Which would you prefer: A half a barrel of dimes or a barrel of nickels?

[John_T.Conklin]

@zut

You sure you measured right? The US Mint says the diameter of a dime is about 0.705 in.

I measured again, and got 0.703". :smack:

I’m not quite sure how I managed to be off by .090" Might as well be a mile.

Moreover, this page claims that there are about 5250 nickels per gallon, and about 10500 dimes, for an exact 2:1 ratio. [And, not on topic, but interesting: dimes, quarters, and half dollars work out to the same amount of money per gallon.]

With the new numbers, the cubic volume of the dime is 0.0248 in^3, very close to half the volume of the nickel. Taking the next step, Dimes are ~403 cents/in^3 and nickels are ~95 cents/in^3. So it looks like a half barrel of dimes is still about twice is valuable as a full barrel of nickels.

So I guess I should have taken the half barel after all. I guess that’s the difference between precision and accuracy… :smack:

[chrisk]

@John Corrado

It’s not mathematics, it’s just simple logic.

snip

But, because nickels are larger than dimes, there must be more dimes in the half-barrel than half the number of nickels in the full barrel. Therefore, the half-barrel of dimes is worth more.

The emphasized sentence is a weak logical step, it seems to me. Depending on the size and shape of the dime, it’s not guaranteed that there are more dimes than half the full barrel of nickels… if the dimes are a little smaller and much more awkwardly shaped, there might not even be as many.

Given that dimes and nickels are the same overall shape (highly flattened cylinders,) I think you can make a convincing argument that there are at least as many dimes as half the nickels, and therefore that the dimes are at least as valuable. To prove anything further, you kinda need to go to the maths.

@Kimstu

I don’t think you’re wrong about regular dodecahedra, but the ones that hexagonal-lattice-packed spheres expand into are rhombic dodecahedra, which are space-filling:

Oooh, interesting. I tend to associate those terms, (dodecahedron, tetrahedron, icosahedron, octahedron) so strongly with the platonic solids that I never even thought about irregular solids.

[John_Corrado]

Actually, to express it mathematically:

Let VB= The volume of the Barrel.
Let VD= The volume of a dime.
Let VN= The volume of a nickel.

The question is the relationship between

1/2*(VB/VD)*10 and (VB/VN)*5.

which can be reduced to

(VB/VD)*5 vs. (VB/VN)*5

which goes down to

(VB/VD) vs. (VB/VN)

which can further be reduced to

(1/VD) vs. (1/VN).

Since VD<VN, 1/VD>1/VN.

[Tranquilis]

@Munch

Read the OP again. You pick either:

1. A Full barrel of nickels

-or-

2. A **HALF ** barrel of dimes.

I’d still go with the dimes.

Oops. Quite right. :o

I’d still take dimes - I’m betting they’re less than half the volume of a nickel, and even if they aren’t, they’re still easier to move about.

[HeyHomie]

@zut

Moreover, this page claims that there are about 5250 nickels per gallon, and about 10500 dimes, for an exact 2:1 ratio.

A 30-gallon barrell of nickels: 157,500 nickels = $7,875.

15 gallons of dimes: 157,500 dimes = $15,750.

Take the dimes.

[Bottle_of_Smoke]

I’m with John on this. Unless I’m totally missing something. Which is certainly possible. I don’t know how to write a math formula for it, but logic says the dimnes win.

Pretend that nickles and dimes are exactly the same size coin.
Pretend that a full barrel hold 1,000 coins (that’s one small barrel, but bear with me).

A full barrel of nickels would be 1,000 coins at $0.05 each, or $50.
A half barrel of dimes would be 500 coins at $0.10 each, or $50.

So only in the case of the two coins being the same size would the value of both barrels be the same.

But dimes are clearly much smaller than nickles, so a half barrel of dimes would be much more than 500 coins. Which means that the half barrel would have a much higher value.

(If I missed something, go easy on me. I ain’t had no fancy book larnin’)

[Enright3]

@chrisk

How about a briefcase?

Sorry, can’t do that… only Marsellus Wallace knows what’s in the briefcase.

[Uncommon_Sense]

@Bottle of Smoke

I’m with John on this. Unless I’m totally missing something. Which is certainly possible. I don’t know how to write a math formula for it, but logic says the dimnes win.

Pretend that nickles and dimes are exactly the same size coin.
Pretend that a full barrel hold 1,000 coins (that’s one small barrel, but bear with me).

A full barrel of nickels would be 1,000 coins at $0.05 each, or $50.
A half barrel of dimes would be 500 coins at $0.10 each, or $50.

So only in the case of the two coins being the same size would the value of both barrels be the same.

But dimes are clearly much smaller than nickles, so a half barrel of dimes would be much more than 500 coins. Which means that the half barrel would have a much higher value.

(If I missed something, go easy on me. I ain’t had no fancy book larnin’)

I agree. They’re twice the value at half the size. Dimes win.

[chrisk]

@Enright3

Sorry, can’t do that… only Marsellus Wallace knows what’s in the briefcase.

Not that briefcase. Just an ordinary briefcase full of… well, let’s say one dollar bills. Make your pick between that and the other two choices.

[Xema]

@chrisk

The emphasized sentence is a weak logical step, it seems to me. Depending on the size and shape of the dime, it’s not guaranteed that there are more dimes than half the full barrel of nickels… if the dimes are a little smaller and much more awkwardly shaped, there might not even be as many.

It would be quite surprising if a smaller, thinner coin somehow managed to take up more space than a larger, fatter one.

[Civil_Guy]

@Tranquilis

Oops. Quite right. :o

I’d still take dimes - I’m betting they’re less than half the volume of a nickel, and even if they aren’t, they’re still easier to move about.

I agree. There’s more chance we could move the barrel ourselves, rather than have to cough up a few bucks hiring someone to help us. 'Course, I dunno… I bet even a half barrel of dimes is still pretty heavy…

[Shagnasty]

@chrisk

The emphasized sentence is a weak logical step, it seems to me. Depending on the size and shape of the dime, it’s not guaranteed that there are more dimes than half the full barrel of nickels… if the dimes are a little smaller and much more awkwardly shaped, there might not even be as many.

What are all these different shapes that you have seen dimes come in?