Re: A trickier knight-knave hats puzzle

Ed Murphy wrote:
Arthur J. O'Dwyer wrote:

As before, three natives of the Island of Knights and Knaves (strangers
to each other) are led into a room (blindfolded so they cannot see each
others' hats), seated in a circle, hat-shuffled, and un-blindfolded.
(Each native cannot tell his own hat from any other hat of the same
color.) They make the following statements, in this order:

Dave: "I don't know my hat's color."
Ernest: "I don't know my hat's color."
Fred: "I don't know my hat's color."
Dave: "I don't know my hat's color."
Ernest: "I don't know my hat's color."
Fred: "Now I know my hat's color."

What color is each man's hat?


I've been through this puzzle three times now, and I'm convinced that
it's flawed at statement 4. If I'm letting one of the natives figure
out more than they should be able to, then would someone please point
out where that's occurring?

Once again, we assume that each native is a perfect logician. From
this, let's generalize the observation from the previous puzzle that
each native (right before he makes a statement) is able to work out
at least as much as we've worked out up to that point, since he has
all the same knowledge that we do (plus some that we don't, i.e. his
alignment and all the other hats).

Dave: "I don't know."

As in the previous puzzle, either Dave is a knight and sees at least one
white hat, or Dave is a knave and sees two white hats.

Ernest: "I don't know."

If Fred wears black, then Dave is a knight, Ernest wears white, Ernest
knows and lies about it, so Ernest is a knave.

Summary:
D knight/?, E knave/white, F ?/black


What you just wrote is true, *if Fred wears black*. What if Fred wears white?

--
Mark Thornquist
.

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