This is not the hardest puzzle in Raymond Smullyan’s “The Lady or The Tiger” but I still found it very tricky and could not get it right even though it’s the second time I’ve attempted it.

First some background.

Inspector Craig of Scotland Yard was called over to France to investigate eleven insane asylums where it was suspected that something was wrong. In each of these asylums, the only inhabitants were patients and doctors – the doctors constituted the entire staff. Each inhabitant of each asylum, patient or doctor, was either sane or insane. Moreover, the sane ones were totally sane and a hundred percent accurate in all their beliefs; all true propositions they knew to be true and all false propositions they knew to be false. The insane ones were totally inaccurate in their beliefs; all true propositions they believed to be false and all false propositions they believed to be true. It is to be assumed also that all the inhabitants were always honest – whatever they said, they really believed.

Now the puzzle of the fifth asylum.

Craig asked one of the inhabitants, “Are you a patient?” He replied, “I believe so.”

Is there anything necessarily wrong with this asylum?

[Note from recordmymind: i.e. given the reply by the inhabitant of the asylum, can you conclude that there are sane patients or insane doctors in the asylum?]

From Chapter 3 of Raymond Smullyan’s “The Lady or the Tiger”.

Answers will be provided in the comments section if requested.