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The puzzle:

In my pocket, I have two US coins of total value of 15 cents. One of my coins is NOT a nickel. What are the coins?

A mathematician told me that I was totally wrong when I posted my solution (one coin, a dime; another one, a nickel). The mathematician wrote:

You are totally wrong! A dime and a nickel is a deceiving answer which you should never give. The truth is we were given a piece of information about just ONE coin. They told us: 'One coin is NOT a nickel.' So we know absolutely nothing about the other one! It may also be NOT a nickel as well as the first one.

I analyzed his observation and it's essentially true. Indeed, they told us a bit of information referring to one coin only. Absolutely no information about the other one. So is he right?

Furthermore, he made another strange observation. He said it's a mathematical problem and not an economical one. Thus, children aren't obliged to know US coin denominations, so 3 and 12 cents is a totally correct answer. And so is 4 and 11 cents. And so on.

Is this problem a good puzzle at all?

Personally I consider it extremely simple but very, very good. For a child, of course. But an adult can enjoy it too. It was very strange to hear such words from a professional mathematician.

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    $\begingroup$ I guess the mathematician is of the ilk who knows the exact volume of a jar, but not how to open it. Obviously, they are completely unfamiliar with money. And logic too. I quite liked the puzzle – I did have to think for a moment! The mathematician IMO is wrong to say "the other coin might not be a nickel too" because if that is true then there can't be any solution. The other coin must be a nickel. $\endgroup$ Commented Mar 2 at 12:40
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    $\begingroup$ I have a mathematics degree from Cambridge University, and this "mathematician" is a pillock. $\endgroup$ Commented Mar 2 at 13:02
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    $\begingroup$ @F1Krazy saying "one of the coins is not a nickel" is what makes it a (simple) puzzle, rather than a math exercise. $\endgroup$ Commented Mar 2 at 14:31
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    $\begingroup$ The part about knowing nothing about the other coin is a bit…weird? Like, if the rule specifically states that one of the coins is not a nickel, one can assume that the others can. $\endgroup$
    – Someone
    Commented Mar 2 at 15:35
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    $\begingroup$ @FlorianF a [dim-wit term] forger goes into a bar and asks the barman "Can you change this 18 dollar bill for me?" "Sure, would you like two 9's or three 6's?" $\endgroup$ Commented Mar 2 at 18:17

1 Answer 1

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If the puzzle had said that neither coin was a nickel, a solution could have consisted of:

A dime and a half dime, a US coin also worth five cents that predates the nickel by 70 years.

But with the puzzle as actually posed, your answer was correct, and the person who responded to you was both rude and wrong. The puzzle was clearly leaving open the possibility that the second coin was a nickel, and it clearly cared about actual US coin denominations, as you correctly pointed out.

Someone's status and profession doesn't make their answer correct; the content of their answer is what really matters.

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