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#1
09-23-2008, 12:26 PM
 HeyHomie Charter Member Join Date: Sep 1999 Location: Viburnum, MO Posts: 9,140
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.

Last edited by HeyHomie; 09-23-2008 at 12:28 PM.
#2
09-23-2008, 12:34 PM
 Ethilrist Guest Join Date: Nov 2000 Location: Saint Paul Posts: 26,175
I was with you up to the 80% packing efficiency; where'd you get that?
#3
09-23-2008, 12:38 PM
 ShibbOleth Guest Join Date: Jul 2001 Location: Schlaraffenland Posts: 20,611
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.
#4
09-23-2008, 12:39 PM
 Parthol Guest Join Date: Jul 2002 Posts: 578
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.
#5
09-23-2008, 12:50 PM
 Santo Rugger Guest Join Date: Nov 2006 Location: Obama Fe, NM Posts: 7,292
The packing efficiency of M&Ms is 73.5, and you can fit about 7,500 is a 5 liter flask.
Quote:
 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.
Quote:
 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/gene...y_than_spheres
#6
09-23-2008, 01:27 PM
 HeyHomie Charter Member Join Date: Sep 1999 Location: Viburnum, MO Posts: 9,140
Quote:
 Originally Posted by Ethilrist I was with you up to the 80% packing efficiency; where'd you get that?
I pulled it out of my ass.
#7
09-23-2008, 01:28 PM
 Antinor01 Guest Join Date: Dec 2005 Location: Van Nuys, CA Posts: 11,663
The trick is to sneak back after everyone has left and count them.
#8
09-23-2008, 01:32 PM
 CookingWithGas Charter Member Join Date: Mar 1999 Location: Tysons Corner, VA, USA Posts: 11,482
Quote:
 Originally Posted by 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/gene...y_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.
#9
09-23-2008, 01:37 PM
 Joey P Charter Member Join Date: Jun 1999 Location: Milwaukee, WI Posts: 26,539
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; 09-23-2008 at 01:37 PM.
#10
09-23-2008, 01:40 PM
 Chronos Charter Member Moderator Join Date: Jan 2000 Location: The Land of Cleves Posts: 72,719
Quote:
 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.
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#11
09-23-2008, 01:42 PM
 Iteki Guest Join Date: Feb 2001 Location: Sweden based Dubliner Posts: 1,882
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/trail...ailblazer.html
#12
09-23-2008, 01:44 PM
 Schnitte Intermittently active Join Date: Feb 2001 Location: Frankfurt, Germany Posts: 3,440
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.
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#13
09-23-2008, 02:38 PM
 Duckster Charter Member Join Date: Aug 2001 Posts: 14,421
Quote:
 Originally Posted by HeyHomie I pulled it out of my ass.
Plain or peanut?
#14
09-23-2008, 04:15 PM
 42fish Guest Join Date: Sep 2004 Posts: 3,558
Quote:
 Originally Posted by 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?
#15
09-23-2008, 04:20 PM
 running coach Charter Member Join Date: Nov 2000 Location: Riding my handcycle Posts: 31,896
#16
09-23-2008, 08:22 PM
 Xema Guest Join Date: Mar 2002 Posts: 11,566
Quote:
 Originally Posted by 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.
#17
09-23-2008, 08:35 PM
 Yllaria Charter Member Join Date: Nov 2001 Location: Stockton Posts: 9,966
Quote:
 Originally Posted by 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.
#18
09-23-2008, 09:21 PM
 Chez Guevara Guest Join Date: Aug 2001 Location: Gloucestershire, UK Posts: 3,970
Quote:
 Originally Posted by 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.
#19
09-23-2008, 10:29 PM
 Shawn1767 Guest Join Date: May 2000 Location: New Orleans Proper Posts: 940

http://www.cockeyed.com/inside/trail...ailblazer.html
#20
09-23-2008, 11:36 PM
 Askance Charter Member Join Date: May 2003 Location: Sydney, Australia Posts: 7,037
Quote:
 Originally Posted by 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?
#21
09-24-2008, 12:08 AM
 AdmiralCrunch Guest Join Date: Aug 2004 Location: Rocket City Posts: 392
Quote:
 Originally Posted by HeyHomie I pulled it out of my ass.
According to my calculations, you have an asshole the size of Manhattan.
#22
09-24-2008, 12:14 AM
 Attack from the 3rd dimension Guest Join Date: Jul 2007 Location: Soviet Canuckistan Posts: 5,732
Quote:
 Originally Posted by 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/gene...y_than_spheres
Amazing that you found this. Where can I apply for work as an M&M imager?
#23
09-24-2008, 12:15 AM
 GuanoLad Charter Member Join Date: Sep 1999 Location: Where the wild roses grow Posts: 23,427
Surely "packing efficiency" would only count towards a volume calculation, and not an array calculation.
#24
09-24-2008, 01:28 AM
 Santo Rugger Guest Join Date: Nov 2006 Location: Obama Fe, NM Posts: 7,292
Quote:
 Originally Posted by Attack from the 3rd dimension Amazing that you found this. Where can I apply for work as an M&M imager?
I read this as, "Where can I apply for work as an M&M engineer." No clue for either of them, though.

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.

Quote:
 Originally Posted by GuanoLad Surely "packing efficiency" would only count towards a volume calculation, and not an array calculation.
Huh?
#25
09-24-2008, 01:35 AM
 Saint Cad Guest Join Date: Jul 2005 Location: N of Denver & S of Sanity Posts: 12,218
Quote:
 Originally Posted by Askance That will only be correct if the jar is a rectangular prism, which is a bit unusual ... is it?
That's what I thought when I read this.
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
09-24-2008, 06:04 AM
 Colophon Guest Join Date: Sep 2002 Location: Hampshire, England Posts: 13,340
Quote:
 Originally Posted by Santo Rugger Huh?
GuanoLad was saying what JoeyP said, i.e.
Quote:
 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.
And I think they are right. If you are counting how many M&Ms are present in a given direction, then that *is* how they are packed, so you don't need to factor in a packing efficiency.

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; 09-24-2008 at 06:05 AM.
#27
09-26-2008, 03:34 PM
 HeyHomie Charter Member Join Date: Sep 1999 Location: Viburnum, MO Posts: 9,140
Quote:
 Originally Posted by HeyHomie 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.
I won.
#28
09-26-2008, 04:06 PM
 Ponderoid Guest Join Date: Jan 2008 Location: Off the Deep End Posts: 579
Quote:
 Originally Posted by HeyHomie I won.
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; 09-26-2008 at 04:07 PM.
#29
09-26-2008, 04:47 PM
 SmellMyWort Guest Join Date: Mar 2006 Location: Wisconsin Posts: 2,764
The Dope triumphs!!!
#30
09-26-2008, 05:12 PM
 Santo Rugger Guest Join Date: Nov 2006 Location: Obama Fe, NM Posts: 7,292
Quote:
 Originally Posted by Colophon GuanoLad was saying what JoeyP said, i.e. And I think they are right. If you are counting how many M&Ms are present in a given direction, then that *is* how they are packed, so you don't need to factor in a packing efficiency. 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!!!
Yeah, that makes sense. It's probably be best to do each direction three times and average (or use the middle) result to account for randomness.

Congrats, Homie! I'll take my fee in M&Ms, please!
#31
09-26-2008, 05:15 PM
 KneadToKnow Voodoo Adult (Slight Return) Charter Member Join Date: Jul 2000 Location: Charlotte, NC, USA Posts: 24,869
Wait a minute!

There's no x in jar.
#32
09-26-2008, 05:23 PM
 Yllaria Charter Member Join Date: Nov 2001 Location: Stockton Posts: 9,966
Quote:
 Originally Posted by Chez Guevara 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.
My experience with M&Ms that were warmed in the packet (they don't stay in my hand long enough to get warm there) is that the heat expansion of the chocolate ruptures the candy shell, which is then further displaced by the flow of the melted chocolate. I'm guessing that this happens because the shell does not expand as much with heat, and because the shell shape is weak when force is applied from inside.

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; 09-26-2008 at 05:25 PM.
#33
09-26-2008, 05:54 PM
 Santo Rugger Guest Join Date: Nov 2006 Location: Obama Fe, NM Posts: 7,292
Quote:
 Originally Posted by KneadToKnow Wait a minute! There's no x in jar.
Then how are we going to get the elephant in there?

SPOILER:
How do you fit an elephant into a Safeway bag?

Take the S out of Safe and the f out of way.

There's no f in way!
#34
09-26-2008, 08:42 PM
 Yeticus Rex Member Join Date: Feb 2003 Location: Himalayas & California Posts: 6,766
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
09-27-2008, 12:03 AM
 Joey P Charter Member Join Date: Jun 1999 Location: Milwaukee, WI Posts: 26,539
Quote:
 Originally Posted by KneadToKnow Wait a minute! There's no x in jar.
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; 09-27-2008 at 12:05 AM.
#36
09-27-2008, 02:01 AM
 Kevbo Guest Join Date: May 2005 Posts: 5,889
Quote:
 Originally Posted by Joey P 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'.
I'm pretty sure I saw a bunch of W's in there too.
#37
09-27-2008, 07:55 AM
 KneadToKnow Voodoo Adult (Slight Return) Charter Member Join Date: Jul 2000 Location: Charlotte, NC, USA Posts: 24,869
Quote:
 Originally Posted by Joey P Are you implying that the Teeming Millions would try to catch someone on a technicality? Noooo, not us.
Well, the OP did ask if it was a trick.

Quote:
 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'.
You can't fool me that easy. There's no x in the, either. And no m!

There are four lights!
#38
09-27-2008, 08:11 AM
 Joey P Charter Member Join Date: Jun 1999 Location: Milwaukee, WI Posts: 26,539
Quote:
 Originally Posted by KneadToKnow You can't fool me that easy. There's no x in the, either. And no m!
Rats. Foiled again.
#39
09-27-2008, 02:16 PM
 SpecialAgentJem Guest Join Date: Aug 2008 Location: Bonny Scotland Posts: 136
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
09-28-2008, 07:48 PM
 HeyHomie Charter Member Join Date: Sep 1999 Location: Viburnum, MO Posts: 9,140
Quote:
 Originally Posted by Ponderoid 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
There were four jars: one Skittles, one M & M's, one off-brand malted milk balls, and one a mix of candy corn and candy pumpkins.

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
09-28-2008, 11:28 PM
 Princhester Charter Member Join Date: Jan 2001 Location: Brisbane, Australia Posts: 14,257
We really need to learn to negotiate our commission before we help with this sort of problem!
#42
09-29-2008, 02:49 PM
 Slypork Guest Join Date: Sep 2005 Posts: 2,137
Quote:
 Originally Posted by Santo Rugger Yeah, that makes sense. It's probably be best to do each direction three times and average (or use the middle) result to account for randomness. Congrats, Homie! I'll take my fee in M&Ms, please!
After seeing where some people plan on stashing them, I'd insist on them still being in an unopened package.
#43
09-29-2008, 03:09 PM
 Musicat Charter Member Join Date: Oct 1999 Location: Sturgeon Bay, WI USA Posts: 19,901

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
09-29-2008, 10:32 PM
 kaylasdad99 Charter Member Join Date: Sep 1999 Location: Anaheim, CA Posts: 27,904
Quote:
 Originally Posted by Chez Guevara 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.
Rectoconfectobiologist is my new favorite scientific discipline.
#45
09-30-2008, 01:54 AM
 flight Guest Join Date: Mar 2000 Location: Newport News, VA, USA Posts: 2,704
Quote:
 Originally Posted by Musicat 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.
This is what I came to say, though my reference was, "The Wisdom of Crowds", rather than Wieman.
#46
09-30-2008, 02:36 PM
 Klytus Guest Join Date: Jun 1999 Location: Frederick, MD Posts: 171
Quote:
 Originally Posted by Schnitte 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.
[hijack]
Ah... the halcyon days of family friendly cartoons. Still, my favorite "They-could-never-get-away-with-THAT-today" 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
10-03-2008, 11:35 AM
 Yllaria Charter Member Join Date: Nov 2001 Location: Stockton Posts: 9,966
Quote:
 Originally Posted by Musicat 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.
That could work with M&Ms and a sufficiently large and diverse group of friends. There are a number of things that could interfere with a good result, though. I once won a Guess the Number of Nematodes in the Jar contest where my guess was a complete outlier. It was a gallon jar of water with tiny little nematodes swimming in it. The next lower guess was x10^4 lower than mine.

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
10-08-2008, 10:31 AM
 Pentimental Guest Join Date: Oct 2008 Posts: 2
Quote:
 Originally Posted by 42fish But is the packing efficiency the same in your ass as it would be in a glass jar?
No, because fudge packing inevitably leads to pillow biting.
#49
10-08-2008, 06:04 PM
 Astroboy14 Guest Join Date: Jun 2000 Location: Winslow, ME Posts: 6,322
Quote:
 Originally Posted by Chez Guevara so we must await the arrival of a rectoconfectobiologist
I wasted many hours as a child dreaming of my future career as a rectoconfectobiologist, but alas, the large lollypops defeated me and I was drummed out of rectoconfectobiology school in disgrace.
#50
10-09-2008, 01:56 PM
 Mama Zappa Charter Member Join Date: Feb 2003 Posts: 11,403
Quote:
 Originally Posted by kaylasdad99 Rectoconfectobiologist is my new favorite scientific discipline.
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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