Hello everyone, welcome back in this video we're doing the 3rd and final puzzle again. I will be doing this with the help of my friends Yellow, red and blue.

But you may know that this time they're facing to the side. This is because in this puzzle, division is bit different. I will give each of my copies ahead bend. It's either Gray.

Alright, because of the way they are facing you will be able to see the headbands of red and yellow. Red will see the headband of yellow and yellow will see nothing.

This seems a bit unfair to yellow though, so after I have given everybody their heads, I will quietly inform yellow about whether they have the same color headband as blue.

Note that I will do this quietly, so only yellow will know whether yellow and blue have the same head back.

Now there's one more thing that I should mention. I have 3 white headbands, but only two Gray ones, so I am somewhat limited in how I can assign the headbands.

Before I assign advanced, though, you should first design A model like it did last time.

Alright, so the set of world seems pretty similar to last time. It could be that yellow, red and the olive white.

Maybe only yellow has a grey bag. Maybe only red dolls?

Maybe only I do maybe red and yellow have Gray, maybe yellow and I have Gray, maybe red and I have Gray. Finally, maybe all of us have great.

Hold on for a moment. That last one doesn't work. Young, yes. 2 Gray headband, so we can't all have Gray.

Good point that one is wrong and should be removed.

Duck.

Right, let's continue with the relations red. If we were to have, say, grey, white, white, what worlds would be acceptable to you?

Well Gray, white, white would appear to me. Yes, great question mark question mark. So any world satisfying that pattern would be accessible to me, so that's great. Great white, grey, white, grey and grey, white, white.

So I'm drawing errors with Windows 3 worlds.

OK, and what if we were to have white, white, white?

That would appear to me as white question Mark question Mark. So the world accessible to me would be white, white, white, grey, white, white, white, grey and white. Great great. So I need to add arrows there.

I think that's all for red, blue. What about you if we are in white, white, white? What do you see I see white. Why question mark? So the iaccessible words for me would be Wi-Fi fight and white grey. So I did not know if there.

More generally, I can't distinguish between any two worlds at different only in my head that color.

So we need to add arrows, there and there.

The fact that the great, great, Great World is missing is important here, since it means that the grey, grey, white world has nothing that differs from it. Only in my headband color, so there are no outdoor outgoing arrows for me from that world.

And that's all for me, yellow your turn.

Right, so if we were in Wight Wight Wight I would mostly just see question mark, question Mark question Mark, but not entirely.

Remember, I will be told whether Blue and I have the same color headband, so in white, white, white, I will see that blue and I have the same color, so I'll know that must be white, white, white, white, grey, white or great white. Great, so I need to add arrows between those 3 words.

Similarly, if we are in, say, white, white, grey, then I will know that you and I have different headbands, so I will know that we are in one of the four search world wide, white, grey, white, grey, grey, grey, white, white or grey grey white.

So I have arrows between those four worlds.

Most elegant or model as we had anybody children, puzzle but I think we have it right.

I agree this seems correct, so let's assign you your headband, shall we?

So not going to pretend to whisper for a moment to indicate me telling yellow whether he has saved headband's blue.

Now blue, do you know the color of your head any? I do not.

Alright, you know the drill that was a public announcement. What's the formula that was being announced that blue does not know the color of his head back, so not KB white B and not KB Grady?

That formula is true in all but except one. In a world where random and I both have grey, blue knows that he is what. So this announcement delete that world for the model.

Leaving us with this.

Alright, now Red do you know the color of your head? Yes, I do.

That's a public announcement again of the formula KR White R or KRVR.

This formula is false into four world in front, since each of these worlds and our successor web reader, Whitehead Bag and one very as a Gray one.

It's true for the two words in the back though, so the effect of the announcement is this.

Alright, yellow do you now know the color of your headband? I dude, that's another public announcement, of course, namely KYGY or Ky White, why?

That doesn't help me though, because it's already common knowledge.

So it removes no further worlds.

Indeed, I'm afraid you won't figure out your color at this time.

So we just did the formal formal way, K1. If you give an informal explanation of what happened, sure, if yellow and I both would have had Gray, than blue would have known his own color. Since there were only two Gray headbands, I saw that you know, had a grey headband we couldn't both have grade, so I had to have white.

Note that in order for read to know my color, I had to have Gray. After all, if I had white then it would not have been possible that both had white. So I'm from the fact that he knew his color. I could determine that I had grey.

Alright.

Let's do one final run, same puzzle, but I may or may not give you different colors of hats this time.

We're back at the beginning of the puzzle, so our model is once again this one.

Let's make it a bit harder this time, though. Yellow does blue know the color of his headband?

No, no he doesn't.

That's a public announcement. What is being announced that I don't know my color. So not Katie white. Be an not KB gravy.

Wait, that's not quite correct. Yellow wouldn't say that if you have inserted so denouncement isn't just that you don't know your color is that he knows that you don't know.

So it's Ky.

Not KBYP and not baby baby.

Good point, the only world where I know my color is grey, grey, white. So Yellows announcement is false in any world that has Gray, Gray, white as a white successor.

That's the four words on the right.

So after the announcement I'm new model is this one.

Huh, that's quite funny.

Now.

Now I know my color hurt, but it doesn't help you guys. So when I say that because it was already common knowledge.

Indeed, now read. Do you know your head? In fact I do. That's an announcement KR White R or KR Gray R denouncement is true only in the world grey, white, grey. So the order to get deleted.

Since there's only one world left.

I now also know the color of my headband.

Good good.

Informal explanation anyone? OK sure.

Bluewood knows old color. If you and me both had great. In that case, blue would have had to have it white headband, so blue and yellow would have had different colors. The only way for yellow to no that gluten knows uncolored, therefore was for yellow and blue to have the same color. So effectively the announcement told us that blue and yellow had the same color.

Which means that, oddly enough, by saying that blue denotes on color, yellow made sure that you didn't know.

And then you asked red better he do his own color, since blue and I had the same color. If I had a grey headband, then blue also had one.

Meaning of red couldn't have one, since there were only two, but if I had white headband then red would not know that color. Since all of us could've had wiped.

So regardless of Reds answer, I would know my own color. In this case, reading his color so I had to have great.

Right, excellent.

Well done, all of me and thank you for your assistance. This is the end of the video. Furthermore, this is the last video about absent logic, so I will see you all next week in the 1st.

Week of videos about description. Logic layers.