# Those "Guess How Many X's Are in the Jar" Games - Is There a Trick?

My workplace is giving a prize for whoever can provide the closest guess (without going over) as to how many M & M’s are in what looks like a 2-quart jar.

For my guess, I counted the number of M & M’s side to side (16), front to back (11), and top to bottom (12), and did my calculations accordingly (16 X 11 X 12 = 2112). Then I assumed an 80% packing efficiency, so I multiplied my first number by .80, giving me 1689. This seems absurdly high, but then again, short of emptying the jar and counting them one-by-one, who knows?

Is there some kind of trick to these games? I’ve seen them dozens of times in my life, and in various permutations (my favorite was back when I was in high school: how many closed styrofoam Big-Mac boxes (this was before they started using paper instead of cardboard)were in a Honda Civic? Guess correctly and win… a Big Mac), and I’m sure that, with some science, I might be able to develop an edge.

I was with you up to the 80% packing efficiency; where’d you get that?

We won one once for a jar of Jelly Bellies by using a rough estimation of the volume of a cylinder. IIRC we came within about 10-20 of the actual number.

The trick can be that sometimes the people putting the game together hide something inside of the jar, so that will throw you way off. At least the count should never really exceed (by much) a standard volume guesstimate.

I’m not sure this counts as a “trick” or “brute force,” but you could always get some M&M’s and a similarly-shaped jar (but smaller, presumably) to determine accurate “packing efficiency” for yourself. Then take that result and apply it mathematically to the real jar.

The packing efficiency of M&Ms is 73.5, and you can fit about 7,500 is a 5 liter flask.

http://www.sciencenews.org/view/generic/id/4738/title/Candy_Science_M%2BMs_pack_more_tightly_than_spheres

I pulled it out of my ass.

The trick is to sneak back after everyone has left and count them.

My highest commendations on providing this story for this thread!

In this experiment, the packing efficiency was based on random packing. You could probably increase the packing efficiency by vibrating the jar. The article noted that the packing efficiency of random spheres is only 64% but increases to 74% in a closest-packed configuration.

Wouldn’t the packing efficiency have been ‘automatically’ calculated when you counted the number of m&m’s on each side? My understanding of packing efficiency is that would use it if you found the volume of an m&m and divided it into the volume of the container, then multiply by the packing efficiency.

[MH]Awww man, how 'bout you just give me some m&m’s
Let’s comprimise, why don’t you guess how many I want…if you guessed a handful, you’re right.[/MH]

It’s also more difficult if there’s more than one type of object in the jar (a mixture of three different candies, say). They’ll tend to segregate themselves by size to some extent.

And I must admit to being surprised that M&Ms (which appear to be ellipsoids) can be packed more efficiently than spheres.

This seems pretty much asked and answered to me, but here is an interesting story of when Cockeyed.com tried to compete in a similar competition (how many ping-pong-balls in a Trailblazer).
http://www.cockeyed.com/inside/trailblazer/trailblazer.html

There’s a 1940s Donald Duck strip in which Huey, Dewey, and Louie stage such a game with a jar of beans. Donald wants to win the first prize, so he gets a jar of equal dimensions and fills it with beans, one by one, counting them. The trick is that a stone was hidden among the beans, making his estimate too high (in the last frame, Donald beats up his nephews).

Just goes to show how old these games are.

Plain or peanut?

But is the packing efficiency the same in your ass as it would be in a glass jar?

The only general trick is that the correct number usually seems quite large - provided the jar actually is full of M&Ms, most guesses will be too small.

Unless you have an exceptionally cold ass, I’m guessing that’s not true. I’m not willing to do the experiment though. I have too much admiration for M&Ms to do that to one.

An M&M inserted into the rectum might melt on the inside but would it melt on the outside? I thought the product required saliva to break down the outer shell and release the chocolate from within.

Regrettably I don’t have either an M&M or a proctoscope about my person right now, so we must await the arrival of a rectoconfectobiologist who, hopefully, can get to the bottom of this matter without further delay.