Skittles
Over the last year or so, I’ve been very preoccupied with this claim on the back of all Skittles packets:
This started as a five-minute talk at Mathsjam, and has grown into a one-hour interactive talk that’s perfect for Sixth Formers. I currently run it at our Departmental Open Days but I’m very happy to come and deliver it at a school.
We use some combinatorics to work out how many different packets there are, some probability to think about the likelihood of finding a matching pair of packets, and then some statistics to test our hypotheses…
I now have data about 425 packets of Skittles (and counting): you can download it here if you’re interested.
Spoilers: the maths
This whole ordeal starts with the unlikely-seeming claim that no two packets of Skittles are the same. I’m willing to go along with the idea for the bigger (152g) bags, and maybe even for 45g bags (on which more later), but I first noticed it written on the “trick-or-treat” size bags, which are only 18g:
%picture
It seemed that in such a small bag, there couldn’t possibly be that many different variations.
After some “data gathering” %picture I established that there are either 16 or 17 Skittles in each bag.