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. 

The Numbered Hats Test!

One teacher decided to test three of his students, Frank, Gary and Henry. The teacher took three hats, wrote on each hat an integer number greater than 0, and put the hats on the heads of the students. Each student could see the numbers written on the hats of the other two students but not the number written on his own hat.

The teacher said that one of the numbers is sum of the other two and started asking the students:

— Frank, do you know the number on your hat?

— No, I don’t.

— Gary, do you know the number on your hat?

— No, I don’t.

— Henry, do you know the number on your hat?

— No, I don’t.

Then the teacher started another round of questioning:

— Frank, do you know the number on your hat?

— No, I don’t.

— Gary, do you know the number on your hat?

— No, I don’t.

— Henry, do you know the number on your hat?

— Yes, it is 144.

What were the numbers which the teacher wrote on the hats?

Here are the other numbers!

Source 

Cracking Down The Numbered Hats Test

What was the test?

Even before the teacher starts asking, the student must have realized 2 facts.

1. In order to identify numbers in this case, the numbers on the hats has to be in proportion i.e. multiples of other(s). Like if one has x then other must have 2x,3x etc.

2. Two hats can't have the same number say x as in that case third student can easily guess the own number as 2x since x-x = 0 is not allowed.

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Now, if numbers on the hats were distributed as x, 2x, 3x then the student wearing hat of number 3x would have quickly responded with correct guess. That's because he can see 2 number as x and 2x on others hats and he can conclude his number as x + 2x = 3x since 
2x - x = x is invalid combination (x, x, 2x) where 2 numbers are equal.

Other way, he can think that the student with hat 2x would have guessed own number correctly if I had x on my own hat. Hence, he may conclude that the number on his hat must be 3x.

But in the case, all responded negatively in the first round of questioning. So x, 2x, 3x combination is eliminated after first round.

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That means it could be x, 3x, 4x combination of numbers on the hats.

In second round of questioning, Henry guessed his number correctly.

If he had seen 3x and 4x on other 2 hats then he wouldn't have been sure with his number whether it is x or 7x.

Similarly, he must not have seen x and 4x as in that case as well he couldn't have concluded whether his number is either 5x or 3x.

But when he sees x and 3x on other hats he can tell that his number must be 4x as 2x (x,2x,3x combination) is eliminated in previous round!

So Henry can conclude that his number must be 4x.

Since, he said his number is 144,

4x = 144

x = 36

3x = 108.

Hence, the numbers are 36, 108, 144.

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.

"Make The Line Shorter!"

Once a teacher asked student the question that Akbar once has asked to Birbal. Teacher drawn a line on a paper with pencil & posted paper on a board. He asked students to make the line shorter without erasing by eraser or extending it with pencil.

One of the student who knew that story of Akbar - Birbal came & just draws another bigger line ahead of previous line. Now the other line looked shorter.

   
Now teacher decides to trick the students. 'Now without touching any line it make left line longer & right line shorter', he asks further.

The student was smart & just rotated the paper upside down. That way, now left line looked longer & right one shorter!