PUZZLES AND PARADOXES

PUZZLES

  1. The 7 Monks
  2. How old are my children ?
  3. Kitty Race

PARADOXES

  1. The Hangman

The 7 monks

There once was a monastry with 30 monks living in it. These monks never said a word to each other. The only form of social life they had, was the daily meeting in the biggest room of the monastry. This happened every day at eight 'o clock sharp. In these meetings they sat down in a big circle, silently looking at each other. One night the king of the country decided that 7 monks had to join him in the war. (Note that only the king knows how many monks are selected. The monks themself only know that there is at least one of them selected). A knight entered the monastry at night and indicated these 7 monks by applying a black spot on their forehead. He also ordered that every monk who knew that he was elected had to leave the monastry imediately and join the king. But these monks did not have any mirrors in their monastry and they could not say to the others if they had a black spot or not, so how could they know if they were elected or not ?

Well, they have found a solution for this problem. Can you find it too ? And if so, how long will it take until the last monk with a black spot left the monastry ?

PS It's not a trick. Just logical reasoning will do. So no "they took a photograph and distributed it" and stuff like that.

SOLUTION

Even if you found the solution by yourself, take a look at this solution, because there is interesting discusion associated with it.

How old are my children ?

Two friends Jack and Daniel Meet each other in a pub. It was years ago that they had seen eachother. Jack invites Daniel to his home to talk a little bit about the old times. At home Daniel asks Jack if he has children. "Well, yes", answers Jack," I have three children." "Oh", says Daniel,"How old are they ?". Jack remembers that Daniel loves to solve puzzles so he decides to make a puzzle of it. He says that the product of their ages equals 36 and the sum of their ages equals his housenumber. Daniel goes outside the house, takes a look at the housenumber, returns back inside and says that he does not have enough information to solve this. "You are right", says Jack, I'll give you one more hint: "The eldest is with his grandmother now". Can you give the ages of the tree children and the housenumber ?

PS. It can be done. You do not need more information

SOLUTION

Kitty Race

This is one for the mathematicians among you. Their are two little kittens on each side of a soccer field. This soccer field is exactly 100 meter long en has a little red bal in the middle. The mother of these kittens sits together with one of her kittens on the left hand side of the field. Now the two kittens start to run towards the little red ball. They do this at a speed of 1 meter/s. Their mother starts to run from one kitten to the other and back at 10 times the speed of the kittens. Suppose that the mother does not need any time to turn, how far does she got to run until the two little kittens meet in the middle ?

SOLUTION

PARADOXES

The Hangman

One day Sam the serial killer was condamned to death by hanging. However, the judge wanted to make it even worse for Sam and he said:"You'll be hang in the next week, but I don't say when exactly. It will be a complete surprise to you when it happens". At that moment the lawer of Sam began to smile. "Sam", he said,"don't worry they can't do that". "Why not",Sam asked. Well, suppose that you are still living on saturday. You will agree with me that it can not be a surprise for you that you will killed on sunday. But the judge said that it was going to be a surprise, so they have to kill you before sunday. However, knowing this, if you are still alive on friday night, you know that you have to be killed at saturday, because we just said that you have to be killed before sunday. So this eleminates saturday. Therefor they have to kill you before saturday. Do I have to proceed further ? Thinking this way I can exclude every possible day, so they have to leave you alive. So Sam was very glad and went laughing to his cell.
But, justice strikes again, Sam was killed on tuesday by a complete surprise.

This paradox was invented by the swedish mathematician Lennart Ekbom after he heard the following announcement over the radio:
This week a civil security exercise will be held. To be sure that this exercise is well practiced, nobody shall know in advance the exact day of the exercise.

If you want to read more about this paradox (and a lot of others), I can advice you the following book: Labyrinths of Reason by William Poundstone, ISBN 90-254-6769-5

Enjoy ! Click here for a discusion about this paradox