# Those "Guess How Many X's Are in the Jar" Games - Is There a Trick? **URL:** \ **Category:** Factual Questions\ **Created:** [September 23, 2008, 4:26pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852 "2008-09-23T16:26:57Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![HeyHomie](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/heyhomie/32/207_2.png) [@HeyHomie](https://boards.straightdope.com/u/HeyHomie)\ **Post date:** [September 23, 2008, 4:26pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/1 "2008-09-23T16:26:57Z")
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. Any advice? ---
**Author:** ![Ethilrist](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ethilrist/32/4604_2.png) [@Ethilrist](https://boards.straightdope.com/u/Ethilrist)\ **Post date:** [September 23, 2008, 4:34pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/2 "2008-09-23T16:34:48Z")
I was with you up to the 80% packing efficiency; where’d you get that? ---
**Author:** ![ShibbOleth](https://avatars.discourse-cdn.com/v4/letter/s/848f3c/32.png) [@ShibbOleth](https://boards.straightdope.com/u/ShibbOleth)\ **Post date:** [September 23, 2008, 4:38pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/3 "2008-09-23T16:38:48Z")
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. ---
**Author:** ![Parthol](https://avatars.discourse-cdn.com/v4/letter/p/dec6dc/32.png) [@Parthol](https://boards.straightdope.com/u/Parthol)\ **Post date:** [September 23, 2008, 4:39pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/4 "2008-09-23T16:39:24Z")
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. ---
**Author:** ![Santo\_Rugger](https://avatars.discourse-cdn.com/v4/letter/s/e95f7d/32.png) [@Santo\_Rugger](https://boards.straightdope.com/u/Santo_Rugger)\ **Post date:** [September 23, 2008, 4:50pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/5 "2008-09-23T16:50:34Z")
The packing efficiency of M&Ms is 73.5, and you can fit about 7,500 is a 5 liter flask. > [@](#): > > For both actual and simulated ellipsoids, Torquato and his colleagues now find that random packings fill as much as 73.5 percent of the space, just a smidgeon less than hand-stacked spheres do. > [@](#): > > To confirm the randomness of the internal packing, the team took magnetic resonance imaging scans of a 5-liter flask filled with about 7,500 regular-size M&Ms. [http://www.sciencenews.org/view/generic/id/4738/title/Candy\_Science\_M%2BMs\_pack\_more\_tightly\_than\_spheres](http://www.sciencenews.org/view/generic/id/4738/title/Candy_Science_M%2BMs_pack_more_tightly_than_spheres) ---
**Author:** ![HeyHomie](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/heyhomie/32/207_2.png) [@HeyHomie](https://boards.straightdope.com/u/HeyHomie)\ **Post date:** [September 23, 2008, 5:27pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/6 "2008-09-23T17:27:27Z")
> [@Ethilrist](#): > > I was with you up to the 80% packing efficiency; where’d you get that? I pulled it out of my ass. ---
**Author:** ![Antinor01](https://avatars.discourse-cdn.com/v4/letter/a/ecae2f/32.png) [@Antinor01](https://boards.straightdope.com/u/Antinor01)\ **Post date:** [September 23, 2008, 5:28pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/7 "2008-09-23T17:28:28Z")
The trick is to sneak back after everyone has left and count them. ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [September 23, 2008, 5:32pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/8 "2008-09-23T17:32:44Z")
> [@Santo\_Rugger](#): > > 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](http://www.sciencenews.org/view/generic/id/4738/title/Candy_Science_M%2BMs_pack_more_tightly_than_spheres) 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. ---
**Author:** ![Joey\_P](https://avatars.discourse-cdn.com/v4/letter/j/919ad9/32.png) [@Joey\_P](https://boards.straightdope.com/u/Joey_P)\ **Post date:** [September 23, 2008, 5:37pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/9 "2008-09-23T17:37:10Z")
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] ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 23, 2008, 5:40pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/10 "2008-09-23T17:40:31Z")
> [@](#): > > 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. 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. ---
**Author:** ![Iteki](https://avatars.discourse-cdn.com/v4/letter/i/eada6e/32.png) [@Iteki](https://boards.straightdope.com/u/Iteki)\ **Post date:** [September 23, 2008, 5:42pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/11 "2008-09-23T17:42:47Z")
This seems pretty much asked and answered to me, but here is an interesting story of when [Cockeyed.com](http://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](http://www.cockeyed.com/inside/trailblazer/trailblazer.html) ---
**Author:** ![Schnitte](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/schnitte/32/9033_2.png) [@Schnitte](https://boards.straightdope.com/u/Schnitte)\ **Post date:** [September 23, 2008, 5:44pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/12 "2008-09-23T17:44:08Z")
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. ---
**Author:** ![Duckster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/duckster/32/1244_2.png) [@Duckster](https://boards.straightdope.com/u/Duckster)\ **Post date:** [September 23, 2008, 6:38pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/13 "2008-09-23T18:38:58Z")
> [@HeyHomie](#): > > I pulled it out of my ass. Plain or peanut? ---
**Author:** ![42fish](https://avatars.discourse-cdn.com/v4/letter/4/b487fb/32.png) [@42fish](https://boards.straightdope.com/u/42fish)\ **Post date:** [September 23, 2008, 8:15pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/14 "2008-09-23T20:15:59Z")
> [@HeyHomie](#): > > I pulled it out of my ass. But is the packing efficiency the same in your ass as it would be in a glass jar? ---
**Author:** ![running\_coach](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/running_coach/32/15836_2.png) [@running\_coach](https://boards.straightdope.com/u/running_coach)\ **Post date:** [September 23, 2008, 8:20pm UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/15 "2008-09-23T20:20:55Z")
They melt in your mouth, not in your ass. ---
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [September 24, 2008, 12:22am UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/16 "2008-09-24T00:22:47Z")
> [@HeyHomie](#): > > Is there a trick? 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. ---
**Author:** ![Yllaria](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/yllaria/32/3452_2.png) [@Yllaria](https://boards.straightdope.com/u/Yllaria)\ **Post date:** [September 24, 2008, 12:35am UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/17 "2008-09-24T00:35:12Z")
> [@runner pat](#): > > They melt in your mouth, not in your ass. 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. ---
**Author:** ![Chez\_Guevara](https://avatars.discourse-cdn.com/v4/letter/c/aeb1de/32.png) [@Chez\_Guevara](https://boards.straightdope.com/u/Chez_Guevara)\ **Post date:** [September 24, 2008, 1:21am UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/18 "2008-09-24T01:21:09Z")
> [@Yllaria](#): > > 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. ---
**Author:** ![Shawn1767](https://avatars.discourse-cdn.com/v4/letter/s/ee7513/32.png) [@Shawn1767](https://boards.straightdope.com/u/Shawn1767)\ **Post date:** [September 24, 2008, 2:29am UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/19 "2008-09-24T02:29:31Z")
There was this attempt documented by Rob Cockerham: [http://www.cockeyed.com/inside/trailblazer/trailblazer.html](http://www.cockeyed.com/inside/trailblazer/trailblazer.html) ---
**Author:** ![Askance](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/askance/32/8281_2.png) [@Askance](https://boards.straightdope.com/u/Askance)\ **Post date:** [September 24, 2008, 3:36am UTC](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852/20 "2008-09-24T03:36:38Z")
> [@HeyHomie](#): > > 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). That will only be correct if the jar is a rectangular prism, which is a bit unusual … is it? [Next page](https://boards.straightdope.com/t/those-guess-how-many-xs-are-in-the-jar-games-is-there-a-trick/464852.md?page=2)