Puzzles to puzzle you

[Ashutosh]

Imagine you are an ant sitting on the face of a Rubik's cube made of cheese. You have been assigned the following task: Eat the whole cube by starting with any subcube on the face. Once you're done with a given subcube, you can move to another subcube which shares a face with the one you just finished. The catch is this: The subcube at the center of the Rubik's cube must be the last subcube eaten.

So the puzzle is: Can you do it?

[Ashutosh]

Here's another tantalizing puzzle (Source: Terence Tao's blog)

There is an island upon which a tribe resides. The tribe consists of 1000 people, with various eye colours. Yet, their religion forbids them to know their own eye color, or even to discuss the topic; thus, each resident can (and does) see the eye colors of all other residents, but has no way of discovering his or her own (there are no reflective surfaces). If a tribesperson does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness. All the tribespeople are highly logical and devout, and they all know that each other is also highly logical and devout (and they all know that they all know that each other is highly logical and devout, and so forth).

For the purposes of this logic puzzle, "highly logical" means that any conclusion that can logically deduced from the information and observations available to an islander, will automatically be known to that islander.

Of the 1000 islanders, it turns out that 100 of them have blue eyes and 900 of them have brown eyes, although the islanders are not initially aware of these statistics (each of them can of course only see 999 of the 1000 tribespeople).

One day, a blue-eyed foreigner visits to the island and wins the complete trust of the tribe.

One evening, he addresses the entire tribe to thank them for their hospitality.

However, not knowing the customs, the foreigner makes the mistake of mentioning eye color in his address, remarking “how unusual it is to see another blue-eyed person like myself in this region of the world”.

What effect, if anything, does this faux pas have on the tribe? Choose among these two (Do support your answer with a reason):

Effect 1. The foreigner has no effect, because his comments do not tell the tribe anything that they do not already know (everyone in the tribe can already see that there are several blue-eyed people in their tribe).

Effect 2. 100 days after the address, all the blue eyed people commit suicide .

[abhisays]

Give me some time, I will try to solve these puzzles.

By the way, good job.

[Ashutosh]

The island puzzle is insane. I'm sure that the answer will drive you nuts.

[abhisays]

Originally Posted by Ashutosh

The island puzzle is insane. I'm sure that the answer will drive you nuts.

That's why I renamed the thread to "Puzzles to puzzle you"

[Ashutosh]

A highly addictive chess puzzle:

What are the five moves in a chess game that starts with the white king's pawn moving 2 squares ahead (e2-e4) and ends with a black knight capturing a white rook leading to a check-mate?

Kasparov and Karpov couldn't solve it .

There an interesting story about this here.

I won't post more until someone cracks one of these. Remember: The fun is in trying and not reading the answers.

[abhisays]

Originally Posted by Ashutosh

Imagine you are an ant sitting on the face of a Rubik's cube made of cheese. You have been assigned the following task: Eat the whole cube by starting with any subcube on the face. Once you're done with a given subcube, you can move to another subcube which shares a face with the one you just finished. The catch is this: The subcube at the center of the Rubik's cube must be the last subcube eaten.

So the puzzle is: Can you do it?

I think the answer is NO.

Let's divide the rubik Cube (27 pieces)

• eight 3 faced pieces which are corner Pieces, I will call them '3F'
• twelve 2 faced pieces ('2F')
• Six 1 face pieces('1F')
• And there is one center piece (not visible in rubik Cube, let's call it 'OF')

It is clear that each of the Odd faced piece(3F,1F) is always adjacent to an even faced piece(2F,0F).

So if the ant starts from 3F and after completing 26 pieces, I think it should be at an even faced piece which can't be adjacent to 0F because 0F is also an even faced piece.

That's why the answer should be NO, it is not possible for eat the centre subcube.

[Ashutosh]

Awesome solution!

You explained the case when the ant starts at 3F. The other cases are also easy to eliminate as follows:

Once again note that there are 14 odd faced squares but only 12 even faced (discounting the center). Suppose you start at an odd face. Then the 25th square visited by you must be odd and you are left with 1 odd and the central square. The next square that you visit must be the center and you lose this way. If, on the other hand, you start with an even face, then the 24th square visited by you is odd and you're left with 2 odd squares and the central square. The next square that you can eat is again the central square and you lose pretty bad in this case.

A small remark: If you visualized the rubik's cube as being made of black and white squares like a checker board then your odd/even terminology corresponds to black/white squares.

[jitendragarg]

For the eye colour problem, second situation will occur, if the foreigner mentioned number of blue coloured eyed people.

Else, even if the blue eyed people can see 999 other people, they won't be able to logically decide if their eye colour is blue or not. So, every blue eyed person will see atleast 99 other blue eyed person, hence, the statement of foreigner will be valid even if the 100th person is not blue eyed. So, 100th person will never know if he is blue eyed or not. So, he should not commit suicide, unless other members of the group tell him about his eye colour.

I might be wrong here, but I guess, my logic stands valid. If not, I will wait for your solution.

[jitendragarg]

I have added tags for this thread.

Also, puzzles are really good, and not the same old crap, I am used to solve during interviews.