The Straight Dope

Go Back   Straight Dope Message Board > Main > General Questions

Closed Thread
 
Thread Tools Display Modes
  #1  
Old 09-17-2006, 03:43 PM
Jurph Jurph is offline
Guest
 
Join Date: Oct 2003
Estimating the value of a mass of US coins

So I was in my cousin's office this weekend and I saw a 5 gallon water bottle that had been emptied of water and filled with spare change. My first thought was that it must be terribly heavy, and when I tried to lift it I discovered I was correct -- it's extremely heavy. I was able to tip it to get my hands under it, but I was unable to lift it. Perhaps with help from another person I could even carry it around.

The bottle is 18.93 liters, give or take, which is .667 cubic feet. Combined with this page I have what I consider to be a lower bound for the value of the bottle: $328, if it's full of pennies and not packed optimally. I could probably compute an upper bound as well, assuming it's made of the highest value-per-volume coin (I think that's going to be dimes, but I'm not sure).

If I were able to obtain an accurate weight for the full jug (and a reasonably precise estimate for the mass of the empty jug), how closely could I estimate the value of all of the coins inside? I'd like to think that simple linear algebra would do the trick, but I can only think of three equations -- one for total mass of the coins, one for volume, and one for total value -- and I know I've got at least four unknowns (number of each type of coin).

So:
.25q + .10d + .05n + .01p = $(some large number)
Mq*q + Md*d + Mn*n + Mp * p = (some large number of kilograms), where M(x) is the mass, in kilograms, of coin x.
Vq*q + Vd * d + Vn * n + Vp * p = .667 cubic feet, where V(x) is the volume, in cubic feet, of coin x.

M(x) and V(x) are almost certainly public information, but that still leaves me with three equations and five unknowns, even if I do know the mass to within a few grams. I think my only hope is to find an equation governing the frequency with which each coin is circulated relative to the others. Assuming that's possible, could one estimate the value of the coins inside without knowing the mass of the full jug at all?
Advertisements  
  #2  
Old 09-17-2006, 03:49 PM
ultrafilter ultrafilter is offline
Guest
 
Join Date: May 2001
Since you know the volume, you could calculate the number of coins of each denomination that fit in that volume, given a less than optimal packing. You could then take the weighted average based on the frequency of each coin. It's not necessarily a great estimate, but as a first approximation, it should be OK.
  #3  
Old 09-17-2006, 04:09 PM
jnglmassiv jnglmassiv is offline
Charter Member
 
Join Date: Nov 2002
Location: Chicago's Northside
Posts: 2,011
I don't think you could do it even with a known mass. You have 4 non-uniform parts (coins) with unknown proportions that don't fit together nicely.
  #4  
Old 09-17-2006, 04:56 PM
Khadaji Khadaji is offline
Member
 
Join Date: Mar 2002
Location: Southern Pennsylvania
Posts: 21,600
I've been wondering the same thing. I have a big pepsi bottle full of coins. It is about 3 feet high. I know that I put more than 100 dollars worth each year and have been doing so for many years. I'm guessing it is more than a thousand dollars worth. (I have a separate place for pennies, so it is all quarter, dimes and nickels.
  #5  
Old 09-17-2006, 05:57 PM
John DiFool John DiFool is offline
Guest
 
Join Date: Jun 2006
If you want to cash it in, interesting choice:

A) Spend an entire weekend rolling the coins, or

B) Brave the 10-15% vigorish that those coin machines typically take.
  #6  
Old 09-17-2006, 06:17 PM
Telemark Telemark is offline
Charter Member
 
Join Date: Apr 2000
Location: Hub of the sports world
Posts: 15,385
Quote:
Originally Posted by John DiFool
If you want to cash it in, interesting choice:

A) Spend an entire weekend rolling the coins, or

B) Brave the 10-15% vigorish that those coin machines typically take.
or C) go to your bank where (if it's a good bank) they'll let you use the coin counting machine for free.
  #7  
Old 09-17-2006, 06:22 PM
Khadaji Khadaji is offline
Member
 
Join Date: Mar 2002
Location: Southern Pennsylvania
Posts: 21,600
Quote:
Originally Posted by John DiFool
If you want to cash it in, interesting choice:

A) Spend an entire weekend rolling the coins, or

B) Brave the 10-15% vigorish that those coin machines typically take.
In our area there is a bank that will let you use their change counter for free. You don't even have to be a customer. Those small things are what will make me go to them if I ever need a bank again (currently I use the credit union.)
  #8  
Old 09-17-2006, 06:40 PM
galt galt is offline
Guest
 
Join Date: Apr 1999
I'd be willing to bet that the dollars-per-unit-volume of the average american pocket change bucket is pretty constant, especially if you aren't dealing with someone who intentionally biases their coin collecting habits (e.g. someone who does coin-op laundry habitually seperating out their quarters). Now the question is how to figure that out. It would probably be interesting to know the actual distribution of US coins, so that you could predict the value of a randomly chosen sample from that pool, but it's important to note that the contents of a pocket change bucket are not randomly chosen (resulting as they are from transactions where there are 99 core permutations that make the most sense to get), so the "value density" (warning: invented term) of the average bucket is likely different from that of the US coin circulation as a whole.
  #9  
Old 09-17-2006, 06:42 PM
Triskadecamus Triskadecamus is offline
Guest
 
Join Date: Oct 1999
A glass jar full of coins has another characteristic as well, that should be considered. It is under a very large tension from the "fluid" pressure of the coins. It can sit for decades, with no hint of problems, and then the drop of a single coin, or the torsion of trying to lift it will put some small flaw over the edge.

The failure is catastrophic, startling, and one hell of a mess to clean up.

Or, it can be one of those silly twist of fate things. A good friend of mine had a glass carboy full of coins. Someone opened the window just above his desk, and a very cold wind blew in. (VPI, dead of winter, from steam heat to plateau wind chill) There was a sharp crack. He looked at the carboy, and there was a neat crack all the way around the very bottom. He made the mistake of checking it.
Then the coins squirted out around the base faster and wider than you would ever imagine.

Tris
  #10  
Old 09-17-2006, 07:07 PM
galt galt is offline
Guest
 
Join Date: Apr 1999
This one's got me curious so I did a little exercise.

Assumption 1: change will be given from a particular transaction in the most logical way, e.g. 45 cents will be given as a quarter and two dimes, not as four dimes and a nickel. Obviously, this is not always true, but is probably true enough not to affect the results too much.

Assumption 2: all sub-dollar totals are equally likely (you're just as likely to have a transaction ending in .23 as in .99). This one is probably wrong enough to impact the results, due to retail pricing practices, but I'll continue anyway, and maybe someone can come up with a way to correct this one and weight the results.

If you got all 99 different change amounts once each, you would have:
200 pennies, 40 nickels, 60 dimes and 150 quarters.

So given the assumptions above, the average change jar should be 44.4% pennies, 8.8% nickels, 13.3% dimes, and 33.3% quarters. Note that this is just the relative number of each coin, not the relative weight, so you need to know how many coins there are total in order to apply them. More calculations are necessary to say that a given jar filled this way is n% pennies by weight, etc. Hang tight...

On preview: wow, Tris, I wish I could have seen that.
  #11  
Old 09-17-2006, 07:30 PM
galt galt is offline
Guest
 
Join Date: Apr 1999
Ok, plugging those numbers and weights of coins from here into a spreadsheet, I get:

By weight, a bucket of pocket change (using my assumptions about collection from above) is 29.6% pennies, 11.9% nickels, 8.1% dimes and 50.42% quarters.

So a pound (453.6g) of said change contains:

134.5 grams of pennies (= $0.53)
53.8 grams of nickels (= $0.53)
36.6 grams of dimes (= $1.61)
228.7 grams of quarters (= $10.09)

... giving this hypothetical change mixture a value of $12.77 per pound


Ok, anyone see anything blatantly wrong with my calculations?
  #12  
Old 09-17-2006, 08:02 PM
Khadaji Khadaji is offline
Member
 
Join Date: Mar 2002
Location: Southern Pennsylvania
Posts: 21,600
My change weighs 55 lbs - no pennies.
  #13  
Old 09-17-2006, 08:34 PM
ScoobyTX ScoobyTX is offline
Guest
 
Join Date: Dec 2000
If you are able to get an accurate total weight and empty container weight, perhaps the best way to estimate the total value is through sampling. Take out a couple to a few pounds of coins at random, count out the value of this sample and weigh it. From this you can obtain a $/lb value that you can extrapolate to the entire container full of coins. The only assumption required is that the composition of the coin mixture is fairly uniform.
  #14  
Old 09-17-2006, 08:41 PM
galt galt is offline
Guest
 
Join Date: Apr 1999
Well if you took a sample of my hypothetical standard change mixture and simply threw out all the pennies, it would be (by weight) 16.9% nickels, 11.5% dimes, and 71.7% quarters, putting its value at about $17.39 per pound.
  #15  
Old 09-17-2006, 08:44 PM
Johnny L.A. Johnny L.A. is online now
Charter Member
 
Join Date: Jan 2000
Location: NoWA
Posts: 49,326
FWIW I keep my pennies, nickles and dimes* in a one-quart glass milk bottle. I shake it from time to time to get the coins to settle. When it's full I usually have $45-$55 in change.

*I save the quarters for laundry. When I'm home (with my washer and dryer) I just save them.
  #16  
Old 09-17-2006, 09:01 PM
galt galt is offline
Guest
 
Join Date: Apr 1999
Quote:
Originally Posted by Johnny L.A.
FWIW I keep my pennies, nickles and dimes* in a one-quart glass milk bottle. I shake it from time to time to get the coins to settle. When it's full I usually have $45-$55 in change.
I would like to make a prediction. Next time your jar is full, if you weigh it, it will be between 8 and 10 pounds. (my spreadsheet says that without quarters, pocket change will be $5.43 per pound)
  #17  
Old 09-17-2006, 10:52 PM
DanBlather DanBlather is offline
Guest
 
Join Date: Jul 2001
Quote:
Originally Posted by galt
This one's got me curious so I did a little exercise.

Assumption 1: change will be given from a particular transaction in the most logical way, e.g. 45 cents will be given as a quarter and two dimes, not as four dimes and a nickel. Obviously, this is not always true, but is probably true enough not to affect the results too much.

Assumption 2: all sub-dollar totals are equally likely (you're just as likely to have a transaction ending in .23 as in .99). This one is probably wrong enough to impact the results, due to retail pricing practices, but I'll continue anyway, and maybe someone can come up with a way to correct this one and weight the results.

If you got all 99 different change amounts once each, you would have:
200 pennies, 40 nickels, 60 dimes and 150 quarters.

So given the assumptions above, the average change jar should be 44.4% pennies, 8.8% nickels, 13.3% dimes, and 33.3% quarters. Note that this is just the relative number of each coin, not the relative weight, so you need to know how many coins there are total in order to apply them. More calculations are necessary to say that a given jar filled this way is n% pennies by weight, etc.
That was a great analysis.
  #18  
Old 09-18-2006, 12:27 AM
Jurph Jurph is offline
Guest
 
Join Date: Oct 2003
Quote:
Originally Posted by Johnny L.A.
FWIW I keep my pennies, nickels and dimes* in a one-quart glass milk bottle. I shake it from time to time to get the coins to settle. When it's full I usually have $45-$55 in change.
Given galt's earlier math, can we deduce that a quart of change with quarters would be worth (12.77/5.43)*100% more, or about 2.35 times as much? If so, then my cousin's five gallon jug is probably worth:

5 gallons * (4 quarts / 1 gallon) * (12.77 with quarters / 5.43 without quarters) * $50 per quart-without-quarters = about $2,350!

Also, for anyone interested in playing around with the numbers, I've put together a Google Spreadsheet here that includes mass estimates for full distributions of coins, and the "no pennies" and "no quarters" mixes.
  #19  
Old 09-18-2006, 12:48 AM
Bergebo Bergebo is offline
Guest
 
Join Date: Sep 2006
For some strange reason I've been tallying the coins in my coffee can before taking them to the bank. It's how I deal with change.

2.5 years worth of coins.

10,843 coins worth $1204.36 (I excluded 253 $1 coins.)
Average coin value is $.1111.

Quarters at 33.9%.
Dimes at 16.5%.
Nickels at 12.2%.
Pennies at 37.4%.

I'm pretty good at emptying the pockets and rarely raid the can for prime coins. Hope this helps.
  #20  
Old 09-18-2006, 02:59 AM
galt galt is offline
Guest
 
Join Date: Apr 1999
Quote:
Originally Posted by Bergebo
2.5 years worth of coins.
...
Quarters at 33.9%.
Dimes at 16.5%.
Nickels at 12.2%.
Pennies at 37.4%.
Fantastic. Earlier today I found myself wishing I had done this in the past so I could find out how close my numbers were.

My prediction by coin count was:
Quarters at 33.3%
Dimes at 13.3%
Nickels at 8.8%
Pennies at 44.4%

My percentages would have come up with a prediction of $1142.74 for 10,843 coins, which is off by 5%. I have to say, I feel like that's not too bad.
  #21  
Old 09-18-2006, 03:16 AM
galt galt is offline
Guest
 
Join Date: Apr 1999
Quote:
Originally Posted by Jurph
Also, for anyone interested in playing around with the numbers, I've put together a Google Spreadsheet here that includes mass estimates for full distributions of coins, and the "no pennies" and "no quarters" mixes.
I took a look at your spreadsheet, and I don't fully follow the terminology you used, but our results differ for the "no pennies" and "no quarters" mixes. They seem to diverge in the calculation of how much of the total mass the individual coins make up.

For example, in my "no pennies" mix, 16.9% of the weight is from nickels, 11.5% of the weight is from dimes, and 71.7% of the weight is from quarters. It appears that you came up with 21.34%, 14.52%, and 90.77%, respectively, which adds up to more than 100%, so I think you made a mistake there. I might be overlooking something obvious, though.

Our $/lb numbers agree for the regular mix of all coins ($12.77), but I got $17.39/lb for "no pennies" and $5.43/lb for "no quarters".
  #22  
Old 09-18-2006, 03:31 AM
galt galt is offline
Guest
 
Join Date: Apr 1999
I uploaded my spreadsheet too so you can take a look. Mine's not as pretty.

http://spreadsheets.google.com/ccc?k...LvwFr0KgXDeSbA
  #23  
Old 09-18-2006, 06:45 AM
Jurph Jurph is offline
Guest
 
Join Date: Oct 2003
Quote:
Originally Posted by galt
Our $/lb numbers agree for the regular mix of all coins ($12.77), but I got $17.39/lb for "no pennies" and $5.43/lb for "no quarters".
I've adjusted the spreadsheet -- I was still dividing by the total mass of all four coins, even when only three coins were in the mix (cut/paste left in an absolute reference rather than a dynamic reference). Our values agree now. I'm also going to add a second set of values to my spreadsheet to account for Bergebo's change sample.
  #24  
Old 09-18-2006, 07:26 AM
Bergebo Bergebo is offline
Guest
 
Join Date: Sep 2006
From Jurph's spreadsheet.
Quote:
Bergebo's sample differs from expected results by 2.68%.
That's amazing work you two did. So a pound of change is worth ~ $13. Should help people out if they can drag their cache onto the bathroom scale.
  #25  
Old 09-18-2006, 08:27 AM
Khadaji Khadaji is offline
Member
 
Join Date: Mar 2002
Location: Southern Pennsylvania
Posts: 21,600
Quote:
Originally Posted by galt
Well if you took a sample of my hypothetical standard change mixture and simply threw out all the pennies, it would be (by weight) 16.9% nickels, 11.5% dimes, and 71.7% quarters, putting its value at about $17.39 per pound.
Based on that estimate that puts my piggy bank at 956.45. My estimate is over 1000, so we aren't too far apart. I have severay years to go before the bottle is full, so I won't know for a long time.
  #26  
Old 09-18-2006, 10:30 AM
DrDeth DrDeth is offline
Charter Member
 
Join Date: Mar 2001
Location: San Jose
Posts: 23,034
Whenever I go to either spreadsheet, there's a sign in?
  #27  
Old 09-18-2006, 10:43 AM
Jurph Jurph is offline
Guest
 
Join Date: Oct 2003
Quote:
Originally Posted by Johnny L.A.
FWIW I keep my pennies, nickles and dimes* in a one-quart glass milk bottle. I shake it from time to time to get the coins to settle. When it's full I usually have $45-$55 in change.

*I save the quarters for laundry. When I'm home (with my washer and dryer) I just save them.
I have now added volume and density calculations to put an upper bound on what you can expect a given volume of change to be worth. Assuming perfect packing, a quart of change with no quarters ("laundry mix") should be worth $66.80 (SDMB estimated distribution) or $78.70 (Bergebo's sampled distribution).

If we had more data points with known volumes, we'd probably be able to determine a useful (but imperfect) packing factor by which we could multiply a given volume to approximate the mass of normally-distributed coins therein. It would also be interesting to measure the volume of water that could be poured into a container "full" of coins. Assuming the water displaces all the air between the coins, you could get really good data on packing factor from that, too.

Of course then you'd want to disperse and dry the coins ASAP to avoid corrosion and ending up with a jar-shaped ingot of US currency...
  #28  
Old 09-18-2006, 11:02 AM
Sunspace Sunspace is online now
Charter Member
 
Join Date: Jun 1999
Location: Near the GT eeehhhh...
Posts: 26,673
When I come down to visit you folks, I'll surreptitiously throw a Canadian two-dollar coin into your change jar. It'll completely destroy your math.

Bwa-ha-ha-ha-ha!

Seriously, I wonder what the equivalent calculations are for other countries? Canada? Europe? Japan?

In Canada, we have two-dollar and one-dollar coins in common usage, but they tend to be used often and quickly disappear from one's change pouch. Quarters disappear almost as quickly, and the remaining change accumulates pennies disproportionately. Real-world Canadian change jars are mostly pennies, I suspect.
__________________
Rigardu, kaj vi ekvidos.
Look, and you will begin to see.
  #29  
Old 09-18-2006, 11:05 AM
mnemosyne mnemosyne is offline
Charter Member
 
Join Date: Feb 2000
Location: Montréal, Québec
Posts: 8,772
This thread, right here, is why I love the SDMB!
  #30  
Old 09-18-2006, 12:32 PM
Flipshod Flipshod is offline
Guest
 
Join Date: Oct 2004
Quote:
Originally Posted by mnemosyne
This thread, right here, is why I love the SDMB!
Me too.

One more possible complexity though. Haven't the weights of coins changed over the years. (particularly the quarter) So you'd have to find the distribution of "old" quarters vs "new" quarters, (and nickels too I think) ?

Or is it only volume that matters in your calculations???

Just a thought, and now I go and leave it up to all you intelligent industrious folks
  #31  
Old 09-18-2006, 02:00 PM
galt galt is offline
Guest
 
Join Date: Apr 1999
Quote:
Originally Posted by Flipshod
One more possible complexity though. Haven't the weights of coins changed over the years. (particularly the quarter) So you'd have to find the distribution of "old" quarters vs "new" quarters, (and nickels too I think) ?
Weight is critical to the calculations, but I'm pretty sure that the old quarters and new quarters are identical in weight. That was one of the requirements for making replacement quarters, as far as I know.
  #32  
Old 09-18-2006, 02:22 PM
Jurph Jurph is offline
Guest
 
Join Date: Oct 2003
I had worried about coins' ages affecting their mass, too, which was why I was tempted to go with volume first.

The two most relevant dates for that line of questioning are 1965 and 1982 -- by 1965, none of the coins we're considering* contained any silver; in 1982 the penny was changed from 3.1g to 2.5g. I suspect that the very small percentage of marginally-heavier "silver" coins is going to disappear in the noise of normal coin distribution; note that the theoretical distribution galt worked out and the observed distribution from Bergebo vary by more than 2% in mass.

If we assume that all coins minted in the last fifty years are equally distributed in the pockets of America, then pre-1965 "silver" coins would comprise ~20% of the samples, and the average mass of (for example) a dime would shift up from 2.27 grams to 2.32 grams -- about a 2% weight gain. The penny is a more severe case; an even distribution over the last fifty years would yield an almost 50/50 distribution of heavier (3.1g) pennies, making the average penny weigh 2.8g, a 12% error. Quarters went from 6.25 grams down to 5.67 grams in 1965, so even distribution would yield about a 2% gain in mass. The mass of the nickel remained unchanged.

The effects of such a sample would be interesting; the sheer volume of pre-1982 pennies along with minor contributions from dimes and quarters would mean that a large sample would be almost 6% heavier than the same distribution of all-modern coins. Once you add in their relative values**, it turns out that my hypothetical 50-year "perfect" sample of coins (galt's distribution) is worth about 5% less by mass: about $26.73 per kilogram. An evenly-distributed twenty-year sample would be much closer to expectations; "silver" coins would have constant mass and pennies would add less than 1% phantom mass (that is, a change of mass with no corresponding change in value). As a curiosity, a sample of coins that were all from before 1965 would be worth $24.64 per kilogram -- a 12.5% drop in value (by mass)!

I really doubt we'll see an even distribution out there; in fact, I suspect that coins have a "half life" and that as time goes on, fewer and fewer coins from each year are available. Mint production volume also fluctuates: in the last 3 years the number of pennies produced annually varied from 6.1 billion (2006) to 7.7 billion (2005) with 2004 coming in between with 6.8 billion. Other coin production varied similarly. I'm sure somebody out there knows how the coin years are distributed within the set of circulating coins, but if they do, they know it from sampling. If you're aiming for accuracy, and you know that the coin sample contains pre-1982 coins, then you should probably shave your value estimate down by maybe one percent, at most.

So now we know that the presence of older coins hurts our ability to estimate value by mass alone. Unless we can predict the packing factor for flat cylinders in mostly-cylindrical containers, we can't estimate by volume alone except to determine an upper bound. But both estimates together, taken with an assumption of the distribution of change in circulation, can give solid upper and lower bounds for the value of a known mass/volume of coins.

* - the circulated half dollar retained its silver content until 1970, but is almost never seen in circulation.

** - and ignore the possibility that you've got an ultra-rare coin worth $300 in your coin jar.
  #33  
Old 09-18-2006, 04:38 PM
iamthewalrus(:3= iamthewalrus(:3= is offline
Guest
 
Join Date: Jul 2000
The metal in pre-1965 silver coins is worth considerably more than their face value, isn't it? It's probably a reasonable assumption to make that they've been nearly entirely removed from the circulating currency. In fact, since they do have a different weight, the chance of them being removed goes up rapdily, since it's easy to mechanically remove them from mixed change.

Based on a brief sampling of websites with relatively absurd investment advice* provided by Google, it seems my assumption above is true. There are likely few to no pre-1965 90% silver coins in circulation.

*This is not meant as a comment on the validity of buying precious metals as an investment, only as a comment on the logical fallacies displayed at sites like this.
  #34  
Old 09-19-2006, 11:49 AM
gemdave gemdave is offline
Guest
 
Join Date: Sep 2006
us treasury coin bags

Quote:
Originally Posted by jnglmassiv
I don't think you could do it even with a known mass. You have 4 non-uniform parts (coins) with unknown proportions that don't fit together nicely.
Standard coin bags from U S Treasury hold $1000 for dimes and quarters and $200 for nickels a bag of dimes weigh 49.15 pounds quarters 50.13 pounds and nickels 43 lbs.
  #35  
Old 09-19-2006, 12:06 PM
Jurph Jurph is offline
Guest
 
Join Date: Oct 2003
Quote:
Originally Posted by gemdave
Standard coin bags from U S Treasury hold $1000 for dimes and quarters and $200 for nickels a bag of dimes weigh 49.15 pounds quarters 50.13 pounds and nickels 43 lbs.
Are the coins in those large bags loose, or counted and wrapped? If they're loose, then we could get a feel for the approximate volume of same-denomination coins. It wouldn't be perfect but we might be able to finagle some sort of packing factor from that. So, gemdave, tell us - how much volume does a bag full of nickels take up? A bag of pennies? Quarters? And is there a standard volume for a dime bag?
  #36  
Old 09-19-2006, 12:33 PM
gemdave gemdave is offline
Guest
 
Join Date: Sep 2006
Quote:
Originally Posted by Jurph
Are the coins in those large bags loose, or counted and wrapped? If they're loose, then we could get a feel for the approximate volume of same-denomination coins. It wouldn't be perfect but we might be able to finagle some sort of packing factor from that. So, gemdave, tell us - how much volume does a bag full of nickels take up? A bag of pennies? Quarters? And is there a standard volume for a dime bag?
The coins in the bag are loose and are measured by weight, the bag is approximately 12 inches wide by about 18 inches high. Sorry I cannot give you the inside volume of a full bag...when bag is closed about 3 inches at the top of the bag can be twisted to allow for sealing with heavy string
  #37  
Old 09-19-2006, 03:16 PM
Chronos Chronos is offline
Charter Member
 
Join Date: Jan 2000
Location: The Land of Cleves
Posts: 55,535
One possibly simplifying fact: If I recall correctly, pennies have the same "value density" as nickels, and dimes have the same as quarters. So we could deal with only two types of coin, "base" coins and "silver" coins.

One possibly complicating fact: Optimum packing density is, in principle, higher for objects of a mix of sizes than for objects of uniform size (the smaller ones can fit into gaps between the bigger ones). So it's conceivable that a container of mixed coins could have a higher value than the bounds calculated. I doubt this would be significant, though, since the packing probably isn't too close to optimal anyway.
__________________
Time travels in divers paces with divers persons.
--As You Like It, III:ii:328
  #38  
Old 09-19-2006, 04:25 PM
Jurph Jurph is offline
Guest
 
Join Date: Oct 2003
Quote:
Originally Posted by Chronos
One possibly simplifying fact: If I recall correctly, pennies have the same "value density" as nickels, and dimes have the same as quarters. So we could deal with only two types of coin, "base" coins and "silver" coins.
I'm not sure how you're arriving at value density, but I can't see that being accurate. If you're dividing value by coin volume (and ignoring packing factors) the penny is about $21,000/m3. The nickel is a hefty $72,500/m3; the dime a stunning $294,000/m3, and the quarter is worth $309,000/m3. All of those values assume that the entire cubic meter is full of coins -- no air! You'll have to melt down $310,000 worth of quarters to find out if I'm right on this one...

Quote:
One possibly complicating fact: Optimum packing density is, in principle, higher for objects of a mix of sizes than for objects of uniform size (the smaller ones can fit into gaps between the bigger ones). So it's conceivable that a container of mixed coins could have a higher value than the bounds calculated. I doubt this would be significant, though, since the packing probably isn't too close to optimal anyway.
I think you're right about that. I would guess that in a thoroughly-shaken coin jar, there may be as little as 20% air by volume, but it's probably closer to 30% or even 40%. I just back-of-the-enveloped the best packing of circles on an infinite plane and got ~91%, and I figure coins in a finite jar will do much worse thanks to edge cases.

I can't believe I didn't think of this earlier, but Coinstar.com has a utility that will estimate how much change is in your change container. They note that the "actual value may vary based on container and coin mix," and estimate that one gallon of change is worth $228.32. Of course their estimates are done by volume, but they do take packing factors into account.
  #39  
Old 09-20-2006, 05:57 PM
MelCthefirst MelCthefirst is offline
Guest
 
Join Date: Mar 2002
Our coins have just changed and the 5cent one is going to become obsolete. Imagine if you had $1000 of five cent coins and you don't take them to the bank in time!
  #40  
Old 09-21-2006, 03:12 AM
Orville mogul Orville mogul is offline
Guest
 
Join Date: Apr 2004
Quote:
Originally Posted by Jurph
Of course then you'd want to disperse and dry the coins ASAP to avoid corrosion and ending up with a jar-shaped ingot of US currency...
That would be really cool!
  #41  
Old 09-21-2006, 09:39 AM
Spiff Spiff is offline
Charter Member
 
Join Date: May 2000
Location: In the SPIFF Bunker
Posts: 2,611
Quote:
Originally Posted by Jurph
And is there a standard volume for a dime bag?
The dime bags I buy are very small, very light, and can be stashed in even the smallest jeans pocket.










What?!?!?
__________________
"Immigrants! That's all they do, you know. Just driving around listening to the raps and shooting all the jobs."
  #42  
Old 06-09-2010, 11:00 AM
tremsensgirl tremsensgirl is offline
Guest
 
Join Date: Jun 2010
Theft of quarters vs pigguy bank

Recently my husband and I were victims of a theft. The person stole 15 rolls of quarters=$150. We know the individual who stole from us. He said that he was at the coin counting machine turning in his daughters piggy bank, not our quarters...he is obviously full of poop. He is on video unwrapping coins for 6.30 minutes!Number 1: It does not take 6.30 minutes to empty a piggy bank in the machine. Number 2: I was wondering if anyone thought it possible for him to receive $130 from a child's medium piggy bank dimensions 71/2" W x 8" H. I truly want to believe this kid! He was a good worker with a family he needed to support. Please help me by letting me know if #2 is a possibility! Thanks!
  #43  
Old 06-09-2010, 04:07 PM
Gary Robson Gary Robson is offline
Charter Member
Charter Member
 
Join Date: Mar 2003
Location: Montana, U.S.A.
Posts: 9,448
Quote:
Originally Posted by tremsensgirl View Post
Recently my husband and I were victims of a theft. The person stole 15 rolls of quarters=$150. We know the individual who stole from us. He said that he was at the coin counting machine turning in his daughters piggy bank, not our quarters...he is obviously full of poop. He is on video unwrapping coins for 6.30 minutes!Number 1: It does not take 6.30 minutes to empty a piggy bank in the machine. Number 2: I was wondering if anyone thought it possible for him to receive $130 from a child's medium piggy bank dimensions 71/2" W x 8" H. I truly want to believe this kid! He was a good worker with a family he needed to support. Please help me by letting me know if #2 is a possibility! Thanks!
[moderating]
This is a perfectly reasonable question to ask, but please don't ask it at the end of someone else's four-year-old thread. Feel free to start a new thread. I'm closing this one.
[/moderating]
__________________
---
Yes, I have joined the ranks of former moderators. Being a mod was eating my life. Now I'm a member just like you. Except smarter and better looking.
Closed Thread



Bookmarks

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is Off
HTML code is Off

Forum Jump


All times are GMT -5. The time now is 10:59 PM.


Powered by vBulletin® Version 3.8.7
Copyright ©2000 - 2014, vBulletin Solutions, Inc.

Send questions for Cecil Adams to: cecil@chicagoreader.com

Send comments about this website to: webmaster@straightdope.com

Terms of Use / Privacy Policy

Advertise on the Straight Dope!
(Your direct line to thousands of the smartest, hippest people on the planet, plus a few total dipsticks.)

Publishers - interested in subscribing to the Straight Dope?
Write to: sdsubscriptions@chicagoreader.com.

Copyright © 2013 Sun-Times Media, LLC.