Spot The Liar Among

There is a party of 100 politicians. All of them are either honest or liars. You walk in knowing two things:

1. At least one of them is honest.

2. If you take any two politicians, at least one of them is a liar.

From this information, can you know how many are liars and how many are honest?

Know the total number of liars here! 

Source

Knowing The Number of Liars

What is the question?

The information that we have - 

1. At least one of them is honest.

2. If you take any two politicians, at least one of them is a liar. 

Only one of them must be honest and other 99 must be liars. 

Those are the only numbers that can justify the second piece of information. In the case, if any 2 are selected at least 1 of them liar while other may or may not liar (i.e. may be honest). 

PUZZLE : The Case of Honest Suspects

Handel has been killed and Beethoven is on the case. 

He has interviewed the four suspects and their statements are shown below. Each suspect has said two sentences. One sentence of each suspect is a lie and one sentence is the truth. 

Help Beethoven figure out who the killer is.

Joplin: I did not kill Handel. Either Grieg is the killer or none of us is.

Grieg: I did not kill Handel. Gershwin is the killer.

Strauss: I did not kill Handel. Grieg is lying when he says Gershwin is the killer.

Gershwin: I did not kill Handel. If Joplin did not kill him, then Grieg did.

Click here to know who is the killer! 

DETECTION : Killer in The Case of Honest Suspects

What was the case?

Let's first see what are the statements made by 4 suspects.

Joplin: I did not kill Handel. Either Grieg is the killer or none of us is.

Grieg: I did not kill Handel. Gershwin is the killer.

Strauss: I did not kill Handel. Grieg is lying when he says Gershwin is the killer.

Gershwin: I did not kill Handel. If Joplin did not kill him, then Grieg did. 

ANALYSIS :

1] If Joplin is the killer then his first statement would be lie & other statement must be true. But his second statement contradicts assumption that he is killer. So Joplin can't be the killer.

2] Let's assume Grieg is the killer. His first statement must be lie and second must be true. His second statement points to Gershwin as a killer. But there is one killer among 4 so Grieg and Gershwin can't be killers together. Therefore, Grieg can't be the killer.

3] Suppose Gershwin is the killer. Again, his first statement is lie and second is true. His true second statement suggests that Grieg is the killer as Joplin is assumed to be innocent in the case. Again, both Grieg and Gershwin can't be killers together since there is only one killer. Hence, Gershwin is not the killer.

4] Therefore, Strauss must be the killer. His first statement is lie and second statement is true. And that's how Grieg is lying when he is saying Gershwin is the killer.

CONCLUSION : 

STRAUSS is the one who committed the crime and his first statement is lie and second is true.

The first statements of rest of all suspects are true and second statements of each are lie.  

 

Who is the President of Logitopia?

Larry, Matt, and Nick live in the strange country of Logitopia. 

This country is inhabited by three races of people: the type A people who always tell the truth, the type B people who always lie, and the type C people who alternately tell the truth and lie. One of the three is the president of Logitopia.

Larry makes these two statements:

1. "The president is of a different race from the other two."
2. "Matt is not the president."

Matt makes these two statements:

1. "The president is a type B person."
2. "Larry is not the president."

Nick makes these two statements:

1. "Exactly two of us are of the same race."
2. "I am not the president."

Who is the president?

Know the NAME of the President!
 

Larry is the President of Logitopia

What was the puzzle?

First thing to note that it's not mentioned any where that three people are three different types; there may be 2 who are the same type.

Let's have a look at the statements made by 3.

Larry makes these two statements:

1. "The president is of a different race from the other two."
2. "Matt is not the president."

Matt makes these two statements:

1. "The president is a type B person."
2. "Larry is not the president."

Nick makes these two statements:

1. "Exactly two of us are of the same race."
2. "I am not the president."
  
We'll refer Larry's statements as L1 & L2, Matt's as M1 & M2 and those of Nick's as N1 & N2.

ANALYSIS : 

1] Suppose Matt's first statement M1 is TRUE. So, he is not a TYPE B person for sure & hence not the president. Therefore, L2 must be TRUE making sure Larry is not TYPE B person nor a president. So, Nick must be the president & TYPE B person whose both statements are FALSE. Since, N1 is turning out to be FALSE, neither Matt nor Larry can be TYPE B or both of them can't be of the same type i.e. TYPE A or TYPE C. 

However, since M2 turns out to be TRUE, Matt must be TYPE A person and hence leaving Larry as a TYPE C person. In that case, since L2 is TRUE, L1 must be FALSE. But in the case the president (TYPE B) is really different from the other two (TYPE A and TYPE C) making L1 TRUE. So, the assumption that M1 is TRUE goes wrong here in the case.

2] Now, let's suppose that Matt himself is the president. Then, L2 must be FALSE and M2, N2 would be TRUE. Since, M2 is TRUE, Matt (the president) can't be TYPE B & we know M1 is FALSE,  Matt must be TYPE C person & president.

Anyhow, Larry's first statement L1 can't be TRUE as in that case, he too will be TYPE C person as president Matt which is against the statement L1 itself. Since, his other statement L2 is FALSE, he must be TYPE B person.

Now, with N2 to be TRUE, if N1 is assumed to be TRUE then Nick would be TYPE A person. So, all three would belong to 3 different races which contradicts statement N1 itself. Hence, N1 must be FALSE. 

And if N1 FALSE and N2 TRUE, Nick would be TYPE C person as president Matt while Larry being TYPE B person. But this makes statement N1 TRUE which again contradicts our conclusion above. 

Therefore, Matt too can't be the president.

3] Suppose Nick is the president. That would make N2 FALSE and L2, M2 TRUE.
As concluded in STEP 1 above, we know M1 has to be FALSE. Then the President Nick can't be TYPE B person. With one of his false statement N2, Nick must be TYPE C person. Therefore, N1 must be TRUE. So, both Matt and Nick are TYPE C persons. 

That indicates president isn't of a different race than other two. That is L1 turns out to be FALSE. With L2 proved TRUE already, Larry would be TYPE C person. So all three would be TYPE C which contradicts TRUE statement N1.

4] Therefore, Larry must be the president.

That is L2, N2 must be TRUE and M2 must be FALSE. With M1 proved FALSE already in [1] above, Matt must be TYPE B person. Nick can't be TYPE B person with TRUE N2. 

If N1 is TRUE (i.e. Nick is TYPE A person) then Larry must be the other person with TYPE A (since Matt is TYPE B person) along with Nick for N1 to be TRUE. So, L1 too has to be TRUE. But, the president Larry is of the same race as that of Nick which is against L1 itself.

Hence, N1 must be FALSE and Nick must be TYPE C person. And therefore, L1 has to be TRUE making president Larry as a TYPE A person.

CONCLUSION : 

The President of Logitopia is Larry who is TYPE A person. Matt is TYPE B person and Nick is TYPE C person. 

"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. 

 

Strange Creatures on Island

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.

Who are the following two guys?

A: B is a lying monkey. I am human.

B: A is telling the truth.

Know who are they! 

 

Identifying the Strange Creature

What was the situation?

 Let's first have statements by 2 creatures - 

A: B is a lying monkey. I am human.

B: A is telling the truth.

If we assume B is telling the truth then A is also telling the truth. But A in statement says B is lying which contradicts our assumption. 

Hence, B must be lying. If B is lying then statement of B suggest that A is also must be lying. That mean 'B is lying monkey' part of statement made by A is too lie. Since we have deduced already B is lying, the lying statement of A suggests that B is not monkey. Hence B is the lying man!

Other lie spoken by A is that it is human. Hence A must be a lying monkey! 

 

Black or White Dot on Forehead

There are five men, let's say Tarun, Harish, Lavesh, Manoj and Manish. All of them have a dot mark in their forehead. They can't see the dot on their own forehead, but can see the ones on others. The owner of WHITE dot is an honest person and will never lie, while the owner of BLACK dot always tell the lie.

This are the statement from Tarun, Harish, Lavesh, and Manish:

Tarun: 'I see 3 whites and 1 black'

Harish: 'I see 4 black'

Lavesh: 'I see 3 black and 1 white'

Manish: 'I see 4 white'

What color is the dot on each Tarun, Harish, Lavesh, Manoj, Manish forehead?

Know color of dot on each forehead!

Source 

Men with White Dots on Foreheads

Read this story first!

Let's take a look at who said what. 

Tarun: 'I see 3 whites and 1 black'
Harish: 'I see 4 black'
Lavesh: 'I see 3 black and 1 white'
Manish: 'I see 4 white'
 
Harish and Manish made very contracting statements; so are statement of Tarun and Lavesh. That means, only one of them is telling the truth. Hence, only one of 4 have WHITE dot on his forehead. Till now we don't have idea of what Manoj had on his forehead. Even if he has WHITE dot then there can be maximum 2 WHITE dots among those 5.    

Truth of Tarun and Manish:

Tarun and Manish must be lying as they are saying that they have seen 3 and 4 WHITE dots respectively. According to our first conclusion, there can be maximum 2 WHITE dots possible.

Truth of Harish:

Next if we assume Harish has WHITE dot and telling the truth then all other must be lying including Manoj and Lavesh. As per Lavesh, he had seen 3 BLACK and 1 WHITE dot. Now he must have seen BLACK dots on foreheads of Manoj, Tarun, Manish and WHITE dot on forehead of Harish as assumed. That mean he is telling truth though he has BLACK dot. But the man with BLACK is always lying, hence this case is also INVALID. 

Truth of Lavesh:

So the only person left is Lavesh and must be telling the TRUTH with WHITE dot on his forehead. Hence, as his statement is suggesting, the Manoj must have WHITE dot and other three Tarun, Lavesh, Harish have BLACK dots (we already concluded these 3 are lying). 

Who knocked over the monitor?

Melissa and Jessica were working on the computer along with their friends Sandy and Nicole.  Suddenly, I heard a crash and then lots of shouts.  I rushed in to find out what was going on, finding the computer monitor on the ground, surrounded with broken glass!  Sandy and Jessica spoke almost at the same time:

Jessica saying, "It wasn't me!"

Sandy saying, "It was Nicole!"

Melissa yelled, "No, it was Sandy!"

With a pretty straight face Nicole said, "Sandy is a liar."

Only one of them was telling the truth, so who knocked over the monitor? 

Find here who did it! 

Source 
  

Person Who knocked Over Monitor!

What's the entire matter? 

If we assume Jessica speaking the truth & she is not the culprit then other 3 must be liar. The truth that comes from Nicole's statement is that Sandy is telling truth. But only 1 is speaking truth not 2 as here Sandy & Jessica.

That means Jessica is lying. Which in turn means it was she who done that damage. Now Sandy's statement can't be true as we already have got culprit Jessica. 

Similarly, Mellisa lying as she is pointing towards Sandy.Two person not telling truth at a time as per provided information.

So only left with Nicole who is telling the truth that Sandy is liar.

Hence we can conclude that, Jessica knocked over the monitor & Nicole is telling the truth.

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.