Alex, Bert, Carl, and Dave are all brothers, with two of them being twins. At least one of them is a knight and makes all true statements. At least one of them is a liar and makes all false statements. And at least one of them is a knave and makes alternating true and false statements. The two which are the same type are the twins. From the statements below, determine who the twins are.

Alex:
1) Bert is one of the twins.
2) Carl is a liar.

Bert:
1) Carl is one of the twins.
2) Alex is a knight.

Carl:
1) I am not one of the twins.

Assume Carl is one of the twins. Then Carl's statement 1 is false, and Bert's statement 1 is true.

If Bert were a knight, then Alex would also be a knight, which can't happen. If Bert were a knave, then Carl must be a knave. So Alex makes one true statement, and one false statement, but there's fewer than 3 knaves. So this can't happen.

Thus, Carl is not one of the twins. So Carl's first statement is true, and Bert's first statement is false.

Since Carl makes a true statement, he can't be a liar, so we see Alex makes at least one false statement, and thus both Bert's statements are false. If Bert is not one of the twins, then Alex is a liar and Bert is a liar, which can't happen.

So Bert is one of the twins, then Alex is a knave, Bert is a liar, and Carl is a knight, which means Bert and Dave are twins.

Posted by Gamer on 2009-01-07 18:23:57