First ever Wild About Math! contest

13Nov/074

First ever Wild About Math! contest

Hi everybody,

Here's a nice little problem I found in a book, published in 1967. I won't give away the source until the contest is over.

This contest has just one question. The first person to write a comment with the right answer plus a justification of the answer, gets glory on this blog and the admiration of many. Here's the question:

If a millionaire offered you your choice between a barrel filled with half dollars and the same barrel filled with dimes, which would you choose?

Glory and admiration aside this question makes for a nice exploration for children (and adults).

Enjoy!

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Jonathan
November 13th, 2007 - 19:50

Hmm. We need to know the diameter and thickness of each. We’ll get value per unit volume, and not worry if we are filling a drinking glass or an oil drum. And then that unit volume should be expanded to include the dead space (assume planar hexagonal packing? or can we do much better with a jumble?)

OK, now a start.
Half Dollar: diameter 30.61mm, thickness 2.15mm
Dime: diameter 17.91mm, thickness 1.35mm

Good luck
Sol
November 13th, 2007 - 20:09

Jonathan,

Either you have a very sensitive instrument for measuring dimensions of coins or you found the same US Mint coin specification web-site I found.

Planar hexagonal packing sounds good to me.
What’s “jumble”?
Jonathan
November 13th, 2007 - 21:53

Found them on wikipedia. Does the info fit in a table? Then some boy has actually put it into a table on Wikipedia. Works every time.

Jumble? Like the coins in my coffee can?
Pseudonym
November 13th, 2007 - 22:20

Surely the packing doesn’t make a difference. That only matters if you want to know roughly how much money you’re getting.
For the purpose of this problem, all you need to know is which is the better deal of the two. All that matters is that the barrels are the same size, and large enough compared to the size of a coin that no matter how you pack, the packing fraction is roughly the same.
Given that, the question is really asking which of the two coins contains the most monetary value per unit volume.
So based on those figures, the half dollars contain 0.0316 cents per cubic millimeter, and the dimes contain 0.0294 cents per cubic millimeter.
Take the half dollars.
Oh, and the zinc in pennies (which makes up 97.5% of their weight) is only worth about 0.81c on the open market, so you would not be better off taking pennies and melting them down.
The best deal of all US coins is dollar coins. Susan B. Anthony, Sacagawea and President’s dollars are all the same dimensions, and are worth 0.09 cents per cubic millimeter.