# A puzzle about two coins of total value of 15 cents, one of which is not a nickel. Is it correct at all?

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.

• 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. Commented Mar 2 at 12:40
• I have a mathematics degree from Cambridge University, and this "mathematician" is a pillock. Commented Mar 2 at 13:02
• @F1Krazy saying "one of the coins is not a nickel" is what makes it a (simple) puzzle, rather than a math exercise. Commented Mar 2 at 14:31
• 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. Commented Mar 2 at 15:35
• @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?" Commented Mar 2 at 18:17