If you asked me...

Logic Level 2

You visit an island with only knights, who always tell the truth, and knaves, who always lie. You meet two islanders named Alpha and Bravo. They each make two statements:

Alpha: "If you asked me, 'If I asked you if you are a knight, what would you say?' I would say (blank)." "Bravo is a knave."

Bravo: "If you asked me, 'If I asked you, 'if I asked you if you were a knight, what would you say?'' I would say (blank)." "Alpha is a knave."

Which of these is true?

A) If Alpha said yes, then Bravo is a knave. B) If Alpha said no, then Bravo is a knight. C) If Bravo said no, then Alpha is a knight. D) If Bravo said yes, then Alpha is a knave. E) None of these

only A E C and D only B only D only C

Vince Cimino by Vince Cimino , 16, USA

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2 solutions

Saya Suka
Apr 26, 2021

The possible answers are :
1) A, B, C & D, or
2) A & B, or
3) C & D

Only the 3rd one is present in the options given, so C AND D it is.

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Vince Cimino
Jun 25, 2018

You can solve this with formal logic. Let A mean that Alpha is a knight. Lets assume Alpha is a knave. For any statement, Alpha will return not A, the opposite of A, the truth. For the last part of the statement, "I would say (blank)," a knave will return, "not A." Moving outwards, a knave knows that they will return not A. When asked what he will say, he must return the opposite(again). So, Alpha's statement can be translated to, "not not A." The nots cancel each other out, so it means, "if A, then A."This tells us nothing because a knight and knave will both return, "if A, then B." Bravo's statement is the same as Alpha's except for one key difference. It has an extra degree away from the A, an extra not. So, if Bravo is a knave, he will return, "not not not B." This translates to , "if B, then not B." So if Bravo is a knave then you will know it. Bravo and Alpha cannot be the same type because of their statements that the other is a knave. So C and D are true, that you can tell what type Bravo based on what he said, and then take the opposite to get what Alpha is.

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