Puzzle : The Story of 3 Dragons

I met three dragons. One always tells the truth, other one always lies and the last one alternates between lie and truth.

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

I asked the first dragon a question

Me: 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 I asked a second question addressing the three dragons…… But they remained silent.

And, I solved the puzzle in 90 sec.

So, which dragon is which?

Know the TRUTH of each dragon here! 

Source

Solution : Inside The Story of 3 Dragons

What was the story?

Let's see what are key statements in the story once again.

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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.

I asked the first dragon a question.

Me: 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 I asked a second question addressing the three dragons…… But they remained silent.

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On second question, they remained silent clearly indicates that only 1 question was allowed to ask. Hence, Dragon 2 must be lying for sure.

After knowing the fact that Dragon 2 lied in it's first statement, we know that first statements of Dragon 1 and Dragon 3 are true. 

Now, there are 2 cases possible for Dragon 1 and Dragon 3.

CASE 1 : Dragon 1 speaks alternate and Dragon 3 always tells the truth.

That means the Dragon 1 should lie in it's next statement given in response of my question. 

If Dragon 3 is always telling the truth, the Dragon 2 will always say that Dragon 3 is liar. 

Let's simplify my question to the Dragon 1 as - 

"What will Dragon 2 say if I ask it whether Dragon 3 is lying?" 

Now as per our logic the Dragon 1 should lie in response as - 

Dragon 1: He’d say, “Nope, the 3rd dragon is telling the truth” 

This is contradictory the actual response given by Dragon 1 to the question - 

"What will Dragon 2 say if I ask it whether Dragon 3 is lying?" 

Dragon 1: He’d say, “Yes, the 3rd dragon was lying”

Hence, assumption that Dragon 1 speaks alternate and Dragon 3 tells the truth goes wrong here.

CASE 2 : Dragon 1 tells the truth and Dragon 3 speaks alternate.

That means Dragon 1 will tell truth in response to my question. Since, Dragon 3 is telling truth in it's first statement the always lying Dragon 2 will say that Dragon 3 is lying if asked about Dragon 3.

This is the truth that Dragon 1 tells us in response to my question as - 

"What will Dragon 2 say if I ask it whether Dragon 3 is lying?" 

Dragon 1: He’d say, “Yes, the 3rd dragon was lying”

Hence, this assumption i.e. Dragon 1 tells the truth and Dragon 3 speaks alternate should be correct.

To conclude, Dragon 1 is telling the truth, Dragon 2 always lies and Dragon 3 speaks alternate.   
 

The Unfair Arrangement!

Andy and Bill are traveling when they meet Carl. Andy has 5 loaves of bread and Bill has 3; Carl has none and asks to share theirs, promising to pay them 8 gold pieces when they reach the next town.

They agree and divide the bread equally among them. When they reach the next town, Carl offers 5 gold pieces to Andy and 3 to Bill.

“Excuse me,” says Andy. “That’s not equitable.” He proposes another arrangement, which, on consideration, Bill and Carl agree is correct and fair.

How do they divide the 8 gold pieces?

This is fair arrangement of gold distribution! 

Source 

Correcting The Unfair Arrangement!

How unfair the arrangement was?

First we need to know how 8 loaves (5 of Andy & 3 of Bill) are equally distributes among 3.

If each of them is cut into 2 parts then total 16 loaves would be there which can't be divided equally among 3.

Suppose, each of loaves is divided into 3 parts making total 24 loaves available.

Now, Andy makes 15 pieces of his 5 loaves. He eats 8 and gives the remaining 7 to Carl.

Bill makes 9 pieces of his 3 loaves. He eats 8 and gives the remaining 1 to Carl.

This way, Carl too gets 8 pieces and 8 breads are distributed equally among 3.

 
Obviously, Carl should pay 7 gold pieces to Andy for his 7 pieces and 1 gold piece to Bill for the only piece offered by Bill.