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The problem with your logic is that if the birthday was June 17, how would Albert be so confident that Bernard doesn't know the birthday?
Albert sees only June. From his perspective, it's possible that the birthday is June 18, in which case Bernard would know simply by seeing 18.
The problem with your logic is that if the birthday was June 17, how would Albert be so confident that Bernard doesn't know the birthday?
Albert sees only June. From his perspective, it's possible that the birthday is June 18, in which case Bernard would know simply by seeing 18.