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?

Because Logician A and Logician C wears the same hat.

Four perfect logicians sat around a table that had a dish with 11 oranges in it. The chat was intense, and they ended up eating all of the oranges. Everybody had at least one orange, and everyone knew that fact, and each logician knew the number of oranges that he ate. They didn't know how many oranges each of the other ate, though. They agreed to ask only questions that they didn't know the answers to.

Their queries are as follows:

A: Did you eat more oranges that I did, B?

B: I don't know. Did you, C, eat more oranges than I did?

Four perfect logicians sat around a table that had a dish with 11 oranges in it. The chat was intense, and they ended up eating all of the oranges. Everybody had at least one orange, and everyone knew that fact, and each logician knew the number of oranges that he ate. They didn't know how many oranges each of the other ate, though. They agreed to ask only questions that they didn't know the answers to.

Their queries are as follows:

A: Did you eat more oranges that I did, B?

B: I don't know. Did you, C, eat more oranges than I did?

C: I don't know.

D figured out how many oranges each person ate.

How many oranges did each person eat?

Well, considering they had to ask one another, that means A, B & C all ate less than 5 oranges.

D could easily know if he ate 8 oranges. Greedy bastard.

Four perfect logicians sat around a table that had a dish with 11 oranges in it. The chat was intense, and they ended up eating all of the oranges. Everybody had at least one orange, and everyone knew that fact, and each logician knew the number of oranges that he ate. They didn't know how many oranges each of the other ate, though. They agreed to ask only questions that they didn't know the answers to.

Their queries are as follows:

A: Did you eat more oranges that I did, B?

B: I don't know. Did you, C, eat more oranges than I did?

Well, considering they had to ask one another, that means A, B & C all ate less than 5 oranges.

D could easily know if he ate 8 oranges. Greedy bastard.

B said "I don't know". So he didn't eat just one orange. He would have known it was impossible for him to have eaten more than A so he would have said no. So he ate at least 2.

Same logic --> C ate at least 3.

And since 5 is the only number that comes up only once if you try to list all possibilities, D = 5.

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.

Here is the general idea.

You have 3 options, A B and C. One of them is correct and 2 of them are wrong, meaning you have a 33.3% chance of picking the correct answer.

After picking 1 of the 3 choices, the host reveals one of the 'bad' doors, leaving you with 1 good and 1 bad, of which your door could be either.

The host asks you if you'd like to switch.

By NOT switching, you are keeping yourself at a 33.3% chance(aka 1 of 3 doors)

By switching, you are inherently picking the door the host reveal AND the new door, meaning you are picking 2 doors against 1, aka a 66.6% chance.

This DOESN'T mean you are picking the right door, it just improves your chances.

You have 3 options, A B and C. One of them is correct and 2 of them are wrong, meaning you have a 33.3% chance of picking the correct answer.

After picking 1 of the 3 choices, the host reveals one of the 'bad' doors, leaving you with 1 good and 1 bad, of which your door could be either.

The host asks you if you'd like to switch.

By NOT switching, you are keeping yourself at a 33.3% chance(aka 1 of 3 doors)

By switching, you are inherently picking the door the host reveal AND the new door, meaning you are picking 2 doors against 1, aka a 66.6% chance.

This DOESN'T mean you are picking the right door, it just improves your chances.

What I don't get is how does that improve the chance of the prize being in that door if you switch? You said that if you switched doors, that your chance becomes 66.6%, but that doesn't make any sense because the host already said that one of the doors has nothing in it. Each door has 33.3% chance of having the prize when you eliminate one that means the chance switches from 33.3% to 50% not 66.6%, for you to have 66.6% you would need 3 choices, but since one door has been eliminated you only have 2 choices.