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.

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:

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*.