#1




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 2quart 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 onebyone, 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 BigMac 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? Last edited by HeyHomie; 09232008 at 12:28 PM.. 
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#2




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

#3




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 1020 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. 
#4




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

#5




The packing efficiency of M&Ms is 73.5, and you can fit about 7,500 is a 5 liter flask.
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#6




I pulled it out of my ass.

#7




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

#8




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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 closestpacked configuration. 
#9




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] Last edited by Joey P; 09232008 at 01:37 PM.. 
#10




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And I must admit to being surprised that M&Ms (which appear to be ellipsoids) can be packed more efficiently than spheres.
__________________
Time travels in divers paces with divers persons. As You Like It, III:ii:328 
#11




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 pingpongballs in a Trailblazer).
http://www.cockeyed.com/inside/trail...ailblazer.html 
#12




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.
__________________
PLEONASM: An army of words escorting a corporal of thought.  Ambrose Bierce 
#13




#14




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

#15




They melt in your mouth, not in your ass.

#16




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.

#17




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.

#18




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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. 
#19




There was this attempt documented by Rob Cockerham:
http://www.cockeyed.com/inside/trail...ailblazer.html 
#20




That will only be correct if the jar is a rectangular prism, which is a bit unusual ... is it?

#21




According to my calculations, you have an asshole the size of Manhattan.

#22




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#23




Surely "packing efficiency" would only count towards a volume calculation, and not an array calculation.

#24




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I read that link quite a time ago, it's one of those things that just sticks in your head. I may have posted about it, if the search function was working I'd try to find the thread. There was an accompanying article that was a bit more scientific, but I can't seem to find the link for that one anymore. Huh? 
#25




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A math approach may be to count the M&M around the bottom giving you the circumference. Square this then multiply this by the height and divide by 4pi. I don't think this would have to be multiplied by 0.74. 
#26




GuanoLad was saying what JoeyP said, i.e.
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The packing efficiency figure describes how much of the total volume available can be taken up by M&M's. If you assume 74%, then you would: 1) Calculate volume of jar 2) Multiply volume of jar by 0.74 3) Divide the result by the volume of one M&M. 4) Profit!!! Last edited by Colophon; 09242008 at 06:05 AM.. 
#27




I won.

#28




So what was your guess, what was the actual number, and how close were your nearest competitors? Did anyone go over? What did you win?
*** Ponder Last edited by Ponderoid; 09262008 at 04:07 PM.. 
#29




The Dope triumphs!!!

#30




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Congrats, Homie! I'll take my fee in M&Ms, please! 
#31




Wait a minute!
There's no x in jar. 
#32




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Even if it didn't rupture from the expansion of the chocolate, an M&M with a melted chocolate interior would have very little structural integrity. The slightest pressure and it will break and smear. Those shells just aren't that strong without the solid chocolate to back them up. Sorry for the hijack HeyHomie. Congratulations on your win. May your estimating skills ever increase. Last edited by Yllaria; 09262008 at 05:25 PM.. 
#33




Then how are we going to get the elephant in there?
SPOILER:

#34




For any uniform shape or volume, just fill up a known volume container with items in question (M&Ms, jelly bellys, etc) to the line and then fill the rest with water. Quickly separate the two mediums with a strainer and measure the water. Then solve for the packing efficiency. Repeat several times to get a more precise P.E. Then apply that P.E. to the container in question.

#35




Are you implying that the Teeming Millions would try to catch someone on a technicality? Noooo, not us.
ETA, the questions was "How many X's are in THE jar?". The answer would still be zero, as the only letter contained in said jar was 'm'. Last edited by Joey P; 09272008 at 12:05 AM.. 
#36




I'm pretty sure I saw a bunch of W's in there too.

#37




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There are four lights! 
#38




Rats. Foiled again.

#39




My trick would be to buy an identical jar and bags of the same sweets. Fill the jar and count how many you pull out until the jar is empty. Costly, time consuming and pathetic! Oh and it may not work  you could be one sweet out and someone else may snatch the prize! Worth a try though, eh?

#40




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My guess on the Skittles (which I won): 1,468. Actual number of Skittles: 1,489. I was within 21 Skittles (I'll leave it to a Doper better at math to figure out how many percentage points I was away). The other guesses weren't revealed. For correctly guessing how many Skittles were in a jar I won... a jar of Skittles. I have no idea what my guesses were on the other products. I did hear that, on the M & M's, there were two identical guesses, and the winner was determined by a flip of a coin. 
#41




We really need to learn to negotiate our commission before we help with this sort of problem!

#42




After seeing where some people plan on stashing them, I'd insist on them still being in an unopened package.

#43




Y'all are going about this task all wrong.
According to Dr. Richard Wiseman, when a large number of people independently estimate how many somethings are in a large group, although most guesses are wildly off, the average of all the guesses is very accurate. So get all your friends to guess and average the results. 
#44




Rectoconfectobiologist is my new favorite scientific discipline.

#45




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#46




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Ah... the halcyon days of family friendly cartoons. Still, my favorite "TheycouldnevergetawaywithTHATtoday" cartoon moment was the one where Buggs Bunny was filling in for the Easter Bunny, and his first stop is a Hillbilly house where there's a kid in a crib sucking on the barrel of a gun like its a pacifier. [/hijack] 
#47




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I guess most of the other folks just weren't comfortable with numbers that high when applied to an average sized object. I won a bucket of gummy worms. The kids loved it. The crowd was not wise that day. 
#48




No, because fudge packing inevitably leads to pillow biting.

#50




Indeed! (though the name is too long for a band, so if the scientists ever start jammin' together, they'd have to call themselves "Ass Candy").

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