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[I'd got a draft partial I forgot to post before a busy weekend - now revised very slightly, but plan to revisit soon]

It seems particularly relevant that in step 3 [since edited to make this particular phrasing nonsense...]

the direction of the quarter turn (clockwise or anti-clockwise) from their initial position facing the warden (who by implication is to the side observing the whole line) is not stated. Some prisoners can be facing left and others right, which allows all hats to be observed.

I also accidentally deleted a comment along the lines that I think that it will probably be the case that Alice and Bob must observe both ends of the line, and thus be facing opposing directions, but my initial "partial proof" of this was flawed, so it might not be the case.

[I'd got a draft partial I forgot to post before a busy weekend - now revised, but I've not figured out all the interactions yet]

It seems particularly relevant that

the direction each prisoner is facing is not stated. Some prisoners can be facing left and others right, which allows all hats to be observed.

Whoever is at the two end positions

Might as well be facing inwards so they can see everyone else... any conclusion they can make without seeing hats they can also make whilst seeing hats too.

It seems likely that

Alice and Bob are also facing opposite directions, each observing one of the ends of the line, but I've not fully convinced myself this is absolutely certain - I had a "partial proof" that was flawed.

I strongly suspect that

multiple prisoners learn their hat colour only at the last moment, as Earnest declares he knows his hat colour, thus disproving the alternative scenario each had in mind.

Earnest cannot see Bob, but Carol can see both Bob and Earnest. Dennis can see Earnest (in order to know that Earnest cannot see Bob)

So far, we can conclude (without loss of generality) that the line looks something like this:

At this point

Alice and any other prisoners' positions in the line are to be deduced, and we also need to determine all hat colours and which way Bob is facing, as well as which of the 3 logically consistent positions for Carol is in fact the case.

Earnest cannot see Bob, but Carol can see (or conclude the hat colour of) both Bob and Earnest at the time she speaks. Dennis can see Earnest (in order to know that Earnest cannot see Bob)

So far, we seemed to be able to conclude (without loss of generality) that the line looks something like this:

However,

We don't know for sure that Carol can see both Bob and Earnest as initially assumed. For example, in the following arrangement, Carol knows that Bob is behind her as the only prisoner who she cannot see, and she would know his (and her own) hat colour from the earlier statement(s), and Earnest's hat colour from direct observation:

 G   G   ?       G       ?
 B>  C> <A  ...  E> ... <D  ...

or

 G   R       G       ?       ?   (only one other red hat besides Carol's)
 B>  C> ...  E> ... <A  ... <D  ...

or

 G   R   G   ?       G       ?   (only one other red hat besides Carol's)
 B>  C>  F  <A  ...  E> ... <D  ...

At this point

Alice, Carol and any other prisoners' positions in the line are to be deduced relative to the known relative positions of Bob, Ernest and Dennis, and we also need to determine all hat colours and which way Bob is facing.

[I'd got a draft partial I forgot to post before a busy weekend - now revised very slightly, but plan to revisit soon]

It seems particularly relevant that in step 3 [since edited to make this particular phrasing nonsense...]

the direction of the quarter turn (clockwise or anti-clockwise) from their initial position facing the warden (who by implication is to the side observing the whole line) is not stated. Some prisoners can be facing left and others right, which allows all hats to be observed.

Working from the last clue:

Earnest gains additional information from Dennis' comment, combined with what Earnest can see. If Dennis were behind Earnest, facing the same direction, then Dennis would see everything that Earnest does. The only new information that Earnest would gain from this would be which way Dennis was facing, which cannot be combined with any other information to learn Earnest's hat colour. Thus we must conclude that Earnest can see at least one hat which Dennis does not - i.e. Earnest must be facing Dennis.

Earnest cannot see Bob, but Carol can see both Bob and Earnest. Dennis can see Earnest (in order to know that Earnest cannot see Bob)

Given that

Dennis can see Earnest, and Earnest can see at least one person/hat that Dennis cannot (in order to gain additional information), we can conclude that Earnest and Dennis are facing each other, and can see each other.

In order for EVERYONE to know their hat colour

it is necessary that hats at BOTH ends of the line are observed, which is certainly the case as at least one of Dennis and Earnest sees them.

So far, we can conclude (without loss of generality) that the line looks something like this:

      ?       =       =       ?
 ...  C> ...  B  ...  E> ... <D  ...

At this point

Alice and any other prisoners' positions in the line are to be deduced, and we also need to determine all hat colours and which way Bob is facing.

I also accidentally deleted a comment along the lines that I think that it will probably be the case that Alice and Bob must observe both ends of the line, and thus be facing opposing directions, but my initial "partial proof" of this was flawed, so it might not be the case.

[I'd got a draft partial I forgot to post before a busy weekend - now revised very slightly, but plan to revisit soon]

It seems particularly relevant that in step 3 [since edited to make this particular phrasing nonsense...]

the direction of the quarter turn (clockwise or anti-clockwise) from their initial position facing the warden (who by implication is to the side observing the whole line) is not stated. Some prisoners can be facing left and others right, which allows all hats to be observed.

Working from the last clue:

Earnest gains additional information from Dennis' comment, combined with what Earnest can see. If Dennis were behind Earnest, facing the same direction, then Dennis would see everything that Earnest does. The only new information that Earnest would gain from this would be which way Dennis was facing, which cannot be combined with any other information to learn Earnest's hat colour. Thus we must conclude that Earnest can see at least one hat which Dennis does not - i.e. Earnest must be facing Dennis.

Earnest cannot see Bob, but Carol can see both Bob and Earnest. Dennis can see Earnest (in order to know that Earnest cannot see Bob)

Given that

Dennis can see Earnest, and Earnest can see at least one person/hat that Dennis cannot (in order to gain additional information), we can conclude that Earnest and Dennis are facing each other, and can see each other.

In order for EVERYONE to know their hat colour

it is necessary that hats at BOTH ends of the line are observed, which is certainly the case as at least one of Dennis and Earnest sees them.

So far, we can conclude (without loss of generality) that the line looks something like this:

      ?       =       =       ?
 ...  C> ...  B  ...  E> ... <D  ...

or

      =       =       ?       ?
 ...  B  ...  E> ... <C  ... <D  ...

or

      =       =       ?       ?
 ...  B  ...  E> ... <D  ... <C  ...

At this point

Alice and any other prisoners' positions in the line are to be deduced, and we also need to determine all hat colours and which way Bob is facing, as well as which of the 3 logically consistent positions for Carol is in fact the case.

I also accidentally deleted a comment along the lines that I think that it will probably be the case that Alice and Bob must observe both ends of the line, and thus be facing opposing directions, but my initial "partial proof" of this was flawed, so it might not be the case.