Knights, Knaves and Jokers on an island

Logic Level 2

Suppose you are visiting an island in which there are only 3 kinds of people :

  • Knights- they speak only the truth
  • Knaves - they only lie
  • Jokers - they can do either

Now when you come to island, you see 4 people (A,B,C,D) and suppose you know that among those 4 there is atleast one of each kind. You ask them 3 questions :

Person A B C D
Q1: How many of you are Knights ? 2 2 1 1
Q2: How many of you are Knaves ? 1 1 1 2
Q3: How many of you are Jokers ? 1 1 1 2

Now my question is tell me who is/are the Knight(s) ?

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

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2 solutions

Out of A {\color{#D61F06}A} , B {\color{#3D99F6}B} , C {\color{#CEBB00}C} , and D {\color{#20A900}D} , only A {\color{#D61F06}A} and B {\color{#3D99F6}B} would have possible statements if they were k n i g h t s \mathbf{knights} , as they would be the only members that would give values that sum four (seeing there are four people on the island).

Hence, A {\color{#D61F06}A} and B {\color{#3D99F6}B} are k n i g h t s \mathbf{knights}

For determining C {\color{#CEBB00}C} and D {\color{#20A900}D} (not needed): \\

Either C {\color{#CEBB00}C} or D {\color{#20A900}D} must be a j o k e r \mathbf{joker} , and the other must be a k n a v e \mathbf{knave} . \\

C {\color{#CEBB00}C} could only be a j o k e \mathbf{joke } as they give a false value (1 k n i g h t \mathbf{knight} ) and two true values (1 j o k e r \mathbf{joker} and 1 k n a v e \mathbf{knave} ). \\ D {\color{#20A900}D} is therefore the k n a v e \mathbf{knave} .

Saya Suka
Mar 11, 2021

Total up their answers and both A & B got the logical 4, the same number of the people they're answering for. Also, the Knights are united in their truth, so every answer they gave is the same. D is a knave and C a Joker. Batman, help!

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