I would like to thank everyone that read last week's post and either commented or left a calculation or guess about how many M&Ms were in the 1/3 measuring cup. The winner was Russ the Librarian who submitted an outright guess of 72. I will be mailing him a king size bag of M&Ms this weekend. The correct answer was 71 and was illustrated above the contest photo in my photo showing the 'statistical analysis' of color distribution.
What I liked most about the many answers was how they collectively reflected the activity of science. Some started with guesses. Others tried to form a methodology for guessing. Several tried to find prior research to aid them. And some even tried to duplicate the 'experiment' -- although no one actually had M&Ms or my stainless steel measuring cup.
This last technique of attempting to duplicate an experiment to achieve the same or similar results is one of the foundations of science. If an experiment can't be repeated, the results have to be re-examined. In this case, the factors that led to difficulty were not the candies themselves, although no one actually measured any M&Ms. Rather, the very small volume, the shape of the measuring device, and the meniscus or crown of candies extending beyond the top of the measuring cup all made it difficult both to calculate and to duplicate.
Also, those who went to the internet and found 'prior research' were also acting the way scientists often do. Sometimes the role of science is to re-invent the wheel and sometimes it is to discover the properties of the wheel in the first place. Garrett found an accurate and usable formula for estimating candy. However, he forgot to include the volumetric correction -- so note to all aspiring scientists: when you do your homework, do your homework! Despite making the small error of leaving out the volumetric correction, Garrett went right back at the problem with a new methodology. And, although he did not have any M&Ms in the house, he used what he had available and measured chocolate chips for a very credible estimate that was closer to the correct answer than the answer he calculated in his first attempt. Well done. That kind of persistence and problem solving will serve him well as a scientist.
Jay counted the visible candies, estimated the number of layers, and multiplied the two together for another quite close approximation. A great method! Similarly, Stephanie counted colors and used the statistical distribution photo in an attempt to approximate the number. A creative and ambitious method -- I'm terribly sorry if I led her astray with my assumption the the distribution is both even and random.
Finally, Cheryl pointed out that my assumption that the distribution is even was false. The peer review process is crucial to conducting science. Sometimes in science you just can't see the forest for the trees. I am grateful for all who read and posted! Until next week, keep your science hats on... And Russ -- check your mailbox soon!
Read the original candy science post Science Dad on What to Do with All That Candy