[andromeda]

Large group of dwarfs busted into the dragons cave with an intent to steal his treasures. They were clumsy and during the loot they accidentally woke up the dragon.

Dragon found those little thieves very cute and adorable and decided not to kill them, instead he has given them an assignment. Using magic he placed little hats on every dwarf’s head (so every dwarf was wearing either a black or a white hat) and then he told them to walk out of the cave and align themselves in one row, side by side so that all the dwarfs with the white hat on stand on one side of the row, and all the dwarfs with the black hat on at the other end of the row.

None of the dwarfs knew what color is their own hat. There were no mirrors in the cave. Dragon used a magic spell to prevent any kind of communication between the dwarfs (no talking, no whistling, no coughing, no sneezing, no blinking, no gestures of any kind). All they could do is think and walk out of the cave to assume their position in the row.

If they manage to do what dragon assigned them to do he will let them take all the treasures they can carry with them!

The dwarfs did manage to complete the task... how??

Not my riddle, but I think it's an interesting one

Please use spoilers!

[Guest]

assume that white hats on left and black on right.

The dwarfs go one at a time, and the dwarf enters the break point between white and black hats of the ones already lined up.

Then the adjacent dwarfs adjust themselves accordingly

(the adjacent ones are the only dwarfs that don't know their own hat color anymore)

If for example

WWBB is already up

if a W enters it would go

WWWBB

The black hat wouldn't adjust himself because he is either already in the correct spot, or the change is ambiguous. The W hat and the new guy would switch spots because either the change is ambiguous or it is necessary.

If the case was WWBB and a B entered it would be the same logic but the B would switch and the W wouldn't move.

This logic can be applied as many times as need be.

The start up would be

W

then the next person gets on his right

WB or WW

then WBB/WWB or WWB/WWW

then WWBB WBBB WWWB WWBB WWBB WWWB WWWW

(reverse everything for a B start)

therefor the fist four need not adjust themselves at all and after that the case above applies.

[Guest]

Send up two dwarfs to line up.

Then one by one the next dwarf comes and stands in the junction between the black and white hats. If all the hats are the same colour take up a position on either end of the line.

This will ensure the line all all White then Black or vice-verser.

Thanks bunny for a riddle I can finally answer

[andromeda]

Thanks bunny for a riddle I can finally answer

Send up two dwarfs to line up.

Then one by one the next dwarf comes and stands in the junction between the black and white hats. If all the hats are the same colour take up a position on either end of the line.

This will ensure the line all all White then Black or vice-verser.

Yeah...

[Guest]

Nice taliesin!!

I was thinking..

The dwarfs can figure out the color of their own hat by standing in the sun for a while, since a black hat would be a lot warmer because it absorbs radiant energy, while white reflects it.

[Guest]

Nice taliesin!!

I was thinking..

The dwarfs can figure out the color of their own hat by standing in the sun for a while, since a black hat would be a lot warmer because it absorbs radiant energy, while white reflects it.

But... the dwarfs don't know exactly how much effect the hats provide - wether their hat is black or white they would warm up, and they would not know if they've been heated by a white hat amount or a black hat amount.

[Guest]

Yeah...

Yay! Whats my prize?

[andromeda]

assume that white hats on left and black on right.

The dwarfs go one at a time, and the dwarf enters the break point between white and black hats of the ones already lined up.

Then the adjacent dwarfs adjust themselves accordingly

(the adjacent ones are the only dwarfs that don't know their own hat color anymore)

If for example

WWBB is already up

if a W enters it would go

WWWBB

The black hat wouldn't adjust himself because he is either already in the correct spot, or the change is ambiguous. The W hat and the new guy would switch spots because either the change is ambiguous or it is necessary.

If the case was WWBB and a B entered it would be the same logic but the B would switch and the W wouldn't move.

This logic can be applied as many times as need be.

The start up would be

W

then the next person gets on his right

WB or WW

then WBB/WWB or WWB/WWW

then WWBB WBBB WWWB WWBB WWBB WWWB WWWW

(reverse everything for a B start)

therefor the fist four need not adjust themselves at all and after that the case above applies.

I forgot to give you a credit for a job well done

Nice taliesin!!

I was thinking..

The dwarfs can figure out the color of their own hat by standing in the sun for a while, since a black hat would be a lot warmer because it absorbs radiant energy, while white reflects it.

Well...

the dwarfs were standing in the cave and then walk out of it and imediatelly assume their position, and also what armcie said. First you would have to test that, if the color of the hat makes difference. It probably does. Then after what period of time it doesn't make any difference anymore... blah, blah... Nice thinking though!!

But... the dwarfs don't know exactly how much effect the hats provide - wether their hat is black or white they would warm up, and they would not know if they've been heated by a white hat amount or a black hat amount.

Edited November 11, 2008 by andromeda

[Guest]

Hmm yeah guess you're right... Searched too far xP

They could just take off their own hat and look what color it is, since you only said there's no communication possible BETWEEN the dwarfs, and there isn't said that they are not allowed to do that.. But I'm thinking too much again so never mind I guess

[andromeda]

Hmm yeah guess you're right... Searched too far xP

They could just take off their own hat and look what color it is, since you only said there's no communication possible BETWEEN the dwarfs, and there isn't said that they are not allowed to do that.. But I'm thinking too much again so never mind I guess

The Dragon used his magic to prevent any movement other than the movement of their little legs! But yeah... that would be my answer too