[pzhon]

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One day, the queen, who is known to be infallible, ...
Assume that all of the women are completely logical

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Your statement of that problem is incomplete for the usual solution. You have to assume not only that the queen is known to be infallible, but also that fact is known, and that fact is known, etc. You can't let someone know the queen is infallible, but doubt whether everyone else knows this, or doubt whether everyone knows that no one has a doubt about the queen's infallibility, etc.

You have to assume that the women are not only logical, but know that the other women are logical, and know that they know that the other women are logical, etc.