Puzzle | Paradox Dragons
Puzzle: There are 3 dragons. One of them always speaks the truth, one always lies and one alternate between truth and lie. A series of conversation takes between Ram and the 3 dragons which lets you identify the nature of each dragon.
- Dragon 1: “You may ask us one question, then you must guess which dragon is which.”
- Dragon 2: “He’s lying. You may get three questions”
- Dragon 3: “Oh no. It’s definitely one question”
- Ram: “What would the second dragon say if I were to ask it if the 3rd dragon had been lying when it agreed with the first one that I could ask only one question”
- Dragon 1: He’d say, “Yes, the 3rd dragon was lying”
- Then Ram asked a second question addressing the three dragons, but they remained silent. The puzzle was solved, explain.
Solution: Based on the silence after Ram asked the second question, it can be inferred that asking of one question was true as said by Dragon 1. So Dragon 1 and Dragon 3 are speaking the truth for the first time. This raises two cases:
|Dragons||Case 1||Case 2|
|Dragon 1||Always speaks Truth||Column3|
|Dragon 2||Always Lie||Always Lie|
|Dragon 3||Always speaks Truth||Lternates|
Now let’s analyse each case.
Case 1: If this case is true, Dragon 1’s statement “Dragon 2 will say that Dragon 3 is lying” would have been a lie. If Dragon 1 lies, then Dragon 2’s statement would be “Dragon 3 is saying the truth”, but according to Case 1, Dragon 2 always lie and Dragon 3 always speaks the truth. These statements contradict with the case of Dragon 3 always speaking the truth.
Case 2: If this case is True, Dragon 1’s statement “Dragon 2 will say that Dragon 3 is lying” would be true. So Dragon 2’s statement would be “Dragon 3 is lying” which would be a lie. Hence Case 2 is correct.