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  #1  
Old 09-23-2008, 12:26 PM
HeyHomie HeyHomie is online now
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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.

Any advice?

Last edited by HeyHomie; 09-23-2008 at 12:28 PM..
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  #2  
Old 09-23-2008, 12:34 PM
Ethilrist Ethilrist is online now
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I was with you up to the 80% packing efficiency; where'd you get that?
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  #3  
Old 09-23-2008, 12:38 PM
ShibbOleth ShibbOleth is offline
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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.
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Old 09-23-2008, 12:39 PM
Parthol Parthol is offline
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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.
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  #5  
Old 09-23-2008, 12:50 PM
Santo Rugger Santo Rugger is offline
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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
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  #6  
Old 09-23-2008, 01:27 PM
HeyHomie HeyHomie is online now
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Quote:
Originally Posted by Ethilrist View Post
I was with you up to the 80% packing efficiency; where'd you get that?
I pulled it out of my ass.
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  #7  
Old 09-23-2008, 01:28 PM
Antinor01 Antinor01 is online now
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The trick is to sneak back after everyone has left and count them.
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  #8  
Old 09-23-2008, 01:32 PM
CookingWithGas CookingWithGas is offline
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Quote:
Originally Posted by Santo Rugger View Post
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.
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  #9  
Old 09-23-2008, 01:37 PM
Joey P Joey P is offline
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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..
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  #10  
Old 09-23-2008, 01:40 PM
Chronos Chronos is online now
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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  
Old 09-23-2008, 01:42 PM
Iteki Iteki is offline
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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
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  #12  
Old 09-23-2008, 01:44 PM
Schnitte Schnitte is offline
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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  
Old 09-23-2008, 02:38 PM
Duckster Duckster is offline
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Originally Posted by HeyHomie View Post
I pulled it out of my ass.
Plain or peanut?
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  #14  
Old 09-23-2008, 04:15 PM
42fish 42fish is offline
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Originally Posted by HeyHomie View Post
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?
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  #15  
Old 09-23-2008, 04:20 PM
running coach running coach is online now
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They melt in your mouth, not in your ass.
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  #16  
Old 09-23-2008, 08:22 PM
Xema Xema is online now
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Quote:
Originally Posted by HeyHomie View Post
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.
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  #17  
Old 09-23-2008, 08:35 PM
Yllaria Yllaria is offline
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Quote:
Originally Posted by runner pat View Post
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.
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  #18  
Old 09-23-2008, 09:21 PM
Chez Guevara Chez Guevara is offline
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Originally Posted by Yllaria View Post
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.
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  #19  
Old 09-23-2008, 10:29 PM
Shawn1767 Shawn1767 is offline
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There was this attempt documented by Rob Cockerham:

http://www.cockeyed.com/inside/trail...ailblazer.html
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  #20  
Old 09-23-2008, 11:36 PM
Askance Askance is offline
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Quote:
Originally Posted by HeyHomie View Post
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?
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  #21  
Old 09-24-2008, 12:08 AM
AdmiralCrunch AdmiralCrunch is offline
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Originally Posted by HeyHomie View Post
I pulled it out of my ass.
According to my calculations, you have an asshole the size of Manhattan.
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  #22  
Old 09-24-2008, 12:14 AM
Attack from the 3rd dimension Attack from the 3rd dimension is offline
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Quote:
Originally Posted by Santo Rugger View Post
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?
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  #23  
Old 09-24-2008, 12:15 AM
GuanoLad GuanoLad is offline
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Surely "packing efficiency" would only count towards a volume calculation, and not an array calculation.
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  #24  
Old 09-24-2008, 01:28 AM
Santo Rugger Santo Rugger is offline
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Quote:
Originally Posted by Attack from the 3rd dimension View Post
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.

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Originally Posted by GuanoLad View Post
Surely "packing efficiency" would only count towards a volume calculation, and not an array calculation.
Huh?
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  #25  
Old 09-24-2008, 01:35 AM
Saint Cad Saint Cad is online now
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Originally Posted by Askance View Post
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.
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  #26  
Old 09-24-2008, 06:04 AM
Colophon Colophon is offline
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Quote:
Originally Posted by Santo Rugger View Post

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..
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  #27  
Old 09-26-2008, 03:34 PM
HeyHomie HeyHomie is online now
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Quote:
Originally Posted by HeyHomie View Post
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.
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  #28  
Old 09-26-2008, 04:06 PM
Ponderoid Ponderoid is offline
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Originally Posted by HeyHomie View Post
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..
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  #29  
Old 09-26-2008, 04:47 PM
SmellMyWort SmellMyWort is online now
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The Dope triumphs!!!
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  #30  
Old 09-26-2008, 05:12 PM
Santo Rugger Santo Rugger is offline
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Quote:
Originally Posted by Colophon View Post
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!
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  #31  
Old 09-26-2008, 05:15 PM
KneadToKnow KneadToKnow is offline
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Wait a minute!

There's no x in jar.
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  #32  
Old 09-26-2008, 05:23 PM
Yllaria Yllaria is offline
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Quote:
Originally Posted by Chez Guevara View Post
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..
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  #33  
Old 09-26-2008, 05:54 PM
Santo Rugger Santo Rugger is offline
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Originally Posted by KneadToKnow View Post
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!
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  #34  
Old 09-26-2008, 08:42 PM
Yeticus Rex Yeticus Rex is offline
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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.
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  #35  
Old 09-27-2008, 12:03 AM
Joey P Joey P is offline
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Quote:
Originally Posted by KneadToKnow View Post
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..
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  #36  
Old 09-27-2008, 02:01 AM
Kevbo Kevbo is offline
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Originally Posted by Joey P View Post
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.
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  #37  
Old 09-27-2008, 07:55 AM
KneadToKnow KneadToKnow is offline
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Quote:
Originally Posted by Joey P View Post
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!
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  #38  
Old 09-27-2008, 08:11 AM
Joey P Joey P is offline
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Originally Posted by KneadToKnow View Post
You can't fool me that easy. There's no x in the, either. And no m!
Rats. Foiled again.
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  #39  
Old 09-27-2008, 02:16 PM
SpecialAgentJem SpecialAgentJem is offline
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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?
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  #40  
Old 09-28-2008, 07:48 PM
HeyHomie HeyHomie is online now
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Quote:
Originally Posted by Ponderoid View Post
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.
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  #41  
Old 09-28-2008, 11:28 PM
Princhester Princhester is offline
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We really need to learn to negotiate our commission before we help with this sort of problem!
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  #42  
Old 09-29-2008, 02:49 PM
Slypork Slypork is offline
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Originally Posted by Santo Rugger View Post
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.
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  #43  
Old 09-29-2008, 03:09 PM
Musicat Musicat is offline
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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.
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  #44  
Old 09-29-2008, 10:32 PM
kaylasdad99 kaylasdad99 is offline
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Quote:
Originally Posted by Chez Guevara View Post
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.
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  #45  
Old 09-30-2008, 01:54 AM
flight flight is offline
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Originally Posted by Musicat View Post
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.
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  #46  
Old 09-30-2008, 02:36 PM
Klytus Klytus is offline
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Originally Posted by Schnitte View Post
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]
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  #47  
Old 10-03-2008, 11:35 AM
Yllaria Yllaria is offline
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Quote:
Originally Posted by Musicat View Post
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.
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  #48  
Old 10-08-2008, 10:31 AM
Pentimental Pentimental is offline
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Originally Posted by 42fish View Post
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.
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  #49  
Old 10-08-2008, 06:04 PM
Astroboy14 Astroboy14 is online now
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Originally Posted by Chez Guevara View Post
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.
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  #50  
Old 10-09-2008, 01:56 PM
Mama Zappa Mama Zappa is offline
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Originally Posted by kaylasdad99 View Post
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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