An old Puzzle Revisited

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Today I received an e-mail from an astute reader, regarding the Question of the Week for the fourth week of March, 2003. The question was:

Which is worth more, a pound of $5 gold coins, or a pound of $10 gold coins? Explain why.

Before I go into the reader’s observations, let me tell you the answer:

Since gold coins (if they are gold coins, and not some hybrid - and the question did say “gold coins”) are valued by their weight, it stands to reason that a $5 gold coin is worth half of a $10 gold coin.

To make up a pound of $5 gold coins, you would therefore need twice as many as you would to make up a pound of $10 gold coins.

As you can see, twice as many $5 gold coins as $10 gold coins will have the same value. Conversely, that means that half as many $10 gold coins as $5 gold coins will have the same value. In other words, a pound of $10 gold coins has the same value as a pound of $5 gold coins.

So the answer is: “They are worth the same.”

Now back to our reader - he wrote the following:

The fly in the ointment of this question is, “Who minted the coins, and when?”

In the very early days, the government minted the coins and would put $5.00 of gold into the $5.00 gold piece, and a $10.00 gold piece was double the weight. In this scenario, the pound of $5.00 coins might hold 16/1-ounce coins worth $80 total. And the 1/2 pound of $10.00 coins would hold 4/2-ounce coins worth $40.

Simple. But give it time, and the demand for the smaller denomination is great so the government modernizes the $5.00 coins (or worse, privatizes them), so they turn out to have only a gold plating and are made of nickel.

Then the Republicans come along and crash the money markets like everything else: low and behold, the value
of the bags changes in this way:

Let’s define your terms, Brian!

Yours truly,

Pierce Brosnan (Not real name).

My reply:

God, Pierce, I thought I was picky!

OK, to be really, really picky, I DID define my terms. I said “gold coins.” I didn’t say, “gold-style” (as in Kosher-style”), I didn’t say “virtual gold” (as in “virtual reality”), nor did I say “near-gold” (as in “near beer”), nor “faux-gold” (as in Faux News).

I did not call it “trompe le’oiel”
I did not call it “virtual.”
I did not call it “counterfeit”
I did not say that, not one bit.

I did not say that it was “pseudo”
Nor imply it was E.U. dough.
No implication of being “gilded”
“Gold coin” is clearly how I billed it.

I didn’t say ’twas from Franklin Mint.
(Had I done that I would have sinn’t.)
Lest your doubt not be abated,
Rest assured it’s not “gold-plated.”

I simply said it was of gold.
As gold, not “costume,” bought and sold.

I did not say ’twas “nickel-core”
Gold is it’s only stock and store.
It’s just as gold as gold of yore.
Now let the doubt be nevermore.

By the way, would it be OK to use this repartee in the next installment of the “Math Mojo Chronicles”? (I’d change your name. Would “Pierce Brosnan” work for you?)

Hotcha!

Professor Homunculus

The upshot on this whole exchange, is that you must assume that the coins are made of gold for the puzzle to work.

And that is a fair assumption, as my reply explains.

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