Grad students

The following joke/riddle is a mathematician's way of disgusting potential future mathematicians, to see what the impact will be...

N grad students were sitting in a train compartment. They were discussing deep intellectual subjects (free food, math, free food, professors, politics, and the best places for free food), all the while eyeing a platter previously full of (free) meatballs, now containing six meatballs.  Each grad student had a fork and a knife, and was very aware of the fact that taking a meatball would be impolite, however much he/she wanted to. At that moment the train went into a tunnel and everything went dark for a couple of seconds. There was a loud yelp, and the light came back, revealing a platter containing a cut-off hand with a fork stuck in it.  How many grad students were there?


The answer might be at answersdiscarded.blogspot.com. Answer number 5.

How to boil water

This is what I just did while doing a math problem:

Problem number 1.   How do you boil water given a teapot, a turned off stove, and water?
Solution: Fill the teapot with water, turn on the stove, put teapot on stove, wait to boil.

Problem number 2.  How do you boil water given a teapot full of water, a turned on stove, and water?
Solution. Empty the teapot, turn off the stove, and repeat solution to Problem 1.


I feel ridiculous. 

Knights and Knaves (starting easy)

     I think that this may be my favourite type of math/logic riddle.  In a world where there are only knights and knaves...

Knights can only tell the truth.  Knaves can only lie.

     You are on an island with two towns, walking  along a road. One town is where all the knaves live, and the other is where all the knights live. You have to post a letter to your friend, but there is only one post office, and it's in the knights' town.
     You have come to a fork: one road leads to the knaves' town and the other to the knights' town. You see a man sitting at the fork, but you do not know whether he is a knight or a knave.  On this peculiar island, you are always allowed to ask one question to another person.  You have to ask him a question which determines which town is the knights' town.  Remember: you do not know whether he is a knight or a knave.


This is one of the easier questions of this type. Again, the answer is at discardedlogic.blogspot.com, answer number 5.  PLEASE TRY TO FIND THE ANSWER before looking it up. (!)

Are the horizontal lines parallel?

I like this illusion because it actually fools me... even though I always know the answer.

 

And this one's pretty cool too, as long as you're not looking at it.

Choosing a computer

In a very peculiar shop, there are three computers, one each of three types:
-American computers, which always answer any questions truthfully,
-Chinese computers, which always lie,
-Russian computers, which sometimes lie, and sometimes tell the truth.

You want a computer that can answer yes/no questions, and you don't care if it's an American computer or a Chinese one. You do not, however want a Russian one.
The biggest problem with these computers is that they are exactly alike on the outside. The shopkeeper tells you that you are allowed to ask ONE question to ONE computer.

In this one question, you have to find out whether or not this computer is Russian.

What is the question?

To find the answer, go to discardedlogic.blogspot.com, answer number 4, where there may be the answer to the question of the question. (It depends on when you look and when I put the answer up).

How Many Legs?

Princess' Groom

      In a faraway kingdom, the beautiful princess, daughter of the mighty (and unjust) ruler, subject of the courting of many princes and even kings from even farther away kingdoms, suddenly fell in love.  This was a completely new feeling for her, and she really didn't know what to do.  After many hours of thinking and rethinking, forced to use parts of her lovely little head which were normally left idle, the poor creature decided to tell her maid, an elderly woman with much experience. She immediately told the girl to confess to the fortunate man. Little did the maid know that the subject of the princess' love was a swineherd.
      The swineherd, a very sharp young man who hoped to do great things and had already taught larger part of the royal pig population the times two table, reacted very strangely indeed.  Instead of dressing up in furs and gold, bringing gifts to the king, and sucking up to the princess (as did all of her previous suitors), he responded by kissing her. On the whole, thought the princess, happily (and muddily) returning home, it was a most productive evening.
      After about half a year's worth of such evenings, the king found out.  He immediately ordered the poor swineherd's execution and the princess' marriage to the baldest king on the planet. No pleading or tears from his daughter could change his mind. However, his chief counselor advised him that maybe it would be a good idea to appear merciful to his people. He suggested that the condemned man should be publicly given a choice of two papers which he would blindly draw from a bag, and which would determine whether he should be executed or allowed to marry the princess. To make sure that he would die, both papers would have "guilty" written on them.
      The princess, hearing only the first part of the plan, immediately ran to find her beloved in the dungeons.  He, being an optimistic young man, rejoiced and said that it was better than no chance at all.  However, the princess soon found out about the trickery. In tears, she told her swineherd all about it.  Instead of being discouraged, he told her that the fates had turned their way, and he was to be soon united with her for the rest of their lives.
      How?
      Write your answers in comments, but try not to read other people's comments before thinking yourselves.
      I have put the answer on answersdiscarded.blogspot.com. Answer #3.

Please, please, please think about it before looking at the answer.  (!)