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.   
 

What's The Right Answer?

On a multiple-choice test, one of the questions is illegible, but the choice of answers is listed clearly below. 

What’s the right answer?

(a) All of the below.
(b) None of the below.
(c) All of the above.
(d) One of the above.
(e) None of the above.
(f) None of the above.

'THIS' should be the right answer! 

Source
 

Well, 'THIS' is the Right Answer!

What was the question?

Let's recall the question once again.


What’s the right answer?

(a) All of the below.
(b) None of the below.
(c) All of the above.
(d) One of the above.
(e) None of the above.
(f) None of the above.


If (a) is the right answer then as per (a), all below including (b) and (f) are right answers. But (b) & (f) are contradicting each other. So, (a) can't be right.

Now if (c) is right, then as per (c), (a) also must be right. But as concluded above, (a) can't be right. So, (c) also can't be right.

Next, if (b) is correct, then (d) is also correct making 2 options right. Hence, (b) is also false.

If all (a), (b), (c) are false, then (d) has to be false.

If (f) is correct, then what (e) states also is correct making both (e) & (f) correct. Hence, (f) must be false.

That makes (e) is correct answer. 

"Which one of the golfers is Mr. Blue?"

Four golfers named Mr. Black, Mr. White, Mr. Brown and Mr. Blue were competing in a tournament. 

The caddy didn't know their names, so he asked them. One of them, Mr. Brown, told a lie.


The 1st golfer said "The 2nd Golfer is Mr. Black."

The 2nd golfer said "I am not Mr. Blue!"

The 3rd golfer said "Mr. White? That's the 4th golfer."

And the 4th golfer remained silent.

Which one of the golfers is Mr. Blue?

Know here who is named as Mr. Blue! 

The Golfer Whose Name is Mr.Blue!

What was the puzzle?

We know that Mr. Brown told a lie and statements of 3 golfers are - 

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The 1st golfer said "The 2nd Golfer is Mr. Black."

The 2nd golfer said "I am not Mr. Blue!"

The 3rd golfer said "Mr. White? That's the 4th golfer."

And the 4th golfer remained silent. 

----------------------------------------------------------------------------  

Let's name golfers as GOLFER 1, GOLFER 2, GOLFER 3 and GOLFER 4.

1. If we assume the GOLFER 1 is Mr. Brown then his statement must be lie and other 3 must be telling the truth. That is GOLFER 2 must not be Mr. Black and neither Mr. Blue while GOLFER 4 must be Mr. White. 

So, the only name left for GOLFER 2 is Mr. Brown which is already 'occupied' by GOLFER 1 as per our assumption. 

Hence, GOLFER 1 can't be Mr. Brown.

2. Let's suppose the GOLFER 2 himself is Mr. Brown who statement has to be lie. But in his statement he is telling the truth that he is not Mr. Blue. That's contradictory to the given fact that Mr. Brown told a lie.

Hence, GOLFER 2 must not be Mr. Brown.

3. Only golfer left now for the name Mr. Brown is GOLFER 3 who must be lying in his statement. So, the GOLFER 4 must not be Mr. White.

The GOLFER 2 must be Mr. Black as pointed be truly by GOLFER 1 and 'assisted' by true statement made by GOLFER 2.

If GOLFER 2 is Mr. Black, GOLFER 3 is Mr. Brown and GOLFER 4 is not Mr. White then GOLFER 1 must be Mr. White and GOLFER 4 must Mr. Blue.

So the golfer who is named as Mr. Blue is GOLFER 4 i.e. 4th golfer. 

 

Test of an Examiner

Five students - Adam, Cabe, Justin, Michael and Vince appeared for a competitive exam. There were total five questions asked from them from which were two multiple choice questions (a, b or c) and three were true/false questions. Their answers are given as follows:

Name I II III IV V

Cabe c b True True False

Adam c c True True True

Justin a c False True True

Michael b a True True False

Vince b c True False True

Also, no two students got the same number of correct answers. Can you tell the correct answer? Also, what are their individual score?

Know correct answers and scores here!

Source 

Responding To Test of an Examiner

What was the test?

There are 2 possibilities of scores & that are either 0,1,2,3,4 or 1,2,3,4,5. First of all, let's arrange students' responses in order like below.

Table 1

What we notice here is that, there are few responses to same question by different student matching.

For the Question III, only Justin given different answers than other.

Case 1 : If we assume Justin's answer is correct then rest of all are wrong in response to Question III. That means either maximum score in test is 4 or Justin himself has scored 1 to 5.

Let's test that apart from Justin who can have score of 4. If any body other scores 4 then he must share at least 3 similar answers with other (excluding Answer III; refer image below). Only Adam has exact 3 matching responses with Justin.

Table 2

If Adam's score is 4 (Answers to I, II, IV, V are correct) then, Justin too would score 4 (Answers to II, III, IV,V are correct) since Adam & Justin have same responses to Questions II, IV,V).
  
If nobody scoring as 4 then Justin can have score of 4 or 5.

Case 1.1 : If his score is 4 then there has to be somebody has to be there scoring 0. Now Vince and Adam has at least 2 responses matching with the Justin. That means they can't score 0 since even 1 answer is wrong as Justin the other must be correct as Justin. Michael or Cabe can have 0 score in the case. If anybody of them has score 0 then answer as a TRUE to the Question IV is incorrect i.e. correct Answer IV is FALSE. So Justin is WRONG in Answer IV only. In short, a, c, FALSE, FALSE, TRUE is correct combination of answers. But thing is here in the case both Michael and Cabe would have score 0! Hence Justin's score can't be 4 too.

Case 1.2 : If Justin's score is 5, then a, c, FALSE, TRUE, TRUE are the right answers. No one would score 4 in that case with 3 as second highest by Adam.

Wrong Looking Correct Mathematical Equation!

The following question it puts forth you:

25 - 55 + (85 + 65) = ?

Then, you are told that even though you might think its wrong, the correct answer is actually 5!

Whats your reaction to it? How can this be true? 

 That's how it's perfectly correct!

That's How Equation is Correct!

Why it was looking wrong? 

If you read the data carefully then you will notice '!' attached to number 5 which is being claimed answer. Actually claimed answer is 5! not 5 Read it again...

"Then, you are told that even though you might think its wrong, the correct answer is actually 5!."

Now use of '!' is not limited to the sentences only. In mathematics it's a 'factorial'.

So 5! = 5 x 4 x 3 x 2 x 1 = 120 and 25 - 55 + (85 + 65) = 120 and hence,

25 - 55 + (85 + 65) = 5! 

Now doesn't it look the correct equation? 

An Insepection by The Superintendent

One day, a class teacher was told that the school superintendent will be visiting her class on the next day. The superintendent can ask questions from anywhere and it can be easy as well as difficult. The teacher will have the liberty to choose any pupil for answering the question.

Now she is determined that the impression that is cast upon the superintendent after the inspection should be great. How will she instruct the students so that she maximizes the chances of receiving a correct answer for each question? Also, she must create the best impression. How will she do it? 

This is what she should do! 

To Impress Superintendent

What was the resolution of teacher? 

Now what should teacher do here is to devise the 'sign' language to communicate with students. Also she needs to make sure that the superintendent won't have any doubt while questioning students.

She should ask all the students to raise hands for every question that is being asked by superintendent. However, those who know correct answers should raise right hand & rest of all should raise left hand. This way she would be able to know the students who knows the correct answer & choose any of them to answer the question.

All raised hands to each question would definitely leave great impression on the superintendent.

Note : We are assuming superintendent not smart enough to notice that students raising different hands for different questions.

Who is Liar?

Suppose there are twin brothers; one which always tells the truth and one which always lies.  What single yes/no question could you ask to either brother to figure out which one is which? (Condition is you can't ask question whose answer you already know. e.g. does earth rotate around the sun?)

This should be that question! 

Source 

Question To Identify Liar/Truth Teller

First know about twins. 

We should ask one question,

"Would your brother say that you tell the truth?"

Now if the question is asked the truth teller, then he knows his liar brother would say NO to this question. Hence he would say NO straightaway.

And if the question being asked to liar then he knows that his brother is going to say NO to this question but as a liar he would lie once again & would say YES to the question asked.

So depending on what reply we get, we can easily identify the liar & truth teller brother.