By Raymond M. Smullyan

In his so much severely acclaimed work, a celebrated mathematician presents more than 2 hundred more and more advanced and difficult difficulties — puzzles that delve into a few of the private paradoxes of good judgment and set idea. options. "The most unique, so much profound, and so much funny number of leisure common sense and math difficulties ever written." — Martin Gardner.

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Extra info for What is the name of this book?: The riddle of Dracula and other logical puzzles

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Suppose A were normal. ThenB's statement would be true, henceB is a knight or a normal, butB can't be normal (since A is), so B is a knight. This leaves C a knave. But a knave cannot say that he is not normal (because a knave really isn't normal), so we have a contradiction. Therefore A cannot be normal. Hence A is a knave. Then B' s statement is false, soB must be normal (he can't be a knave since A is). Thus A is the knave, B is the normal one, hence C is the knight. 32 LOGICAL RECREATIONS 40 ..

So A is a knight and B is a knave. 29. This problem is a good introduction to the logic of disjunc­ tion. Given any two statements p, q, the statement " either p or q" means that at least one (and possibly both) of the statements p,q are true. If the statement " either p or q" should be false, then both the statements p, q are false. For KNIGHTS AND KNAVES: SOLUTIONS 27 example, if I should say, "Either it is raining or it is snowing," then if my statement is incorrect, it is both false that it is raining and false that it is snowing.

If the first statement is false, then the first one is actually Tweedledee and the second one is Tweedledum, and hence the second statement is also false. Therefore either both statements are true or both statements are false. They can' t both be false, since the brothers never lie on the same day. Therefore both state­ ments must be true. So the first one is Tweedledum and the second one is Tweedledee. Also, the day of the encounter must be Sunday. If ALICE IN THE FOREST OF FORGETFULNESS: SOLUTIONS 47 52.

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