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#1
Old 10-20-2013, 05:16 PM
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Formula for estimating change in a jar?

I have a one gallon pickle jar sitting on my desk. Right now, it's exactly half-full from all the loose change I've collected over the years.

Is there any way to estimate how much money I've gathered? Assume that I have roughly equal numbers of pennies, nickels, dimes, and quarters.
#2
Old 10-20-2013, 05:31 PM
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First off, there wouldn't be an equal number of each coin. You'll have more pennies, then quarters, then nickels, then dimes. You might just weigh the jar (it'll be damn heavy), subtracting the weight of a similar jar, then grab a few handfuls of the coins and weighing them. If you can't get your hand into the jar, just spill some out instead. When you count those handfuls, it's easy to figure the value of the entire jar by dividing the weights and multiplying by the smaller value.
#3
Old 10-20-2013, 05:34 PM
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Quote:
Originally Posted by panache45 View Post
......You'll have more pennies, then quarters, then nickels, then dimes......
How do you figure that?
#4
Old 10-20-2013, 05:39 PM
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Its because of mintages and change. More pennies and quarters are minted an other coins, and for all change of .01 to .99, you will usually get max 4 pennies, max 3 quarters, max 2 dimes, and max 1 nickle.

How accurate do you want to get? I was able to get an extremely accurate estimate by separating 20kg of coins into pennies, nickels, dimes and quarters and then weighing each group on a x.x gram scale. I got within a dollar. But, i also separated all the copper pennies 3.1 gram) from the zincs (2.5 grams.)
#5
Old 10-20-2013, 06:26 PM
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Another method: Maybe you can ask a hundred people (starts at 1:30)? In that experiment, 116 people were asked to estimate the number of jellybeans in a big jar. Their replies ranged from 400 to 30,000, but the final average was within 0.1% of the actual answer...
#6
Old 10-20-2013, 08:53 PM
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If we assume that every purchase you make has a random number of cents, that you always pay with a whole number of dollars and get change, that the change was made with the minimum number of coins, and that all coins you get go into the jar indiscriminately, then your coins will be in the ratio 15 quarters : 8 dimes : 4 nickels : 20 pennies. If you got every possible amount of change, the totals would be 150 quarters, 80 dimes, 40 nickels, and 200 pennies.

In practice, these numbers will be off, with the reality most likely favoring dimes and nickels more than those numbers suggest, for a few reasons. One, you're not always going to pay with a whole number of dollars: If something costs $20.01, for instance, you're probably going to find a penny somewhere (maybe from a leave-a-penny dish) rather than getting 99 cents in change. This will tend to lower the number of pennies. Two, some coins might not ever make it to the jar: If the change is just a few cents, you might just drop them rather than carrying them home at all. This will again tend to lower the number of pennies. Three, you might specifically look for quarters to use for other purposes, such as coin-operated laundry machines, which will tend to lower the number of quarters.
#7
Old 10-20-2013, 09:01 PM
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Originally Posted by Vicullum View Post
I have a one gallon pickle jar sitting on my desk. Right now, it's exactly half-full from all the loose change I've collected over the years.
I would guess around $150-$200. I've seen these "guess the change in a jar" things come up before on Facebook and on the internet, and, typically, they end up about $300-$400 per gallon for random pocket change. YMMV. No formula, just reporting the results I've seen. If it's truly an equal distribution, I would guess at the higher end of the range.

Last edited by pulykamell; 10-20-2013 at 09:03 PM.
#8
Old 10-20-2013, 09:08 PM
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I would just roll up the damn things.
#9
Old 10-20-2013, 09:34 PM
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I just counted my coin jar, there were more $2 coins than any of the lower denominations. $1582 weighed 16.2 kg (or 18.2)
#10
Old 10-20-2013, 09:36 PM
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Originally Posted by Chronos View Post
If we assume that every purchase you make has a random number of cents, that you always pay with a whole number of dollars and get change, that the change was made with the minimum number of coins, and that all coins you get go into the jar indiscriminately, then your coins will be in the ratio 15 quarters : 8 dimes : 4 nickels : 20 pennies. If you got every possible amount of change, the totals would be 150 quarters, 80 dimes, 40 nickels, and 200 pennies...[snip of nice real-world considerations]...
Tell me the logic of the ratio...

Every denomination mod-25 coin?


ETA: Can I use this information to get into MIT and get power?

Last edited by Leo Bloom; 10-20-2013 at 09:37 PM.
#11
Old 10-20-2013, 09:50 PM
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Originally Posted by Cugel View Post
I just counted my coin jar, there were more $2 coins than any of the lower denominations. $1582 weighed 16.2 kg (or 18.2)
What's a $2 coin?
#12
Old 10-20-2013, 09:50 PM
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Basically, I made a huge table with the coins used to make change for 1 cent, for 2 cents, for 3 cents, etc., up to 99 cents, and then (since I was assuming all of those come up equally often) I just totaled them.
#13
Old 10-20-2013, 09:52 PM
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Originally Posted by chacoguy View Post
What's a $2 coin?
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#14
Old 10-20-2013, 09:54 PM
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Originally Posted by pulykamell View Post
I would guess around $150-$200. I've seen these "guess the change in a jar" things come up before on Facebook and on the internet, and, typically, they end up about $300-$400 per gallon for random pocket change. YMMV. No formula, just reporting the results I've seen. If it's truly an equal distribution, I would guess at the higher end of the range.
The best I can tell you is, back in happier financial times, I used to also toss all my change into a coffee can. After a few years I had accumulated about three or four of them, each full to the top with coins. At some point I needed extra money so I would periodically take them to a Coinstar machine to cash them in. Every time it wound up being around $350 (more than I initially expected!)

I don't know exactly how a coffee can converts to a gallon. They contain 39oz of coffee, but that's weight not volume. They look roughly similar in size, a coffee can probably holds a little less than a gallon.

Quote:
Originally Posted by campp View Post
I would just roll up the damn things.
I know a lot of people bemoan the fact that Coinstar machines charge a percentage fee (last time I used one it was 9%) to count your coins, like it's a ripoff or something. But I can't think of a more aggravating, time-consuming, tedious process than sorting, rolling & wrapping freakin' coins! Not to mention the fact that it would probably take all day to do a coffee can's worth. Plus you have to take them to your bank (if you don't have an account banks won't accept large quantities of coins, even rolled) to cash them in. Coinstars are a godsend as far as I'm concerned...
#15
Old 10-20-2013, 09:56 PM
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I thought you had an analytical (mathematical) method. (I always think of Chronos and his cohort here as ratiocinating the fuck out of everything from some single thought, leaving simple counting for mortals.)

There must be a math expression governing the result/problem. Right? Right??!


ETA: to Chronos

Last edited by Leo Bloom; 10-20-2013 at 09:56 PM.
#16
Old 10-20-2013, 10:06 PM
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Originally Posted by Hail Ants View Post
I know a lot of people bemoan the fact that Coinstar machines charge a percentage fee (last time I used one it was 9%) to count your coins, like it's a ripoff or something. But I can't think of a more aggravating, time-consuming, tedious process than sorting, rolling & wrapping freakin' coins! Not to mention the fact that it would probably take all day to do a coffee can's worth. Plus you have to take them to your bank (if you don't have an account banks won't accept large quantities of coins, even rolled) to cash them in. Coinstars are a godsend as far as I'm concerned...
You don't have to roll your coins to take them to a bank; banks have coin counting machines. Maybe not at every small branch, but I've never lived anywhere where there wasn't at least one branch in town that would take your coins, dump 'em in a machine, and deposit them in your account/give you cash.

Yeah, you probably have to have an account at the bank, but even now, in the days of digital everything, I typically have to go to my bank physically at least a couple times a year to do something or other. I just bring my coins in at the same time. Never has been a hassle, or a charge, or have they been anything but happy to do it.
#17
Old 10-20-2013, 10:12 PM
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A quart of pennies is right around $13 (if you can trust a Coinstar machine).

Last edited by blondebear; 10-20-2013 at 10:14 PM.
#18
Old 10-20-2013, 10:15 PM
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Quote:
Originally Posted by Hail Ants View Post
...
I don't know exactly how a coffee can converts to a gallon. They contain 39oz of coffee, but that's weight not volume. They look roughly similar in size, a coffee can probably holds a little less than a gallon.
Fresh beans:
0.52063621494641

Roasted beans:
0.67610397357624

according to http://thecalculatorsite.com/con...httovolume.php
(one of my favorite sites)
#19
Old 10-20-2013, 10:33 PM
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Yeah, I could (and should) have done it smarter than just a big table. But I'm tired, and didn't feel like thinking too hard, and the mechanical brute force method doesn't require much thought and works fine.
#20
Old 10-20-2013, 10:49 PM
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Well, be sure to get some rest. Oh, and by the way, it would be best if you have it on my desk by, I don't know, noon tomorrow, ok?
#21
Old 10-20-2013, 11:19 PM
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The others are right, There are no ways of getting a truly accurate measure other than just counting the coins. The missing factor is someone's spending patterns. Other people got the ratios of average coins stored correct assuming it is truly random but it hardly ever is. It depends on what you buy and what you put in the jar. I spend quarters freely for example but I throw pennies, nickles and dimes into my coin jar. Quarters are the highest value common coin so how you treat those can greatly influence the total value of the jar.

The best way to approach this problem is through statistical trials of similar circumstances. A given person with the same coin jar will end up with very similar value for a given volume of coins. It will also be extremely similar to other people with the same habits.

I can tell you what the result will be within reason for a pickle jar that size because I have done it before myself. It is between $200 and $300 like other people said. My pick is $283.16. Go to a Coinstar machine and check it and post the results. Pro-tips: Most of them offer gift cards from major retailers so it doesn't cost you anything if you have a place to spend it. Rolling coins to take to the bank is a fool's errand. Also, lift the sorting tray up with your fingers so that it is at a downward angle the whole time and then just scrape the coins in with your fingers. Many people don't do it correctly and it takes 5x longer than necessary.

Last edited by Shagnasty; 10-20-2013 at 11:22 PM.
#22
Old 10-21-2013, 12:02 AM
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Originally Posted by Shagnasty View Post
I can tell you what the result will be within reason for a pickle jar that size because I have done it before myself. It is between $200 and $300 like other people said.
Well, actually, I think our spread is much higher than that. I said $150-$200 for the half-filled gallon jar, based on $300-$400 per gallon of mixed change. Leo Bloom's site that 39 oz of roast coffee beans would equal .67 gallons and Hail Ant's reporting that such a filled container returned $350 would put it at $522 per gallon (!), which seems high to me.

This guy got $2212.30 out of a filled-to-the-brim 5 gallon jar, for $442.46 per gallon. Now, my hunch is that is not going to downscale perfectly, and you're going to get a good bit less per gallon with a one gallon jar, but that should leave you in the $300-$400 per gallon range.

That said, as you said, it depends on your spending habits and what change you save. I tend to pick quarters out of the change pile or my pocket, so that would influence the count. If the OP really does have an equal distribution, I could believe the higher end of the estimate.
#23
Old 10-21-2013, 12:42 AM
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As I understand it, most banks no longer want human-rolled coins. Too many people try to use them for fraud. So don't waste your time rolling your own. Just bring them in loose and let them run them through their machine. My bank, in fact, has a self-serve coin counting machine in the lobby. I just put all my loose change into it and it gives me back a receipt that I take to the teller to deposit. And I don't have to pay anyone 9% for this service.

However, I rarely use this machine. Nowadays, I usually get rid of my coins by spending them. But then I buy lots fo stuff with cash that most people use credit cards for, such as groceries and gasoline. I try to (and usually succeed in) paying exact change in these transactions.

But I do have a jar of coins, well two of them. But the coins in them don't come from my change, but rather a different source. I bicycle a lot, and about 10 years ago started noticing a lot of coins on the side of the roads. For reasons I can't quite explain, I started to pick them up and put them in jars. I only put found coins in these jars, never change from transactions. One jar is full, the other is about 75% full. They're one-quart mayonaise jars, although the full one is packed to the brim, so it's closer to a liter of coins.

Some day I'll probably take them to the bank to have them counted. I expect numerous rejects by the machine, though, especially the pennies. You see, it doesn't take too many times being run over before pennies lose most of their copper coating. I assume the machines go by the electrical properties of the coins and roadkilled pennies will not have the same properties as ordinary ones.

Well, if I ever do cash them in, I'll have a guess-the-total contest in the Game Room or somewhere. But I'm in no hurry to do that.
#24
Old 10-21-2013, 01:11 AM
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Quote:
Originally Posted by pulykamell View Post
....Leo Bloom's site that 39 oz of roast coffee beans would equal .67 gallons ...
[nitpick]
0.68
[/nitpick]
#25
Old 10-21-2013, 01:14 AM
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Originally Posted by chacoguy View Post
What's a $2 coin?
Welcome to the Internet, now available in countries other than the US of A!
#26
Old 10-21-2013, 04:23 AM
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Originally Posted by Leo Bloom View Post
There must be a math expression governing the result/problem. Right? Right??!
If each coin is an integral multiple of the smaller coins, it would be easy. For example, if no dimes were used then average change would be 1.5 quarters, 2 nickels and 2 pennies. (These sum to $0.495 as expected.) With K pieces of a quadloon, (K-1)/2 is the expected number of pieces; there are K=4 quarters in a dollar, so (4-1)/2 = 1.5 is expected, and so on.

Multiply these numbers by 100 to get (except for the dimes and nickels) the numbers Chronos posted:
150 : 0 : 200 : 200
Quarters do not have a whole number of dimes, so allowing dimes complicates. Simplest is to just write a table showing how the five equally probable cases of nickels change into nickels and dimes:

0 1 2 3 4 -- nickels only, average 2
-----------
0 1 0 1 0 -- nickels, average 0.4
0 0 1 1 2 -- dimes, average 0.8

Net result
150 : 80 : 40 : 200
Even with the dime "problem", a "greedy" algorithm leads to a minimal number of coins in the U.S., but this isn't generally true. For example, suppose a 7-cent septam were provided instead of 10-cent dime. To provide 11 cents change, a greedy algorithm would give five coins (1 septam, 4 pennies), when only three are needed (2 nickels, 1 penny).
#27
Old 10-21-2013, 06:06 AM
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Originally Posted by Cugel View Post
Top right (the non-furry top right, that is)
http://i.imgur.com/Ni2qMKR.jpg
But most change jars don't contain a cat and that would throw off your average.
#28
Old 10-21-2013, 09:03 AM
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Originally Posted by Hail Ants View Post
I know a lot of people bemoan the fact that Coinstar machines charge a percentage fee (last time I used one it was 9%) to count your coins, like it's a ripoff or something.
All the Coinstar machines I've used have an option for getting gift cards that are at face value, no percentage cut for the house.
#29
Old 10-21-2013, 10:35 AM
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Originally Posted by campp View Post
I would just roll up the damn things.
Pretty much a waste of time, as a lot of banks won't take coin rolls these days. Ours has a coin counting machine in the lobby.
#30
Old 10-21-2013, 10:38 AM
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Originally Posted by Telemark View Post
All the Coinstar machines I've used have an option for getting gift cards that are at face value, no percentage cut for the house.
Protip: self-checkout machines take change just fine. Use your quarters and even dimes at full value.
Use coinstar or similar for pennies and nickels when the jar gets too full.

Also, a hundred pennies weighs a pound, to help answer the OP.

Last edited by aNewLeaf; 10-21-2013 at 10:39 AM.
#31
Old 10-21-2013, 03:15 PM
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One nice thing about living in Nevada is that there is nearly always a casino close by that will run it through their coin counter thingie.

Of course moving to Nevada just to get easy coin counting might not work out well in the long run.
#32
Old 10-21-2013, 03:29 PM
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Originally Posted by Telemark View Post
All the Coinstar machines I've used have an option for getting gift cards that are at face value, no percentage cut for the house.
Exactly. I take my coins to the local CVS and their Coinstar machine. There's no way I'm NOT going to spend several hundred dollars at the CVS in the next few months, so a "gift card" there is as good as cash to me.
#33
Old 10-21-2013, 04:25 PM
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Regarding Coinstar machines: The one I use lists several options for gift certificates. I pick Amazon. (Which of course gets used fairly quickly.) No surcharge. I assume Coinstar makes it's money off of unused gift certificates plus a little bit of kickback from the gift certificate retailer per purchase.
#34
Old 10-21-2013, 06:55 PM
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Originally Posted by aNewLeaf View Post

Also, a hundred pennies weighs a pound, to help answer the OP.
Back when I worked for a convenience store, there were a few times when we ran short of pennies (region-wide shortages). In those cases we encouraged customers to bring their pennies in. The easiest way to cash them in was to weigh them on our produce scale... to do this we had to calculate the per pound price of pennies, which we did by plopping them down on the scale until the weight read "1.00". It took 144 pennies to make a pound. Obviously this could go up or down a few, but I'm pretty sure that 100 pennies is going to come up well short of a pound.

Actually, I have a postal scale, if I have time later I'll post the per pound price of all the common coins.
#35
Old 10-21-2013, 07:23 PM
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separate 'em

it turns out that quarters and dimes both have the same dollar/pound value, and that's about $20/lb - i'm saving just those two in a five gallon water (plastic!!) bottle... it's been a long haul, but it's maybe 2/3 full and weighs over 100 pounds. that's some serious change
#36
Old 10-21-2013, 07:28 PM
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^^^ not surprising since the were originally silver coins. Halves and Eisenhower dollars should work out the same too.
#37
Old 10-21-2013, 09:59 PM
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1.000 Lbs=172 Pennies=91 Nickels=210 Dimes=80 Quarters
(USA coins)

I Only Had Enough Dimes For 1/10 lb, So I Multiplied By 10
Only Had Enough Quarters For 1/4 Lb So Multiplied By 4.
#38
Old 10-22-2013, 02:41 AM
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I do the coffee can thing, fill it to the brim, and it's remarkable how close it comes to $105 every time. I've won prizes from the Coinstar machine for guessing the total value within a certain range. I always guess $105. Last time I was only 16 cents off, which amazed the teller.
#39
Old 10-22-2013, 12:59 PM
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Originally Posted by aNewLeaf View Post
Protip: self-checkout machines take change just fine. Use your quarters and even dimes at full value.
Use coinstar or similar for pennies and nickels when the jar gets too full.

Also, a hundred pennies weighs a pound, to help answer the OP.
Self-checkout machines will even take pennies, at least the ones at the supermarket do. I get rid of a lot of pennies that way.
#40
Old 10-22-2013, 02:57 PM
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I once had a water-cooler jar full of miscellaneous change to deal with.

I found it interesting that dimes and quarters are worth the same amount per unit weight. I forget the coefficient, but it should be easy to look up. Something very simple like $10/lb, IIRC.

The value of pennies and nickels per unit weight is tiny in comparison (IIRC, under 10% of the total in my case).

So, if you can measure the percentage of quarters and dimes by weight in a representative sample and extrapolate to the full weight, that should get you in the ballpark.

IIRC, the water cooler jar had about $1000 in it.
#41
Old 10-22-2013, 03:08 PM
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Missed the edit window. It's $20/lb for dimes and quarters, and the whole thing was closer to $1200. Also, the guy whose bottle it was had started tossing only pennies in and then switched at about 5" depth to tossing all the change in.

I believe the water cooler bottle was 5 gal, so that's $240/gal.

Last edited by Learjeff; 10-22-2013 at 03:09 PM.
#42
Old 10-22-2013, 03:46 PM
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I also use an old glass Vlassic pickle jar I keep in the garage for all my loose change, which I dump from my wallet on my way in from the garage every day. Before the holidays each year, I take it down to the Coinstar machine and convert it into an Amazon gift card (at no cost), which is then used to start my holiday shopping for gifts. Based on my own experience, half a pickle jar nets me around $120. I'm not sure if mine is a gallon. I think it's more like a half gallon.
#43
Old 10-22-2013, 05:01 PM
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I would find some appropriately sized scoop, say a half-measuring cup, but the size of the scoop doesn't matter as long as I can use it to reach in there and pull out a representative sample of the jar's contents. I'd take out two or three scoopfuls, and average the distribution across all of them.

Then I'd weigh the entire lot of coins and assume that the average distribution from the last stop is reasonably close to the total distribution, and calculate the total based on that.
#44
Old 10-22-2013, 05:37 PM
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Originally Posted by Telemark View Post
All the Coinstar machines I've used have an option for getting gift cards that are at face value, no percentage cut for the house.
And sometimes, typically around Christmas, they have promotions where you'll get an extra $10 gift card if you change in at least $50.
#45
Old 10-24-2013, 12:23 AM
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Originally Posted by Ellis Aponte Jr. View Post
I do the coffee can thing, fill it to the brim, and it's remarkable how close it comes to $105 every time. I've won prizes from the Coinstar machine for guessing the total value within a certain range. I always guess $105. Last time I was only 16 cents off, which amazed the teller.
I assume you mean filled with only pennies. I've never seen a Coinstar with the 'prize guessing' option, have to look for it...
#46
Old 10-24-2013, 12:43 AM
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Originally Posted by Hail Ants View Post
I assume you mean filled with only pennies. I've never seen a Coinstar with the 'prize guessing' option, have to look for it...
I should have clarified that... The machine I use is not a Coinstar brand machine, but rather a machine made by another company that works the same basic way as a Coinstar. It's called a Penny Arcade. And my coffee can is filled with all kinds of coins, in their normal distribution.

Last edited by Ellis Aponte Jr.; 10-24-2013 at 12:44 AM.
#47
Old 10-24-2013, 12:59 AM
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This is a good walk-through of the Penny Arcade coin guessing process.
#48
Old 10-24-2013, 02:53 AM
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Quote:
Originally Posted by Superhal View Post
...
But, i also separated all the copper pennies 3.1 gram) from the zincs (2.5 grams.)
(bolding mine)

Quote:
Originally Posted by turtlescanfly View Post
1.000 Lbs=172 Pennies=91 Nickels=210 Dimes=80 Quarters
(USA coins)

I Only Had Enough Dimes For 1/10 lb, So I Multiplied By 10
Only Had Enough Quarters For 1/4 Lb So Multiplied By 4.
(bolding mine)

:nitpick: It looks like you must have had some 'copper' pennies mixed in with 'zinc' pennies if you got 172/lb. All copper pennies would be 145/lb. and all zinc pennies would be 180/lb. (using Superhal's findings).
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#49
Old 10-24-2013, 03:10 AM
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Quote:
Originally Posted by Cugel View Post
Top right (the non-furry top right, that is)
http://i.imgur.com/Ni2qMKR.jpg
What country are you in? Those don't look anything like our $2 coins.
#50
Old 10-24-2013, 03:49 AM
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Join Date: Sep 2009
Location: The Internet. Since '84.
Posts: 6,460
Quarters and dimes are different weights too, before and after 1965.

Not to mention dollars and halves too but those are much rarer.

http://usacoinbook.com/coin-melt-values/
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