I've never bought that though process, I don't understand why just because C has been eliminated as an option it would have any effect on A or B. It seems that after you have eliminated C the choice between A or B would be an independent event from C.

Someone who is good in math could probably explain this, but really from what I can tell it should have no effect.

Let's say you picked box A. At 1st, your chance to get the million dollars is 33.3% (1/3).

That means you have a 66.6% chance of picking the wrong box. Which means there's a 66.6% chance the million dollars is either in box B or C.

Since the host tells you it's not in box C, then there's a 66.6% chance it's in box B, so you should switch.

EDIT : Let's say :

Box A : Nothing
Box B : Nothing
Box C : $1,000,000

There's only 3 possible scenarios :

- You pick box A : The host has no choice but to eliminate box B. Switch = win

- You pick box B : The host has no choice but to eliminate box A. Switch = win

- You pick box C : The host will either eliminate box A or B. Switch = fail

We know you can measure 40 minutes by lighting both ends of the rope. So first you light one rope at two ends and the other rope on one end. Then when the first rope burn out, you'll know 40 minutes has passed and the second rope only has 40 more minutes to burn out. If you immediately light the second rope at the other end, that will measure half of 40 minutes which is 20 minutes. That way 40 minutes + 20 minutes = 60 minutes.

8.. A King tests 3 logicians. He has 8 hats. 4 Black and 4 White. He asks the logicians to close their eyes. While that is being done, he hides 2 of the hats behind him, and puts 2 hats on each logician. When the logicians open their eyes, they can only see the hats of the other 2 logicians, but can't see their own hats nor the hats the king hid.

The king then starts asking them if they can tell which hate they have on:

Logician A: "No Idea"
Logician B: "Don't know"
Logician C: "Not sure"
The King gets mad, and asks around 1 more time
Logician A: "I still don't know"
Logician B: "I've figured it out"

And he gets it correct. What hats was B wearing and why?

I'm guessing Logician B looks around and sees that his two other partners are wearing 2 black hats each, or 2 white hats each, thus he determines that he is wearing 2 of the same color as well.

EDIT: Then Logician B can say which color hat he thinks he's wearing, thus giving the other two the answer as to what they're wearing since they know he'd only speak up if he saw them wearing the same colored hat. So if Logician B says "they are both wearing 2 white hats each", they could determine that the King has 2 black hats behind his back, since they could have a look at Logician B and see he is wearing 2 black hats.

I'm guessing Logician B looks around and sees that his two other partners are wearing 2 black hats each, or 2 white hats each, thus he determines that he is wearing 2 of the same color as well.

EDIT: Then Logician B can say which color hat he thinks he's wearing, thus giving the other two the answer as to what they're wearing since they know he'd only speak up if he saw them wearing the same colored hat. So if Logician B says "they are both wearing 2 white hats each", they could determine that the King has 2 black hats behind his back, since they could have a look at Logician B and see he is wearing 2 black hats.

Am I anywhere on the right track?

Well if that was the case, he would know right away the first time he was asked. But he didn't....you are kind of one the right track...