Transcription
If you like puzzles, well, this video is perfect for you. And if you don’t, well, watch to the end, and you’ll be rewarded with a clip of a baby elephant spinning its trunk. If you have any know-it-all friends, send them this video to see how smart they really are. And if someone sent you this video, well, I guess you should stop acting like a know-it-all.
So, the hardest riddle ever. It’s actually called the 3 Gods riddle, and it was first published in the Harvard Review of Philosophy in 1996. Here's how it works. You’re stranded on an alien planet when your ship crash lands. You come across three beings that can help you repair your ship, but if you want their help, you’ll have to refer to them by name. The one problem: They won’t tell you what their names are. I know, alien gods on an alien planet can be weird like that. They tell you their names are Truth, Liar, and Random. Again, pretty strange names, but just go with it.
The good news is you can ask them three ‘yes or no’ questions to help figure out who’s who, but you can only address each of your questions to a single god, not to all of them. But, you can ask the same god multiple questions. Here’s where we run into another problem, and you might have already realized this one. Whoever is Truth, will answer your questions truthfully, but whoever is Liar will always lie, and Random, well, he’ll just make up an answer based on how he’s feeling. Okay, this will be pretty tricky, but there’s one more problem. These are all-powerful beings, so of course, they’ll understand whatever language you ask your questions in, but on this world, it’s customary for them to only speak their native language. When they answer your ‘yes or no’ question, they'll respond with ‘da’ or ‘va’, but you don’t know which word means what. So, three questions; how do you figure out who’s who?
If you want to try and figure it out on your own, pause the video here. I’m sure you figured out that you can’t just pick an alien and ask “Are you Truth?” Truth would answer yes, Liar would lie and say yes, and there’s a 50/50 chance that Random would say yes. You could have a situation where all three say yes they are Truth, and on top of that, you wouldn’t even know if their answer meant yes in the first place.
The trickiest part of this problem is that you don’t need to know what the words da and va actually mean. The way we get around knowing the meaning of the words is with an embedded question, basically a question within a question. This is the trickiest part of the riddle, and unfortunately, it’s also the first part, so let’s walk through it. Let’s take any simple question, like does 2 + 2 = 4. Obviously, we can’t just ask this question to a god for the same reason we couldn't just ask them if they were Truth. So instead, we have to take this question one step further. Instead of just asking ‘does 2+2=4?’ ask “If I asked you whether two plus two equal four would you answer da?”
This might seem like the same question, but let’s play out all the possibilities with Truth and Liar. There are four possible ways this could work, two where da means yes and va means no, and two where va means yes and da means no. And within this, you have two possibilities for your embedded question, either the embedded question is true, or it’s false. Let’s take a closer look at each. If you asked this question to Truth and da meant yes, they would say yes. And if you asked it to Liar, well, the question was “If I asked you whether two plus two equals four would you answer da?” If you asked them “Does 2 + 2 equal 4?” they would lie and say no (or in this case va). But the whole question asks whether they’d say da. Clearly, they wouldn’t, since they’d answer the question with va, but since they always lie, they go ahead and say they would, saying da. So in this scenario, both Truth and the Liar would give the same answer, da.
Now let’s switch it around. If va meant yes, then Truth would’ve still have answered da. Since the question is “If I asked you whether two plus two is four would you answer da (or no)?” Since 2 plus 2 does equal 4, he would want to say yes. So when the question asked if he would say da, he would answer da, basically saying no, he wouldn’t say that 2 + 2 doesn’t equal 4. This works the same way for Liar, and we see that no matter what da and va mean, if that embedded question is true (in this case does 2 + 2 equal 4) the answer will always be da.
Now let’s look at the other two scenarios. What if the embedded question was false ‘like does 2 + 2 equal 5?” Well, then the question is ‘If I asked you if 2 + 2 equals 5, would you say da?” Well, if da means yes, then Truth would say no, or va, because Truth would not say da (or yes) to that question. And Liar would also say va, since if you asked him if 2 + 2 equals 5 he would lie and say da, but since you’re asking him if he would say da, he would lie and say va. And the last scenario, if da meant no, then Truth would see the question ‘If I asked you if 2 + 2 equals 5 would you say no?” and so he would say yes or va. Likewise, Liar would say va.
The important thing to take away from these four scenarios is that if the embedded question is true, then Truth and Liar will always say da, and if it’s false, they'll always say va, and you don’t have to know what each word means. Again, these four scenarios are the trickiest part of this puzzle, and it’s really what the whole puzzle is based on, so if you’re still a little confused with how they worked, rewind the video and watch that part again. And if you're still following, then congratulations, you’ve gotten through the hardest part of the riddle.
Time to ask your first question. Ask the center alien "If I were to ask you if the god to your left is Random, would you say da?" If the god says da, then there are two possibilities; either the embedded question is true and the god in the middle is either Truth or Liar, or the god we asked was Random and just gave us a random answer. Similarly, if the god in the middle says va, then there are two possibilities; either the embedded question was false, so we’re talking to either Truth or Liar (making the god on the right Random), or we were asking Random himself. From here, we would know one god who definitely isn’t Random, so the next step is to figure out if they’re Truth or Liar.
Let’s say the god said da to the first question, so again the embedded question is either truthful making the god to the left Random, or the god we asked was Random and gave us a random answer. Either way, the god on the right can’t be Random. For our second question, we still don’t know the meaning of the words da and va, so we’ll ask another embedded question. Ask the god we know is either Truth or Liar "If I were to ask you if you are Truth, would you say da?” And again, we’ll see that if the embedded question is truthful, both gods will answer with da, telling us we’re talking to Truth, but if the embedded question is false, both Truth or Liar will answer va, telling us we’re speaking to Liar.
At this point, we know the identity of one god and have one question left. You might be thinking we don’t have to ask an embedded question anymore, and can just ask “Is this god in the middle Random?” since we already know if we’re talking to Truth or Liar, but remember, they’ll just say da or va, and we still don’t know what those words mean. So instead, we’ll have to ask one last embedded question to the god we just identified. Simply ask, "If I were to ask you if the god in the middle is Random, would you say da?” And again, based on those four scenarios, if the answer is da, we know the middle god is Random, and if it’s va, we know the god on the left must actually be Random. Since we know two of the three gods, the last one is just whoever’s left.
It turns out you never need to figure out the meaning of da and va (and there’s actually no way to figure it out and identify all of the gods in only three questions, so hopefully, you didn’t spend too much time trying to figure out the words). Hopefully, this brain teaser didn’t mess with your mind too much, although it is the world's hardest puzzle for a reason. If you have any friends or coworkers always bragging about how smart they are, send them this video and see if they can figure it out on their own. And don’t think I forgot about that promise I made in the beginning. For making it through the whole video, here’s that clip of an elephant swinging its trunk. Look at that thing go. If you need to watch this video a few more times to fully wrap your head around the answer, well, me and my watch time thank you. And if you want to cool off instead, check out one of our less brain-teasing videos. And remember, there is always more to learn.