact, I think of us in the math group as Jerry's kids. Be that as it may, during a doughnut craving, I started thinking about this problem. I first of all found a historical perspective. Bernoulli presented the following in Ars Conjectandi:
Let two increasing arithmetic progressions be formed,
the first starting from the number of things to be combined, the other from unity, in both of which the common difference is unity, and let each have as many terms as the degree of the combination has units. Then let the product of the terms of the first progression be divided by the product of the terms of the second progression, and the quotient will be the desired number of combinations.
Certainly, Jerry's explanation was a lot clearer. I was then interested in a generalization and the numbers involved with different numbers of varieties. The generalization was clear from the presentation:
The number of combinations of n items taken r at a time is given by
For the doughnut problem, this formula would be used if there was only 1 of each variety. However, the doughnut problem assumes an inexhaustible supply of each variety. So, as Jerry clearly showed:
The number of combinations of n items taken r at a time for an inexhaustible supply is given by
Jerry considered 6 varieties (including coconut which he does not like). The Krispy Kreme website shows 29.
Editor: Scott S Albert
Critical Thinking in Mathematics Education
The following is a table of the number of selections for varieties from 1 through 29, assuming a dozen are purchased.
I believe this sequence of values should be named the Krusinski sequence
Fun With Numbers