This post is going to discuss a solution proposed by White Raven for Room 8. You can find his description of it here.

I would like to say first that although I don’t consider this solution to be correct, I approve of it being proposed and posted. I think that solving MAZE is going to rely on people sharing lots of possible solutions with the community, an activity which will, for the most part, involve ideas that don’t end up working out. This doesn’t mean the people coming up with them are bad solvers; it means they’re trying to solve something difficult. White Raven’s willingness to suggest theories, even ones I often disagree with, is a genuine boon to the MAZE community. I say all this because I’m about to criticize this theory, and don’t want this to be mistaken for criticizing the theorizer.

The idea here is to find an encoding of “xii,” in a room where the correct door to take is 12. The way he suggests it’s encoded, letter by letter, is as follows:

- x: “SGN” from the SiGN sign
- i: “i” from the SiGN sign
- i: The bowling pin

The i on the sign does obviously match a Roman numeral i. The bowling pin kind of looks like an i, I guess. But why does “SGN” produce x? The explanation given is that sgn is the sign function, often written sgn(x). White Raven says he doesn’t know much about the math involved here himself, but ran this by a mathematician friend. I think that he may have misunderstood what that friend told him, or perhaps conveyed the puzzle idea to him poorly. This solution looks like it involved a breakdown of communication somewhere, anyway.

First of all, the idea of writing “(x)” after a function isn’t as significant as it’s being made out to be. It’s true that if you want to talk about the sign of x, you write “sgn(x).” Smilarly, the logarithm of x is log(x), the cosine of x is cos(x), and so on. This is a feature of notation for functions in general, not the sign function in particular. There’s no reason to think that, in looking for a way to hide the letter x, Manson would decide on “SGN” as being related.

One of the more confusing passages of the post: “The sgn function in simple form is written as ‘sgn(x)’ in a function, and the architypical representation of the function is x=sgn(x).|x| As the math prof put it, ‘sgn is a mathematical representation of absolute value “x”.'” I’m not sure what White Raven is trying to establish here. It may be an attempt to relate the sign function to having some kind of relevance to x itself, but if so, it’s misguided.

I’m going to take a moment to explain the functions discussed here, for those who aren’t familiar.

**Diane’s Math Corner**

The sign function, sgn, is about whether something is positive or negative. You put a number in, and the function gives you a new number telling you something about the sign of that number. If your number is positive, it gives you 1. If your number is negative, you get -1. If it’s 0, 0. So, for example, sgn(8)=1, sgn(-17)=-1, sgn(45)=1, sgn(0)=0. You get the idea.

The absolute value of a number is basically what the number would be if it were positive. We write |x| for the absolute value of x. For a positive number, taking the absolute value doesn’t change it. |5|=5. Negative numbers are switched to positive: |-5|=5. Zero is again just zero. |0|=0.

You’ll notice that these are two different functions, giving (usually) different results. sgn(12)=1, but |12|=12. The sign function is not a representation of the absolute value of a number. They are, however, related.

One way to think about numbers is as points on a line. Everything off to the left of 0 is negative, everything off to the right is positive. The sign of a number tells you which direction from 0 it is. The absolute value tells you how far from 0 it is. If you know both those things, then you can work out exactly what the number is. I’m thinking of a number, which I’ll call n. sgn(n)=-1, and |n|=13. That’s enough information for you to determine what number I’m thinking of. Neither of those pieces of information alone would do it.

All right, now that we’ve had a fun math digression, let’s reiterate that this isn’t a way to clue “x.” Maybe the notation for absolute value led to confusion at some point, with |x| looking like a way of writing x with some emphasis?

Is it possible that Manson also didn’t understand the math involved, and also mistakenly thought that “SGN” would work as a clue for x? This seems very unlikely to me, because it would require an incredibly specific mistake. He would have to not only think, like White Raven, that using the name of a function would mean x, but would also have to think that this mildly obscure function was the one to use for that. It’s a solution idea that would only occur to someone working from the solver’s end, not one that the puzzle constructor would come up with working forwards.

Topic for a later post: Communication misunderstandings and Mansonian verification.