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.
(In reply to
Answer by K Sengupta)
Assume that Bert is a knight. Then, both his statements are true. Accordingly, Alex is a knight, and therefore twin to Alex. Also, Bert's second true statement clearly states that Carl is one of the twins. Thus, each of Alex, Bert and Carl constitute one of the triplets. This is a contradiction.
Assume that Bert is a knave.
If he spoke truthfully on 1st and lied on 2nd, then we observe that Alex is a knight and Carl is NOT one of the twins.In this situation, Alex's first statement is true, which implies that Bert is a twin to another knave. We can easily infer that this knave twin must be Dave. Since A-knight, B-knave, D-knave, this is only possible if Carl is a liar and, then his false statement makes him one of the twins. This is impossible, since it has already been deduced that Bert and Dave are twins. Contradiction.
If Bert spoke falsely on 1st and truthfully on 2nd statement, then we observe that his 2nd true statement implies that Alex is a knight. HIS false 1st statement implies that Carl is not one of the twins, Thus Carl must be a knight or knave. BUt if Carl is a knave, then he would ne twin to Bert, a contradiction. If Carl is a knight, that that would make him a twin to knight Alex. Since C is not one the twins, this is an obvious contradiction.
Therefore, Bert CANNOT be a knave.
Since, it has been proved that Bert is neither a knight, nor a knave- it follows that he must be a LIAR.
This implies that Alex is not a knight and Carl is not a twin. Since Alex is not a knight, it follows that he must be a Knave or a Liar.
Assume that Alex is liar then from his false 1st statement we observe that Bert is NOT one of the twins. But, since Alex and Bert are both liars, it follows that they must be twins. Contradiction. Accordingly, Alex mus be knave
If the knave Alex spoke the 1st statement falsely and the second statement truthfully, then we observe that Bert is not a twin. Carl is a liar whose false statement implies that he is a twin. Since Bert is a liar, we can infer that Bert and Carl are twins.
This is a contradiction.
If the knave Alex spoke the 1st statement truthfully and, the 2nd statement falsely, then we observe that Bert is one of the twins and Carl is not a liar, so he cannot be one of the twins. Also, Bert is a liar, so his twin brother must be a liar. Since Carl is not a knave or liar, it follows that he must only be a knight. Consequently, Bert and Dave must be twin brothers.
Summarizing, we have:
Liars ........ Bert and Dave
Knight....... Carl
Knave ........ Alex
Bert and Dave are twins.
Edited on May 25, 2022, 12:10 am
Explanation to Puzzle Answer
