### Brain Burners

Updates below.

* * *

It's supposed to be the exam week in Ngee Ann Poly, when everyone's brain is supposed to be over-clocked and overheated.

But if your brain is still cool, let me help to warm it up with this little contrived story...

* * *

Part I

Once upon a time, the Calm One went to an interesting place called Ngee Ann.

Ngee Ann is interesting because there are only two types of people there - students (S), who always tell the truth ('S' for 'straight'), and lecturers (L), who always lie ('L' for 'lies'). And you can't tell them apart just by their looks.

Now the Calm One needed to go to Ngee Ann because he needed to borrow an important book from the library.

When the Calm One first stepped into Ngee Ann, he saw 3 people standing at the gates, presumably named Alice, Bob, and Chuck.

"Maybe one of them could tell me how to go to the library," thought the Calm One, "but first, I'll have to find out who's a student."

The Calm One first asked Alice, "are Bob and Chuck both students?"

"Yes," claimed Alice.

"Then is Bob a student?"

To the Calm One's surprise, the answer from Alice was "no".

After a moment's thought, the Calm One knew who exactly are the lecturers and the students.

Do you know as well? If you do, help out those who don't in the comments. Difficulty level: not difficult - just requires a little concentration.

* * *

Part II

When the Calm One reached the library, he knew he had to find the librarian (who happens to be a student). Now the library had only one librarian, but there were 3 people standing there, so he had to find out who the real librarian was.

"Which of you is the librarian?" he asked, without realising that it was probably not the most useful question to ask in Ngee Ann.

"I am," claimed one.

"I am the librarian!" claimed the second.

The third one just smiled like a Mona Lisa.

"What do you have to say?" the Calm One asked the third.

"You know," quipped the third one rather philosophically, "only one of us three tells the truth."

With that, the Calm One knew immediately who the librarian was.

Do you know who? Difficulty level: quite easy.

* * *

Part III

The librarian was obviously quite clever, and it became even more apparent as they chatted.

"Before I retrieve the book for you," said the librarian, "let me issue you a challenge. If you win, you can have the book; if not, you can come back another day."

"Tell me," said the Calm One quite eagerly, "I'm always ready for a challenge."

"Ask me a question to which I must answer yes or no," said the librarian, "but even though the question has a definite correct answer, and even though we both will know the answer, I will be powerless to give you the answer. I will not be able to give you the answer because it will be logically impossible for me to do so."

The Calm One wasn't feeling so calm anymore. Can you help him to think of that question?

Difficulty level: the answer is really very easy, but may require some creativity.

* * *

These are all logic questions, but they are hardly original. If you really want to know the source, email me.

* * *

Update:

Looks like I've just stumbled upon a novel way of getting hate mail. I'll bear that in mind in case I get another craving for hate.

Thanks to our Singaporean need for the "model answer", some of you will never be satisfied until it's given, even though the right answers are already in the comments.

Fine. I'll give in. Model answers are in the comments.

* * *

It's supposed to be the exam week in Ngee Ann Poly, when everyone's brain is supposed to be over-clocked and overheated.

But if your brain is still cool, let me help to warm it up with this little contrived story...

* * *

Part I

Once upon a time, the Calm One went to an interesting place called Ngee Ann.

Ngee Ann is interesting because there are only two types of people there - students (S), who always tell the truth ('S' for 'straight'), and lecturers (L), who always lie ('L' for 'lies'). And you can't tell them apart just by their looks.

Now the Calm One needed to go to Ngee Ann because he needed to borrow an important book from the library.

When the Calm One first stepped into Ngee Ann, he saw 3 people standing at the gates, presumably named Alice, Bob, and Chuck.

"Maybe one of them could tell me how to go to the library," thought the Calm One, "but first, I'll have to find out who's a student."

The Calm One first asked Alice, "are Bob and Chuck both students?"

"Yes," claimed Alice.

"Then is Bob a student?"

To the Calm One's surprise, the answer from Alice was "no".

After a moment's thought, the Calm One knew who exactly are the lecturers and the students.

Do you know as well? If you do, help out those who don't in the comments. Difficulty level: not difficult - just requires a little concentration.

* * *

Part II

When the Calm One reached the library, he knew he had to find the librarian (who happens to be a student). Now the library had only one librarian, but there were 3 people standing there, so he had to find out who the real librarian was.

"Which of you is the librarian?" he asked, without realising that it was probably not the most useful question to ask in Ngee Ann.

"I am," claimed one.

"I am the librarian!" claimed the second.

The third one just smiled like a Mona Lisa.

"What do you have to say?" the Calm One asked the third.

"You know," quipped the third one rather philosophically, "only one of us three tells the truth."

With that, the Calm One knew immediately who the librarian was.

Do you know who? Difficulty level: quite easy.

* * *

Part III

The librarian was obviously quite clever, and it became even more apparent as they chatted.

"Before I retrieve the book for you," said the librarian, "let me issue you a challenge. If you win, you can have the book; if not, you can come back another day."

"Tell me," said the Calm One quite eagerly, "I'm always ready for a challenge."

"Ask me a question to which I must answer yes or no," said the librarian, "but even though the question has a definite correct answer, and even though we both will know the answer, I will be powerless to give you the answer. I will not be able to give you the answer because it will be logically impossible for me to do so."

The Calm One wasn't feeling so calm anymore. Can you help him to think of that question?

Difficulty level: the answer is really very easy, but may require some creativity.

* * *

These are all logic questions, but they are hardly original. If you really want to know the source, email me.

* * *

Update:

Looks like I've just stumbled upon a novel way of getting hate mail. I'll bear that in mind in case I get another craving for hate.

Thanks to our Singaporean need for the "model answer", some of you will never be satisfied until it's given, even though the right answers are already in the comments.

Fine. I'll give in. Model answers are in the comments.

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