Finding two identical packs of Skittles among 468 packs #Candy #Math #Probability @Skittles
On the Possibly Wrong blog, discussing the likelihood of finding two identical packs of Skittles candy, re. 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.
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
The post explains how all the packages were purchased and checked.
The entire data set is available here as well as on GitHub. The following figure shows the photos of all 468 packs (the originals are 1024×768 pixels each), with the found pair of identical packs circled in red.
All 468 packs of Skittles, arranged top to bottom, in columns left to right. Each pair of columns corresponds to a box of 36 packs. The two identical packs are circled in red.
But… why?
So, what’s the point? Why bother with nearly three months of effort to collect this data? One easy answer is that I simply found it interesting. But I think a better answer is that 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.
Do you like applied math or Skittles? Let us know in the comments below.
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