Last Thursday, there was a company-wide party. That morning, they put a big jar full of M&M’s (regular, not peanuts) at the lobby of the Truchard Design Center. You were supposed to estimate how many M&M’s were in there. Whoever makes the best guess, wins a $50 Gift Certificate at Best Buy (and everlasting glory).Continue reading for details on the complicated process involved in this chocolatey adventure.Step 1: What is the size of an M&M?
Find a caliber (Gustavo Castro let me use his digital caliber) and measure a bunch of chocolates. Average the sizes, calculate the volume of a single M&M. In case you’re curious: .636 cubic centimeters.
The measurements could not be repeated for verification… sample chocolates were eaten.
Step 2: What is the size of the jar?
There were no special rules about not getting near the jar. Take some measuring tape and get the perimeter of the jar, then the height of the volume occupied by M&M’s (not counting air between them – yet). Measure the thickness of the glass. Don’t forget concave base and the round corners of the jar. Then calculate the volume.
This is the jar full of m&m’s
Step 3: How much volume do the M&M’s really occupy?
Because of their unique shape, M&M’s occupy a percentage of the volume of the container when poured randomly. I didn’t calculate this… physicist Paul Chaikin and chemist Salvatore Torquato did all the hard work. I remember reading about it months ago, and Google helped me find their study. So, m&m’s poured randomly occupy 68% of the volume calculated above.
Paul Chaikin (left), professor of physics, and Salvatore Torquato, professor of chemistry, used M&M’s candies to reveal fundamental principles governing the random packing of particles at Princeton University. Photo: Denise Applewhite (2004).
With all these numbers, I came up with my answer…. 8608.9669. So I wrote 8608 and submitted my answer.
To the astonishment of everyone who saw me measuring chocolates that morning, I was almost dead on.
So how many M&M’s were really there?
The number of M&M’s in the jar was: 8609. I missed by one. I stupidly rounded down… unbelievable. Fortunately I still won the contest.
And for those who care… this is the breakdown by color (aproximate):
- 1119: Brown
- 1205: Yellow
- 1119: Red
- 2066: Blue
- 1722: Orange
- 1371: Green
[Update October 30th, 2007] Seriously people, I posted detailed instructions on how to calculate this thing. I’m not going to go solve your version of the problem if you request in the comments, no matter how nicely you ask. Now, if you send me a nice PayPal donation for the maintenance of this site, I just might :).