So the traditional answer here is to ask them to point at the door the other guard will say is safe. However, I'm curious, does anyone know of any other valid solutions?

This still doesn't accomplish the goal of knowing which door will kill you. All you've done is determine which guard is the liar.

So you ask them which way leads to the castle and you don't pick the way they say. If we're assuming that these things are actually bound by some kind of rule stating they literally cannot lie or literally cannot tell the truth.

But you asked your one question to the one remaining guard. You gained no intel.

I believe that's the joke. The barbarians intelligence isn't usually very high.

But the other party members haven't

"Is the guard that tells the truth standing in front of the safe door?" If they say yes, you go through their door, if they say no then you go to the other one

In fact, the lying guard is a red herring. You get one question, and need one piece of info: the door. The canonical question doesn't tell you which guard lies, nor do you care to find out.

The riddle only makes sense as such with one question in total. The trick is to ask one guard what the other guard would say is behind a particular door.

The riddle is worded vaguely and we just murdered one of the guys. I think we can lawyer another question out of them.

Start b-ballin' with that head and see how long it takes that guard to change his tune

Pyramids of Mars

Do you think it would suck to be one of the bottom heads?

I mean, he could still lie. He'd just have to afford one more question

The third guard stabs people who ask tricky questions.

My favorite take on this: 

Barbarian just ripped the head off of one of the guards, you think the other guard is going to be able to arrest them? "Answer our questions or you're next."

Just shoot em in the foot  https://www.giantitp.com/comics/oots0327.html

I love playing low Intelligence high *Wisdom* characters. Because Wisdom governs stats like Perception, Insight, and Animal Handling. So your character will *notice* things that the rest of the party misses, but often doesn’t have the intelligence to put the individual pieces together. Once played a high wisdom barbarian. He would notice things like traps or clues, but I would RP it with things like “Hey, why’s that wire stretched across the path? Someone is going to trip over that…” The other players very quickly learned to pay attention whenever I asked stupid questions, because it was *usually* my way of announcing “I noticed something that the rest of you missed.”

That's wild that this works. What.