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.

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

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.

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

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 - 

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

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. 

 

The Lightning Fast Addition!

A  story tells that, as a 10-year-old schoolboy, Carl Friedrich Gauss was asked to find the sum of the first 100 integers. The tyrannical schoolmaster, who had intended this task to occupy the boy for some time, was astonished when Gauss presented the correct answer, 5050, almost immediately.

How did Gauss find it?

Actually, he used this trick! 

 

Trick for The Lightneing Fast Addition!

Why lightning fast speed needed?

Gauss attached 0 to the series and made pairs of numbers having addition 100.

100 + 0 = 100

99 + 1 = 100

98 + 2 = 100

97 + 3 = 100

96 + 4 = 100

95 + 5 = 100
..
..
..
..
..
..
51 + 49 = 100

This way he got 50 pair of integers (ranging in between 1-100) having sum equal to 100.

So sum of these 50 pairs = 100x50 = 5000.

 
And the number 50 left added to above total to get sum of integers 1 - 100 as 5000 + 50 = 5050

Probability of The Correct Answer?

This is a popular probability puzzle in which you have to select the correct answer at random from the four options below.

Can you tell, whats the probability of choosing correct answer in this random manner.

1) 1/4
2) 1/2
3) 1
4) 1/4

And the correct answer is......

Finding The Probability of Correct Answer

What was the question?

It can't be 1/4 as 1/4 appears 2 times in given 4 options as probability of correct answer when random selection of option in that case would be 2/4 = 1/2. This will be contradiction.

It can't be 1/2 either since the probability of the 1 correct answer out of 4 available options on random selection would be 1/4. That will be contradiction again.

It can't be 1 too as again probability of the 1 correct answer out of 4 available options on random selection would be 1/4. Once again this is contradiction.

Hence, the probability of the 1 correct answer out of 4 available options on random selection would be 0.

What's the answer?

Just try to find it!

Here is the answer!

'This' Is The Answer!

What was the question? 

Just count the intersecting points.

First one has 9, second one has only 1 & third has 4. 

Hence, the answer is 4.

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.

The Tuesday Birthday Problem

I ask people at random if they have two children and also if one is a boy born on a Tuesday. After a long search I finally find someone who answers yes. What is the probability that this person has two boys? Assume an equal chance of giving birth to either sex and an equal chance to giving birth on any day.

Tip: Don't conclude too early. 

Click here to know the correct answer! 

Finding The Correct Probability

How tricky it was?

If you think that the probability is 1/2 after reading that the couple has equal chance of having child of either sex then you are in wrong direction.

Take a look at the table below.

There are 27 possible combinations when boy is born on Tuesday. Out of which there are only 13 possible combinations where either boy (first or second) is born on Tuesday. 

Hence the probability that the person having at least 1 boy off his 2 boys born on Tuesday is 13/27.

Only This Cup Will Fill Up!

Purpose of the title of the post!

If you think that cup 4 will fill up first then you are deceived by the creator successfully.  You might have found the order of filling cups as 4,9,7 & 5. Congrats, your brain hasn't processed details! Didn't you notice the blocks? 

   Coffee Cup Puzzle