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 B is a Knight. So being truthful on all counts, C is one of the twins and A is indeed a Knight as well. But this makes A and B the two twin Knights. An obvious contradiction with respect to C being a twin!
Assume B is a Knave. If B answered falsely/truly, C is not a twin, while A is a Knight whose truthful first answer makes B a twin (to another Knave), which could only be D, leaving C as the Liar here. His lie would make him one of the twins, however, resulting in a contradiction with the twin Knaves, B's first statement, etc.
If B answered truly/falsely, C would be a twin, while A would not be a Knight but a Liar or Knave. If A is a Liar, B is not a twin (to any Knave). If A also lied about C, C is not the Liar, but didn't answer truthfully, can't be a Knight and must have given a Knave's false answer. That makes B and C twin Knaves, which contradicts with B not being a twin to another Knave!
That means B is a Liar. C is then not a twin, and A is not a Knight (and must be Liar or Knave). If A is the Liar, then from his 1), B is not a twin, which is again contradictory since A and B would actually be twin Liars. So under this scenario, A must be a Knave.
If Knave A answered falsely/truly, B is not a twin, while C is a Liar whose twin in this scenario is actually Liar B. Another contradiction!
This only leaves Knave A answering truly/falsely. B would indeed be a twin (to another Liar), while C would not be a Liar, and so could only be a Knight. This leaves Liar's B and D as the only possible twins. Edited on January 7, 2009, 7:26 pm
Answer by elimination
