Every once in a while, I come across this little puzzle. I have no idea who made it, or what the intended answer is.

Usually there are a lot of people giving the same answer. And although that answer is reasonable, I don’t think it’s correct. When we modify the calculation to (x * y) + x, we’ll get the answers matching the question. But we’ll need to modify the calculation, and I don’t think that is needed.

Another solution would be to take the previous answer, and add the current sum.

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There’s an old joke among nerds that goes like this:

There’s a hint in that joke that points to a different answer to the puzzle. You can write numbers in different ways. In computer science we use a couple of different number systems, like binary, or Base 2, which deals with the digits 0 and 1. That’s not the only system we use. There’s also octal (Base 8, digits 0 to 7) and hexadecimal (Base 16, digits 0 to 9 and A to F). And of course we still use decimal.

That joke about 10 kind of people, we can do better:

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If we now go back to the puzzle, taking into account these number systems, we can arrive at a solution that doesn’t need to modify the calculation. We only need to modify the representation of the answer.

And there we have it, the answer is 13! Which is written in Base 3 as 111. There’s no need to modify the calculation. All we needed to do is change the representation of the answer.