On the island of Knights and Knaves there live only two type

On the island of Knights and Knaves there live only two types of people: Knights (who always speak the truth) and Knaves (who always lie). I met two men who lived there and asked the taller man if they were both Knights. He replied, but I could not figure out what they were, so I asked the shorter man if the taller was a Knight. He replied, and after that I knew which type they were. Were the men Knights or Knaves? They were both Knights. They were both Knaves. The taller was a Knight and the shorter was a Knave. The taller was a Knave and the shorter was a Knight. Not enough information is given.

Solution

Case 1. Both Knights

Answer to first question to taller knight would be

Yes

Answer to second question to shorter knight would be

Yes

Case 2: Both Knaves

Answer to first question to the taller man would be

Yes because Knaves always lie

Answer to second question to shorter man would be

Yes again because taller man is Knave and Knaves always lie. Hence both answers are Yes same as Case 1. Hence it is impossible to distinguish Case 1 and 2 with these two questions.

Case 3: Taller is Knight and shorter is Knave

Answer to first question to taller one who is a knight

No because only one of them is a knight and knights always tell the truth

Answer to second question to Knave ,the shorter knight, would be

No as the taller one is a knight and knaves always lie.

Case 4. Taller is Knave and shorter is Knight

Answer to first question to Knave would be

Yes as Knaves always lie.

Answer to second question to Knight would be

No as taller one is Knave and knights always tell truth.

So we see Case 3 and Case 4 both have unique answers but note that in only one case ie Case 3 do we get No as answer to first question ie to the taller one. Since at the end of the first question it could not be figured out who they were so it can\'t be Case 3 ie answer to first question must have been a Yes.

Hence it must be Case 4 ie

D) The taller was a Knave and shorter a Knight