“Follow-Up: I Found Two Identical Packs of Skittles, among 468 Packs With a Total of 27,740 Skittles”, 2019-04-06 (; similar):
This is a follow-up to a post from earlier this year discussing the likelihood of encountering two identical packs of Skittles, that is, two packs having exactly the same number of candies of each flavor. Under some reasonable assumptions, it was estimated that we should expect to have to inspect “only about 400–500 packs” on average until encountering a first duplicate. This is interesting, because as described in that earlier post, there are millions of different possible packs—or even if we discount those that are much less likely to occur (like, say, a pack of nothing but red Skittles), then there are still hundreds of thousands of different “likely” packs that we might expect to encounter.
So, on 12 January of this year, I started buying boxes of packs of Skittles. This past week, “only” 82 days, 13 boxes, 468 packs, and 27,740 individual Skittles later, I found the following identical 2.17-ounce packs.
…this seemed like a great opportunity to demonstrate the predictive power of mathematics. A few months ago, we did some calculations on a cocktail napkin, so to speak, predicting that we should be able to find a pair of identical packs of Skittles with a reasonably—and perhaps surprisingly—small amount of effort. Actually seeing that effort through to the finish line can be a vivid demonstration for students of this predictive power of what might otherwise be viewed as “merely abstract” and not concretely useful mathematics.