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# Riddle watch

1. We got set this riddle in my seminar today, and I've been feeling pretty good most of the day since I worked it out without any hints - wooh! (obviously by sods law, i fell into a puddle half an hour later but c'est la vie!) Just wondering if anyone else can work it out:

Mr Brown has 5 hats, 3 are white and 2 are black. He seats 3 students in a row, such that Anne is at the front facing the wall, Bob is behind Anne so he can see her, and Carly sits behind Bob so she can see both Bob and Anne. Mr Brown places the 3 white hats on the students, without them seeing, and the two black hats are hidden. The students know that there are 3 white and 2 black hats in total. After a while of silence, Anne says "I'm wearing a white hat" (this is not a guess). How does she know?
2. I've heard this one before, but slightly differently.
It involves people buried in sand that could have their heads choped off.

There are 2 black and 2 white hats. Each person can only look foward and must call out the colour of their hat correctly or they all lose their heads!

The arrows show the direction they are facing.

B W W B W
> a < < <
l
l

Who correctly calls out and why?
3. (Original post by Digz)
We got set this riddle in my seminar today, and I've been feeling pretty good most of the day since I worked it out without any hints - wooh! (obviously by sods law, i fell into a puddle half an hour later but c'est la vie!) Just wondering if anyone else can work it out:

Mr Brown has 5 hats, 3 are white and 2 are black. He seats 3 students in a row, such that Anne is at the front facing the wall, Bob is behind Anne so he can see her, and Carly sits behind Bob so she can see both Bob and Anne. Mr Brown places the 3 white hats on the students, without them seeing, and the two black hats are hidden. The students know that there are 3 white and 2 black hats in total. After a while of silence, Anne says "I'm wearing a white hat" (this is not a guess). How does she know?

If Carly saw two black hats, then she'd know she had a white hat.
Then, Bob knows that only one of him or anne at most has a black hat, as carly hasn't said her hat colour, but as he sees anne has a white hat, he can't tell which colour hat he has, as he could have a white hat, or a black hat, and Carly still wouldn't have responded, with anne wearing a white hat.
Anne knows that if in any situation she wore a black hat, that one of the others would have been able to say the colour hat they were wearing, but as they haven't, she must be wearing a white hat.

There have been many variations of this on the same theme though, but i may not have explained it quite correctly.
4. (Original post by Iluvatar)
If Carly saw two black hats, then she'd know she had a white hat.
Then, Bob knows that only one of him or anne at most has a black hat, as carly hasn't said her hat colour, but as he sees anne has a white hat, he can't tell which colour hat he has, as he could have a white hat, or a black hat, and Carly still wouldn't have responded, with anne wearing a white hat.
Anne knows that if in any situation she wore a black hat, that one of the others would have been able to say the colour hat they were wearing, but as they haven't, she must be wearing a white hat.

There have been many variations of this on the same theme though, but i may not have explained it quite correctly.
Yup well done thats right. I'd never heard it before actually - learn something new everyday eh!

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