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Long ago,in a planet far far away, there lived three races of intelligent inhabitants: the blues (who always tell the truth), the whites (who always lie), and the pinks (who, when asked a series of questions, start with a lie and then tell the truth and lie alternately). To three creatures, chosen from the planet and seated facing each other at $A$, $B$, and $C$ (see figure), the following three questions are put:

  1. What race is your left-hand neighbour?
  2. What race is your right-hand neighbour?
  3. What race are you?

Here are their answers:

  1. (i) White (ii) Pink (iii) Blue
  2. (i) Pink (ii) Pink (iii) Blue
  3. (i) White (ii) Blue (iii) Blue


What is the actual race of each of the three creatures?

  1. $A$ is Pink, $B$ is White, $C$ is Blue.
  2. $A$ is Blue, $B$ is Pink, $C$ is White.
  3. $A$ is Pink, $B$ is Blue, $C$ is Pink.
  4. $A$ is White, $B$ is Pink, $C$ is Blue.
  5. Cannot be determined from the above data.
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3 Answers

Best answer
28 votes
28 votes

If $A$ is Blue (honest), then

  • Whatever $A$ says about $B$ and $C$ must be True.
  • $A$ says that $B$ is White(liar) and $C$ is Pink(alternating). So, if $A$ is Blue, $B$ must be White and $C$ must be Pink.
  • $B$ says that $C$ is Pink. But $B$ is a liar, and $B$ agrees with $A$ on the race of $C$ (they must not agree). Thus, we reached a contradiction.

So, $A$ can't be Blue.


If $B$ is Blue (honest), then

  • Whatever $B$ says about $A$ and $C$ must be True.
  • $B$ says that $A$ is Pink(alternating) and $C$ is Pink(alternating). So, if $B$ is Blue, $A$ must be Pink and $C$ must be Pink.
  • Since $A$ is pink, it must lie about $B$, say the truth about $C$ and then lie about itself. Which it does.
  • Since $C$ is pink, it must lie about $A$, say the truth about $B$, and then lie about itself. Which it does.

So we see that Blue B, Pink A and Pink C is a possible solution!

Thus, option (C) is correct.


However, there is another option (E), which says Cannot be determined from the above data.

So, what if there are multiple solutions that satisfy these constraints? If that is the case, option e will be correct. Sadly, there is no way of proving that no other solutions work except checking each one of them (using branch and bound to somewhat improve). Sadly, that will be lengthy.

Here is a Python3 program that finds all solutions to this problem: http://ideone.com/7EFXCn

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Blue always say truth , White always say lie and Pink say lie and truth alternatively starting from lie.

1.If we consider the A as Blue then according to A answers B will be white and C will be Pink. 
now if we match the the C answer it will not match. He says right is blue which is white according to A so its a lie which is supposed to be truth.

2. Now consider B as blue then according to to B answer A will be Pink and C will also be Pink.
Then answer of A and C will match.
So answer is Option C A is pink B is blue and C is pink.

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0 votes

According to me, the answer should be option “E- Cannot be determined from the above data.”  Reason being-

 Blue- always tell truth

white- always tell lie

pink- lie/ truth/ lie/ truth/…..

 Now suppose if blue is “A”  then on left is white, right is pink and itself is blue. But why cannot blue be option B or option C ?  because if we assume blue as  option B. then on its left is pink and on its right is also pink and blue always tell truth, so this is not possible

 Also if we assume blue as option C then on its left is white and on its right is blue and itself as blue is also not possible. Hence only possiblity of vertex A is blue. 

now if B is assumed as pink then on its left is pink which is lie, on its right is again pink which should be true as per question but this is not possible so vertex B has to be white

So as vertex B is white then vertex C is pink

so for whits as option B, its left is pink but this is truth whereas white always tells lie so contradictory.

Hence the solution cannot be determined.

Answer:

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