Here is a problem I'll be giving my Math 101 students next week (it's so much fun messing with their heads!)
``On a fictional island known as Rayan, all inhabitants are either knights, who always tell the truth, or knaves, who always lie. Ferdinand finds himself shipwrecked on this island and meets a group of three of the inhabitants. He has heard of this island in his travels, and he knows that in order to survive he must determine who will tell him the truth. Having taken Math 101 he knows something about logic, so he begins to question the three inhabitants. (Let's call them A, B and C for the sake of simplicity!) Ferdinand asks A, ``Are you a knight or a knave?'' But Ferdinand does not hear the answer. B chimes in and says, ``The first guy said that he is a knave.'' C then shouts out, ``Don't believe B! He is lying!''
Given these statements, Ferdinand (who did quite well in Math 101, by the way), is able to figure out who is a knight and who is a knave. Now it's your turn!''
Apologies to Raymond Smullyan.
So what is the answer? If C is a Knave, then B is a Knight and A is a Knave. If C is a Knight, then B is a Knave and A is a Knight. Don't you have to know what C is? I apparently did not do well in Math 101
ReplyDeleteThe key is that NO ONE would say they are a knave, so what B said is a lie and therefore what C said is true.
ReplyDeleteAnyone who tells the truth is a knight and will claim to tell the truth, but anyone who is a knave will lie and will also claim to tell the truth, so what B said A said is impossible.
Therefore B is a liar/knave and A and C are knights.
yes, you are correct
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