Unutterably Silly Quiz

[orlok]

Once again, thanks for the attempts to clarify. I still stick to my position that the elimination process does not hold water if you start from the premise that they are all sitting in the room, and can all see four red hats from the start. Blue hats just don't come into it. Can someone show how you would work out the colour of their own hat starting from this principle?

Otherwise I'll just go sit in the corner with the big hat with a D on it...

[Stitchawl]

Originally Posted by orlok

Otherwise I'll just go sit in the corner with the big hat with a D on it...

It's not just you, big guy. I haven't any idea of how to even approach problems like this. And no matter how many times people try to explain to me, it just gets more and more confusing.

HELP STAMP OUT MATH! HELP STAMP OUT MATH! HELP STAMP OUT MATH!
(No animals have injured in this campaign.)



Stitchawl

[poohbear_nc]

Originally Posted by Stitchawl

It's not just you, big guy. I haven't any idea of how to even approach problems like this. And no matter how many times people try to explain to me, it just gets more and more confusing.

HELP STAMP OUT MATH! HELP STAMP OUT MATH! HELP STAMP OUT MATH!
(No animals have injured in this campaign.)



Stitchawl

I second that emotion! My head reels from trying to read the problem, let alone begin to solve it!
More geography questions!

[Daithi]

Originally Posted by orlok

Once again, thanks for the attempts to clarify. I still stick to my position that the elimination process does not hold water if you start from the premise that they are all sitting in the room, and can all see four red hats from the start. Blue hats just don't come into it. Can someone show how you would work out the colour of their own hat starting from this principle?

Otherwise I'll just go sit in the corner with the big hat with a D on it...

It is because at

11.55. A person comes in the door, says: "I can see a red hat"

therefor, everyone in the room now knows that at least one of them is wearing a red hat. They can also look at the color of the hat of the guy who said he saw a red hat. At this point you can work it out logically.

Here is the thinking process with the scenario 5 showing the thinking process when someone sees 4 red hats.

Scenario 1
I look around and don't see any red hats then I know I MUST have the red hat. So I leave at 12:00.

Scenario 2
I look around and see one red hat. However, it is possible that I too might have a red hat. If I don't have a red hat then the guy with red hats will follow what happens in Scenario 1. If he leaves at 12:00 then I can't have a red hat. If he doesn't leave at 12:00 then I MUST have a red hat. So we both leave at 1:00.

Scenario 3
I look around and see two red hats. However, it is possible that I too might have a red hat. If I don't have a red hat then the guys with red hats will follow what happens in Scenario 2. If they both leave at 1:00 then I can't have a red hat. If they don't leave at 1:00 then I MUST have a red hat. So all three of us leave at 2:00.

Scenario 4
I look around and see three red hats. However, it is possible that I too might have a red hat. If I don't have a red hat then the guys with red hats will follow what happens in Scenario 3. If they all leave at 2:00 then I can't have a red hat. If they don't leave at 2:00 then I MUST have a red hat. So all four of us leave at 3:00.

Scenario 5
I look around and see four red hats. However, it is possible that I too might have a red hat. If I don't have a red hat then the guys with red hats will follow what happens in Scenario 4. If they all leave at 3:00 then I can't have a red hat. If they don't leave at 3:00 then I MUST have a red hat. So all five of us leave at 4:00.

Here is one other way of describing Scenario 5.
I look around and see four red hats. I might have a red hat too. I know that one of the guys wearing a red hat will either see 4 red hats (if I have a red hat) or 3 red hats (if I don't have a red hat). If he sees 3 red hats then he will use the logic from scenario 4 to decide what to do.

If he is using the logic from scenario 4 then he could envision what one of the other guys would see in that scenario. That person would see either 3 red hats or 2 red hats and would use logic from scenario 3 to decide what to do.

If that guy was using the logic from scenario 3 then he could envision what one of the other guys would see in that scenario. That person would see either 2 red hats or 1 red hats and would use logic from scenario 2 to decide what to do.

If that guy was using the logic from scenario 2 then he could envision what the other guy would see in that scenario. That person would see either 1 red hat or no red hats and would use logic from scenario 1 to decide what to do.

[Daithi]

Try the National Geographic Geography Bee Quiz. I received a score of 6400 -- I'm much better at math than geography.

[HomeInMyShoes]

7422.5. I can't believe some of those were "apprentice" questions. And one of the ones I got was a Russian language question and not a geography question.

[Bilbo1967]

Originally Posted by Daithi

Try the National Geographic Geography Bee Quiz. I received a score of 6400 -- I'm much better at math than geography.

7457.5

[pdurrant]

Originally Posted by orlok

Once again, thanks for the attempts to clarify. I still stick to my position that the elimination process does not hold water if you start from the premise that they are all sitting in the room, and can all see four red hats from the start. Blue hats just don't come into it. Can someone show how you would work out the colour of their own hat starting from this principle?

Otherwise I'll just go sit in the corner with the big hat with a D on it...

I'll have one more go, working purely from the perspective of one of the people sitting in the room, seeing four red hats.

OK, I'm in a room with four other people. We're called A, B, C, D and E. (Dull names, but this is a logic puzzle.) I'm A. They are all wearing red hats, but I don't know what colour hat I have. But I know that they can all also see either four red hats (if I also have a red hat) or three red hats (if I have a blue hat).

Now I need to consider what one of them, say B, can see. If my hat is blue, B sees three red hats and one blue hat.

Now B doesn't know that B has a red hat, so if B considers what C can see, B must consider the possibility that C can see either three red hats and one blue hat (if B's hat is red), or two red hats and two blue hats (if B's hat is blue). Now, I, A, know that B's hat is red, but B does not know that, so he can legitimately wonder what C can see if B's hat is blue.

I can think that B might think that C might see two red hats and two blue hats. I can think this, even though I know that C can see at least three red hats. That's because I'm thinking about what B might legitimately think, if my hat were blue.

Now as I can legitimately consider that B can see only three red hats, and so that B might think that C might only see two red hats and two blue hats (mine and B's), I can consider that B can also legitimately consider what C would think that D can see. I think that B could think that C can see two red and two blue, and so I can think that B can think that C might think that D could only see one red hat and three blue ones (mine, B's and C's). I can build a chain of assumptions about what other people might think that other people can see.



In summary:
I can think that B might see only three red hats.
And I can think that B might think that C see only two red hats.
And I can think that B might think that C might think that D can see only one red hat.
And I can think that B might think that C might think that D might think that E can see no red hats, only blue hats.
And I can think that B might think that C might think that D might think that E can't know whether E's hat is red or blue.


Until someone says, at 11:55, that they can see a red hat.

Then I think that B might think that C might think that D might think that E can see no red hats, and so know that E's hat is red, and so would leave at 12:00.

Except, of course, that E does not leave at 12:00.

Then I can no longer think that B might think that C might think that D might think that E sees no red hats.

I must now think that B might think that C might think that D might see one red hat, and I must think that B might think that C might think that D must think that E can also see one red hat. In which case both D & E would leave at 13:00.

Except, of course, that D & E do not leave at 13:00.

I must now think that B might think that C might see two red hats, and I must think that B might think that C must think that D and E can also see two red hats. In which case, C, D & E will leave at 14:00.

Except, of course, that C, D & E do not leave at 14:00.

I must now think that B might see three red hats, and I must think that B must think that C, D, and E also see three red hats. In which B, C, D & E will leave at 15:00.

Except that B, C, D & E do not leave at 15:00.

I can now conclude that B does not see three red hats, but also sees four red hats. My hat must be red, and we all leave at 16:00.



This probably hasn't helped. But I've done my best.

[Shayne Parkinson]

9457.5. I like geography.

[Bilbo1967]

Originally Posted by Shayne Parkinson

9457.5. I like geography.

You certainly do

[orlok]

Originally Posted by Daithi

It is because at <snip>

Originally Posted by pdurrant

I'll have one more go <snip>

Thanks guys. I'm too tired to take these explanations in, but I shall have another go in the morning. From a quick skim I still keep hitting the "but no-one can see a blue hat" issue. I will do my best to rise above it tomorrow .

(you'd never guess I have a degree in Systems Analysis, would you...?)

[poohbear_nc]

7950 - yea! Fun quiz - thanks Daithi!

[Stitchawl]

8990 for me. THAT is my idea of a good quiz! Numbers? Logic? Bah humbug!



Stitchawl

[poohbear_nc]

[anyone try the expert level?]

[Bookpossum]

I managed 7405. I'm bad at maths but geographically challenged as I never studied it. Mind you, some of the questions were pretty simple, so even I got them first go. Definitely not at expert level.