How many M&M’s are in the jar?
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, above 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 post it. Now, if you send me a nice PayPal donation for the maintenance of this site, I just might :).
October 28th, 2004 at 8:29 am
I am trying to figure out how many m& m’s are in a 1 gallon jar approximately 12 inches high and 22 inches in perameter.
October 28th, 2004 at 9:07 am
if the jar is 1 gallon, and it’s full to the top, then you have all you need:
1 US gallon = 3 785.4118 cubic centimeters
1 m&m = .636 cubic centimeters
m&m’s pack 68% of the volume.
That’s all you need to know!.
If the jar is not 100% full, estimate how full it is and use that volume.
Marcos
December 7th, 2004 at 10:58 am
Assuming 12 inches high and 22 inches in circumference is measured in from the INSIDE of the container your answer is:
Constants/Assumtions and Formulas:
2.54 cm = 1 inch
0.636 cm^3 = volume of 1 M&M
68% = packing density of plain chocolate M&M’s
2 * pi * r = Circumference Of Circular Jar
h * pi * r^2 = Volume of Cylindrical Jar
1. Convert Inches to cm:
12 inches = 12 * 2.54 = 30.48 cm
22 inches = 22 * 2.54 = 55.88 cm
2. Calculate the radius using the Circumference:
r = 55.88 / (2 * pi)
3. Calculare the volume using the radius and height:
V = 30.48 * ((55.88 / (2 * pi)) ^ 2) * pi
4. Divide volume by the volume of 1 M&M
# of M&M’s = (30.48 * ((55.88 / (2 * pi)) ^ 2) * pi) / 0.636
5. Adjust for the packing density of 68%
# of M&M’s = ((30.48 * ((55.88 / (2 * pi)) ^ 2) * pi) / 0.636) * 0.68 = 8097.8493 M&M’s
6. Round to whole M&M’s
8098
Note: Your container’s dimensions calculate out to 2 gallons and not 1.
1 gallon = 231 inch^3 and
12 inches * ((22 inches / (2 * pi)) ^ 2) * pi = 462 inch^3 so 462/231 = 2 gallons
December 17th, 2004 at 8:22 pm
Hi!!!
Need your help!!!
How many M&M’s are in a 2 quart jar?
Thanks
December 18th, 2004 at 12:41 pm
2 US quarts = 1 892.7059 cubic centimeters
(Volume / size of M&M) * packing density = #M&Ms
(1 892.7059 / .636) * .68 = 2 023.64782
December 23rd, 2004 at 10:24 am
This is a great formula, someone should turn it into a calulator with selections for different size containers (gallons, quarts, liters, etc.) Great site, thanks!
February 23rd, 2005 at 10:27 am
What about peanut m&m’s? What’s the size? What’s the packing ratio?
Thanks.
February 23rd, 2005 at 11:18 am
It’s left as an exercise to the reader to calculate.
You can figure it out by filling up a bucket of a known volume with peanut M&M’s, and then counting them.
Then calculate the volume of a single peanut M&M. Since the size is irregular, measurements may not work as well as they did on regular M&Ms.
You could take a measuring cup and fill it up to a certain level with water. Drop 10-20 peanut M&M’s and see how much the water level rose (measure quickly before the M&M’s start soaking up too much water or disolving).
If you do the measurements, please post your results here.
Marcos
March 7th, 2005 at 2:37 pm
I’m stymied. How do I calculate the volume of an (somwhat) irregular shaped jar (assuming I can’t empty it and fill it with water). My jar is mostly cubic 9cm per side(if it were straight) and filled with 9cm of m&m’s. Problem is jar is slightly rounded at the four corners. Is there some way to account for this or should I just guess like any normal person would?
March 15th, 2005 at 9:57 pm
I am puzzled with the same problem. I am trying to determine the number of small chocolate eggs are in a vase that is 8″ across, and 24″ high. What do you suggest?
March 15th, 2005 at 10:12 pm
My suggestion is to find out the packing ratio of the chocolate eggs experimentally. You do this by filling a container of known volume with these eggs and then counting the eggs. Read the procedure in the original post above and it should give you a very good idea of what needs to be done.
May 19th, 2005 at 11:14 pm
Very useful information….doing project on this and this site really helped me out. Thanks
October 5th, 2005 at 8:22 am
Does anyone know how big one of those clear glass pumpkin candy jars is? I know that question may be obscure, but I can’t really obtain any more info. Thanks.
October 5th, 2005 at 3:05 pm
Help! I have a jar that contains a combination of plain m&m’s and skittles. The jar is 7 1/8″ tall, 1/16″ thick, 4 1/2″ wide and the candy measures 6 1/4″. Can someone tell me how many pieces of candy are in this jar?
January 16th, 2006 at 8:57 am
I need your help!!!!… im trying to figure out how many m & m’s CHOCOLATe m & ms will fit in 1 x 20 container…. measurements are 5.900mLength x 2.352Width x 2.393M height…. could really do with a answer as soon as possible my friend pls!!!
January 26th, 2006 at 9:18 am
Kim… guess you need your reply by Jan 31….. so do I
January 26th, 2006 at 10:23 am
P&O / Maersk people are here trying to win an 20GB I-POD. Hahaha…
anyway, i have my own answer in mind :p
All the best!
January 30th, 2006 at 8:33 am
haha we been sprung!!
February 3rd, 2006 at 5:17 pm
It is a trick question, the answer is really none because it is bad practice to put a container on its end. Anybody who knows anything knows that.
February 6th, 2006 at 7:25 pm
I find it very pathetic that Maersk employees need someone to tell them the answer when everything was explained in full detail above. It´s a first degree equation for crying out loud! You don´t deserve to win this thing if you´re that dumb.
February 10th, 2006 at 2:30 pm
Kim - youre fired.
February 25th, 2006 at 11:48 am
I’m doing a math project on this exact stuff, and I was wondering if there is a formula for how much volume an object would occupy! Thanks for helping!
February 25th, 2006 at 11:28 pm
I was hoping there was a formula for calculating how much space an object occupies. (ex: M&M’s are 68%)
April 11th, 2006 at 1:45 pm
You did a great job explaining everything. Well done!
June 2nd, 2006 at 9:13 am
[...] Yes, as you can see, the only person to be within the required $5.00 of the actual figure is none other than well-known playboy Moises Kirsch, who also happens to be my own baby brother. He was within $4.88 off. This estimating skills must be genetic or something. I must note that apparently $0.42 worth of non-quarters slipped through, which was enough to make him win. Moi has won a first row ticket to the Gustavo Cerati concert next Monday in Monterrey, Mexico. Congratulations Moi, you lucky bastard! [...]
July 8th, 2006 at 1:13 pm
OK, this is the information I was searching for, however, I found another website with conflicting information. http://www.madsci.org/posts/archives/feb2002/1013032438.Ch.r.html
This website claims that M&M’s are 0.45239 cc instead of .636, and pack at 59.69% instead of 68% as this website says.
Also, what is wrong with rounding down? Because even if, for example, 589.9 fit, you can’t fit .9, so only 588 will fit the way I see it.
September 16th, 2006 at 11:48 am
Do you have the volume of a single PEANUT m&m? Thanks so much for point this into simple terms!!
September 21st, 2006 at 2:37 pm
How tall was the jar of M&Ms in the contest at Truchard Design Center? Thanks!
September 24th, 2006 at 8:53 pm
can someone tell me how many m&ms are in this jar?
http://www.purseblog.com/giveaway/ga4.jpg
i know that the height of the jar is 12.6 inches. please help! i have until september 30th to guess!!
September 24th, 2006 at 8:54 pm
also, if you haven’t noticed by the picture, there are m&ms w/ peanuts mixed with plain ones in the jar.
September 24th, 2006 at 11:34 pm
Cheating kinda takes the fun out of the tPF thing, doesn’t it? Anyway, there are over 100 pages of guesses, someone is bound to have guessed it by now. Cheaters never prosper!
September 28th, 2006 at 8:17 pm
My answer is: There are 3600 m&m’s in the Jar.
October 18th, 2006 at 3:27 pm
my perimeter is 30cm my circumference is 6cm my height is 16cm what do I do now?
October 30th, 2006 at 6:00 pm
HELP!!! i want to know how many m&ms are in a 2000 mL container, however i did the calculations and there doesnt seem to be that many in the container… i dont know what i am doing wrong… please help!!!
November 8th, 2006 at 4:25 pm
Here is what I have……
Regular M&Ms, in a 64oz container
My guess is 64oz=1,892,706 ml x .636(each M&M) / 70%(volume of the jar used) = 1,719.6585 or 1,720 M&Ms
What do you think???
January 11th, 2007 at 4:53 pm
Hi, I’m trying to figure out how many m&m’s (plain, not peanut) are in a 5 gallon (abita water) jug. The winner receives a $200 to best buy. If there’s any way you can help, please let me know.
Thanks!
February 2nd, 2007 at 11:07 am
I can help.
The calculation method is spelled out IN GREAT DETAIL above, with dozens of examples. It’s bad enough that we’ve let someone else do all the hard work and figure out the calculations for us, but do you need an answer given to you? Look at the post just before yours, for crying out loud.
64 oz = 1/2 gallon. How many half gallons in 5 gallons? Yowza! All you have to do is take the last guy’s answer and multiply it by ten.
. . .
I bet you had to use a calculator for that, didn’t you?
March 13th, 2007 at 6:11 pm
My employer had one of these contests and I found the volume of a peanut was around .111 cubic inches. They haven’t announced the winner yet but they told me I was within 20. I used a machinists rule and the ellipsoid formula for volume, it’s just a variation of the sphere volume formula. lwh=length width and height, r = radius. 4/3*pi*Lr*Hr*Wr. I used 6 peanut mms and took the average. I’m trying to get a hold of a micrometer to get better measurements. I know it’s not the most exact form to find volume but I dont grad cylinders or flask to calculate displacement. Lemme know if anyone get a similar number. Oh, and .111 cubic in. is about 1.823 cc
March 20th, 2007 at 6:03 am
How do you fint the Volume for an M&M?
like the simplest way you could put it into a formula ? ? ?
March 21st, 2007 at 4:42 am
how do you find the volume of an M&m (formula)?
And
whats the percentage formula?
ASAP please thanks
September 7th, 2007 at 8:14 am
i have a jar that is 10″ in height and 8″ in width. how many plain m&ms
looks just like this one
http://images.google.com/imgres?imgurl=http://di1.shopping.com/images/di/31/64/65/4c61454f56635676574871676d5362536c7a41-100×100-0-0.jpg&imgrefurl=http://www.glasscandyjars.com/&h=99&w=100&sz=6&hl=en&start=6&um=1&tbnid=VYVa-XcqdEsPHM:&tbnh=81&tbnw=82&prev=/images%3Fq%3Dangled%2Bcandy%2Bjar%26svnum%3D10%26um%3D1%26hl%3Den%26client%3Dfirefox-a%26rls%3Dorg.mozilla:en-US:official%26sa%3DN
September 25th, 2007 at 2:37 pm
How many m&ms can fill a room that is 9×14.5 feet and an 8 feet celing.
October 30th, 2007 at 5:56 pm
well i need help
there is a 5 gallon (abita)water jug containing m&m”s in it how many m&m’s can fit in the jar?? i kno the method just want to check my answer!!! but im thinking about (17,200) please get my answer A.S.A.P. thx a million…
October 30th, 2007 at 6:24 pm
……. continuing from the last post … the amount of m&m’s represent a number of drug related deaths last year that is as specific as i can get because thats all that they provided to me!! but i dot kno what drug what state or anything that is all that i kno!! so get my answer soon please!! (PS)thx
February 13th, 2008 at 4:53 pm
You rock. i love this nd now i am gunna go out and win with all the other sucker 10 yr olds.
March 20th, 2008 at 5:36 pm
fu you were wrong the jar looked exactly like the jar above and there were only 505 green. you loser fu all for making me lose. FFFFFFFFFUUUUUUUUUUU!!!!!!!!!!!!!!!
March 20th, 2008 at 5:38 pm
damn you all!!! you are all nerdy losers that made me lose. so until later FFFFFFFFFUUUUUUUUUUU!!!!!!!!!!!!!!!!!!!!
April 10th, 2008 at 11:04 am
I found someplace that said the volume of a plain M&M was 1/3 the volume of a peanut M&M. I won’t know if I won until next week!! They tried to trick me up by putting half peanut M&Ms and half plain M&Ms but I figured a way around that by halving the height and creating two formulas.
April 10th, 2008 at 12:18 pm
Hey Mystic,
I don’t think what you’re saying works: It’s not about the volume, but about the packing density, which is determined by the shape of the M&M’s. The packing density of mixed peanut and plain M&Ms is not going to be just an average of the corresponding volume.
Good luck though!