Puzzle : "Who Stole My Purse?"

An elementary school teacher had her purse stolen. The thief had to be Lilian, Judy, David, Theo, or Margaret. When questioned, each child made three statements: 

Lilian:
(1) I didn’t take the purse.
(2) I have never in my life stolen anything.
(3) Theo did it. 

Judy:
(4) I didn’t take the purse.
(5) My daddy is rich enough, and I have a purse of my own.
(6) Margaret knows who did it. 

David:
(7) I didn’t take the purse.
(8) I didn’t know Margaret before I enrolled in this school.
(9) Theo did it. 

Theo:
(10) I am not guilty.
(11) Margaret did it.
(12) Lillian is lying when she says I stole the purse. 

Margaret:
(13) I didn’t take the teacher’s purse.
(14) Judy is guilty.
(15) David can vouch for me because he has known me since I was born. 

Later, each child admitted that two of his statements were true and one was false. Assuming this is true, who stole the purse?

Here is name of the thief! 

Source

"Finally Got My Stolen Purse!"

How it was stolen?

Let's recollect all the statements given by all accused.

Lilian:
(1) I didn’t take the purse.
(2) I have never in my life stolen anything.
(3) Theo did it. 

Judy:
(4) I didn’t take the purse.
(5) My daddy is rich enough, and I have a purse of my own.
(6) Margaret knows who did it. 

David:
(7) I didn’t take the purse.
(8) I didn’t know Margaret before I enrolled in this school.
(9) Theo did it. 

Theo:
(10) I am not guilty.
(11) Margaret did it.
(12) Lillian is lying when she says I stole the purse. 

Margaret:
(13) I didn’t take the teacher’s purse.
(14) Judy is guilty.
(15) David can vouch for me because he has known me since I was born. 

Let's not forget that 2 of 3 statements made by each student are true & other is false.

Now, Theo says he is innocent in his 2 statements - (10) and (12). Since, 2 of his statements are true then (10) and (12) must be true. Hence, Theo is really innocent in case.

If Theo is innocent then both (3) and (9) are lie.

If (9) is lie, then other 2 statement of David i.e. (7) and (8) are true. If (8) is true then (15) must be lie. 

And if (15) is lie then both (13) [lie in (12) also suggests same] and (14) must be true. 

Hence, as per (14), Judy is guilty who has stolen the purse. 

Puzzle : Which one is the car thief?

A car thief, who had managed to evade the authorities in the past, unknowingly took the automobile that belonged to Inspector Detweiler. 

The sleuth wasted no time and spared no effort in discovering and carefully examining the available clues. He was able to identify four suspects with certainty that one of them was the culprit.

The four make the statements below. In total, six statements are true and six false.

Suspect A:

1. C and I have met many times before today.
2. B is guilty.
3. The car thief did not know it was the Inspector's car.

Suspect B:

1. D did not do it.
2. D's third statement is false.
3. I am innocent.

Suspect C:
 
1. I have never met A before today.
2. B is not guilty.
3. D knows how to drive.

Suspect D:
 
1. B's first statement is false.
2. I do not know how to drive.
3. A did it.

Which one is the car thief?

Know here who is that car thief? 

Solution : The Unlucky Car Thief

What was the puzzle?

Take a look at the statements made by suspects.

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

Suspect A:

1. C and I have met many times before today.
2. B is guilty.
3. The car thief did not know it was the Inspector's car.

Suspect B:

1. D did not do it.
2. D's third statement is false.
3. I am innocent.

Suspect C:

1. I have never met A before today.
2. B is not guilty.
3. D knows how to drive.

Suspect D:

1. B's first statement is false.
2. I do not know how to drive.
3. A did it.

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

After investigation, it is found that,  in total, six statements are true and six false.

We will name statements as A1 for first statement of A, A2 for his second statement, B1 for B's first statement B2 for his second statement and so on.

1. Since, a car thief, who had managed to evade the authorities in the past, unknowingly took the automobile that belonged to Inspector Detweiler, we assume statement A3 is TRUE.

2. A1 and C1, C3 and D2 are contradicting statements. These statements are having least relevant in the process as they are not pointing to anybody else. Two of them must be TRUE and 2 must be FALSE. There are 4 TRUE and 4 FALSE statements from rest of statements.

We have, 2 FALSE statements among A1, C1, C3 and D2 for sure.

3. Assume A is a car thief. Then only A2, B2 and D3 turns out to be FALSE from rest giving in total of 5 FALSE statements only.

4. Assume C is a car thief. Then only A2, D1 and D3 are FALSE, hence total of 5 FALSE statement among all statements.

5. Assume D is a car thief. Then again only A2, B1 and D3 are FALSE, once again total 5 out of 12 given statements are FALSE in the case.

6. Assume B is a car thief. In this case, B3, C2, D1 and D3 turns out to be FALSE. Hence, total 6 out of 12 given statements are FALSE. 

This is exactly as per fact found in the investigation which suggests that exactly 6 out of 12 statements are FALSE. 

Hence, B must be a car thief. 

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 - 

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


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."

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

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. 

Help The Policeman in Finding The Culprit

Late one evening, a car ran over a pedestrian in a narrow bystreet and drove away without stopping. A policeman who saw the vehicle leave the scene of the accident reported it moving at very high speed. The accident itself was witnessed by six bystanders. They provided the following conflicting accounts of what had happened:

• It was a blue car, driven by a man;
• The car was moving at high speed, its headlights were turned off;
• The car did have license plates, it wasn’t going very fast;
• It was a Toyota, it’s headlights were turned off;
• The car didn’t have license plates, the driver was a woman;
• It was a gray Ford.

When the the car and its driver were finally apprehended, it turned out that only one of the six eyewitnesses gave a fully correct description. Each of the other five provided one true and one false piece of information.

Keeping that in mind, can you determine the following:

— What was the car’s brand?

— What color was the car?

— Was the car going fast or slow?

— Did it have license plates?

— Were its headlights turned on?

— Was the driver a man or a woman? 

Read all the answers here!

To Help The Policeman in Finding The Culprit

But why he needs help? 

Let's recollect all the statements made by all 6 bystanders.

 1.It was a blue car, driven by a man.

 2.The car was moving at high speed, its headlights were turned off.

 3.The car did have license plates, it wasn’t going very fast.

 4.It was a Toyota, it’s headlights were turned off.

 5.The car didn’t have license plates, the driver was a woman.

 6 It was a gray Ford (It was gray car; it was Ford).

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

If we believe in report made by Policeman where he stated that the car was moving at very high speed; then the part of the Statement 3 made by third bystander where he says car wasn't going fast turns out to be false. Hence, other part of his statement must be true. So the car must have license plates.

If the car has license plates; then 1st part of the Statement 5 will be false & other part must be true. Hence, the driver must be a woman.

If the driver was a woman, then 2nd part of the Statement 1 turns false making part 1 to be true. Hence, the color of the car must be blue.

If the car was at high speed then the entire Statement 2 must be true or it's 2nd part must be false.

Let's assume 2nd part of the statement 2 be false. Then 2nd part of statement 4 also must be false leaving 1st part to be true. That means the car was Toyota. But this makes statement 6 entirely false (as we already know color of car is blue). This contradicts the crucial data given - Each of the other five provided one true and one false piece of information. In the case, there will be no eyewitness giving full correct description.

So the entire Statement 2 must be true. Hence, the car was with it's headlight off.

If headlights were turned off then 2nd part of the Statement 4 must be true and 1st part false. That means, car wasn't Toyota.

And if car wasn't Toyota, as per Statement 6, it must be Ford but not of gray color.
This matches our early conclusion where we concludes color of the car was blue.

Conclusions:

1.What was the car’s brand?

   - Ford

2.What color was the car?

   - Blue

3.Was the car going fast or slow?

   - Fast

4.Did it have license plates?

   - Yes, it had.

 

5.Were its headlights turned on?

   - No, those were off.

6.Was the driver a man or a woman?

   - A woman. 

Who Did It?

Three of these statements are false, so who did it?

    Mr Red: “Mr Blue did it.”

    Mr Blue: “Mr Red did it.”

    Mr Green: “Mr Blue’s telling the truth.”

    Mr Yellow: “Mr Green’s not lying.”

Find who did it!

Mr. Blue Did it!

What were the statements by suspects?

If Mr. Yellow is telling the truth then Mr. Green and hence Mr. Blue all are telling the truth. This is against the given data.

This hold true if we assume that Mr. Green is telling the truth or Mr. Blue telling the truth. In all cases, 3 statements would be true.

Hence, only statement of Mr.Red is true and that's why Mr. Blue did it!

 

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.

The True Statement?

A. The number of false statements here is one.

B. The number of false statements here is two.

C. The number of false statements here is three.

D. The number of false statements here is four.

Which of the above statements is true?

     Find it here! 

 Source

The Only True Statement

How it was tricky & what were others? 

One has to be true & other 3 must be false. Let's consider each case one by one.

Case A : According to this statement the number of false statement is 1 which is contrary to given condition that 1 is true & 3 are false. So it can't be true.

Case B : As per this, number of false statements = 2 which is again contrary to given condition of 3 false statements.So it can't be true.

Case C : As per this, number of false statements =3 exactly matching the given condition.

Case D : This implies number of false statements = 4 meaning that all the statements including itself are false. This is opposite to given condition. So this has to be false as well.

   
So the statement C is true & all other are false!