What day of the week is it?

A group of campers have been on vacation so long, that they've forgotten the day of the week. 

The following conversation ensues. 

Darryl: "What's the day? I don't think it is Thursday, Friday or Saturday." 

Tracy: "Well that doesn't narrow it down much. Yesterday was Sunday." 

Melissa: "Yesterday wasn't Sunday, tomorrow is Sunday." 

Ben: "The day after tomorrow is Saturday." 

Adrienne: "The day before yesterday was Thursday." 

Susie: "Tomorrow is Saturday." 

David: "I know that the day after tomorrow is not Friday." 

If only one person's statement is true, what day of the week is it?

So it was THIS day of the week!

The Forgotten Day of Week is Wednesday!

What was the puzzle?

Let's see once again the conversation that campers had - 

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Darryl: "What's the day? I don't think it is Thursday, Friday or Saturday." 

Tracy: "Well that doesn't narrow it down much. Yesterday was Sunday." 

Melissa: "Yesterday wasn't Sunday, tomorrow is Sunday." 

Ben: "The day after tomorrow is Saturday." 

Adrienne: "The day before yesterday was Thursday." 

Susie: "Tomorrow is Saturday." 

David: "I know that the day after tomorrow is not Friday."

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Let's see what day statement of each is suggesting -

Darryl - Sunday, Monday, Tuesday, Wednesday.

Tracy - Monday.

Melissa - Saturday.

Ben - Thursday.

Adrienne - Saturday.

Susie - Friday.

David - Sunday, Monday, Tuesday, Thursday, Friday or Saturday.  

If we assume David's statement is TRUE then one of statements of Darryl (Sunday, Monday, Tuesday are common) or Tracy (Monday is common) or Melissa & Adrienne (Saturday is common) or Susie (Friday is common) or Ben (Thursday is common) has to be also TRUE. But this is against the given data that only 1 of the statement is TRUE.

Hence, David's statement must be FALSE and the only day that isn't pointed by David is Wednesday.

So the day must be Wednesday as suggested correctly by Darryl and thereby making statements of every other camper including David FALSE. 

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. 

What Was the Color of Gabbar Singh's Shirt ?

In Rangeelia, a neighbour situated west of our country, the native people can be divided into three types: Lalpilas, Pilharas and Haralals. 

Lalpilas always get confused between red and yellow (i.e. they see yellow as red and vice versa) but can see any other color properly. Pilharas always get confused between yellow and green (i.e. they see yellow as green and vice versa) but can see any other color properly. Haralals always get confused between green and red (i.e. they see green as red and vice versa) but can see any other color properly.

Three people Amar, Akbar and Anthony, who belong to Rangeelia, made the following statements about Gabbar Singh, the famous dacoit of Rangeelia, when he was last seen by them :-

Amar : Gabbar Singh was wearing a green shirt.

Akbar : Gabbar Singh was not wearing a yellow shirt.

Anthony : Gabbar Singh was wearing a red shirt.

If none of Amar, Akbar or Anthony is a Haralal, then what was the color of Gabbar Singh's shirt ?

THIS is the color of Gabbar Singh's shirt! 

A Door Of Fate Or Logics?

A prisoner is faced with a decision where he must open one of two doors. Behind each door is either a lady or a tiger. They may be both tigers, both ladies or one of each.

If the prisoner opens a door to find a lady he will marry her and if he opens a door to find a tiger he will be eaten alive. Of course, the prisoner would prefer to be married than eaten alive :).

Each of the doors has a statement written on it. The statement on door one says, “In this room there is a lady, and in the other room there is a tiger.”

The statement on door two says, “In one of these rooms there is a lady, and in one of these rooms there is a tiger.”
 
The prisoner is informed that one of the statements is true and one is false.

Which door should the Prisoner open?

This should be his choice!

Logical Choice Of Door

What were the choices?

For a moment, let's assume that first statement is true. The lady is behind the Door 1 and tiger is behind the Door 2. But this makes statement 2 also true where it says there is tiger behind one of these door & lady behind one of these doors. Hence, the statement 1 can't be true.

Hence, statement 2 must be true.

Only possibilities left are -

Door 1 - Tiger
Door 2 - Tiger

Door 1 - Lady
Door 2 - Lady

Door 1 - Tiger
Door 2 - Lady.

Since, the true second statement is suggesting there is lady behind 1 & tiger behind the other door, the possibilities of both tigers or ladies are eliminated.

That's why behind Door 1 is tiger & behind Door 2 is lady.