Another conundrum

[Tomcat]

An old French guy gave me this conundrum.

The puzzle is this ( see picture below)

Am Arab has captured four French Foreign Legionnaire intelligence Officers  and buried them up to their necks in sand. Two have back hats and two have white hats which have been mixed up so that no soldier knows which hat he has on. All the soldiers know is that there are two black hats and two white hats

There is a Wall separating soldier A from the rest.

Soldier A can only see the wall and nothing beyond
Soldier B can only see the wall and nothing beyond
Soldier C can only see soldier B and the wall
Soldier D can only see soldier C and soldier B and the wall



The Arab states that within the time allotted of one hour if any one Soldier can state which colour hat is wearing then they will all be released, otherwise they will all be killed. The soldiers only have one chance between them so that the first guy to chirp up had better be correct or there are all dead.

The soldiers cannot speak to each other other  and there are no reflections in the sand.

Before the hour is up one soldier suddenly states that he knows the colour of his hat and the reason why.  They are all released.

one of these guys knows the colour of his hat by the process of logical deduction.

remember
Two have back hats and two have white hats which have been mixed up so that no soldier knows which hat he has on at the beginning.

[kliome]

I think I know the answer but I won't spoil it so soon, there is another conunndrum which uses the same logic and may help..

There intelligent men are blindfolded and taken into a room filled which hundreds of black and white hats. They each select a hat randomly and put it on. They are then led to another room and sat on three chairs in a triangle. Once the blindfolds are removed they can see each others hats but not their own hat. They are told to tap their feet if they see a black hat and the first person to stand up and say correctly what hat they are wearing wins.

They all begin to tap their feet but no one stands up as no one is sure what colour hat they are wearing.. after a few seconds one of the men stands up and says 'my hat is black', and he is right.
How did he know?

[abba]

These soldiers are used to wearing white hats as part of their uniform.
So (during the day time) soldier D, will know if his hat is a standard coloured white hat, which will feel normal to him.
If it is a black hat, it will have a higher temperature inside the hat, than the white one.

So once he knows which color his hat is,
then the rest of the problem soldier D can figure out,
if his life depends on it.

However, I expect a more fancy solution to come our way soon.

[Tomcat]

Would you honestly chirp up for that reason, you  would have to be pretty brave .

It can be worked out by rational logic.

These are guys are all intelligent men.

[PigDogg]

If B and C were wearing the same color hat, then D could speak up immediately since then D would have the opposite color.

Therefore if D does not speak up then B and C are wearing different colors.

So C can be assured that his hat color is different than B as long as he can trust that D is not an idiot.

[manarak]

Would you honestly chirp up for that reason, you would have to be pretty brave .

Well, the soldiers which wear a white hat as a standard part of their uniform are very brave!