Paradoxes

1. The barber of Seville shaves a man from Seville only if the latter does not shave himself. Does the barber shave himself?

2. The barber of Tilburg shaves only those who do not shave themselves and have no beards. He doesn't shave any of those who shave themselves. Nobody uses both methods. Does the barber of Tilburg have a beard?

In a library are catalogues in which books are registered. There are catalogues which catalogue catalogues. One catalogue catalogues all catalogues which do not catalogue themselves.

Is this catalogue itself in there?

A poacher who got caught was to be executed. However, he was allowed to choose the method of his execution by making a statement: if the statement were true, he would be beheaded; if the statement were false, he would meet his demise by hanging. The poacher saved his life by making a statement which was a paradox.

Can you tell what his statement was?

Eleven new recruits arrive at the army base. But there are only ten beds available. The sergeant comes up with a solution. He puts soldier 1 and 2 temporarily in the first bed. Soldier 3 in the second, soldier 4 in the third, soldier 5 in the fourth, soldier 6 in the fifth, soldier 7 in the sixth, soldier 8 in the seventh, soldier 9 in the eighth and soldier 10 in the ninth bed. Then he calls one of the soldiers from the first bed and directs him to the tenth bed. That way they can all sleep in their own beds.

Can you see what he did?

Three farmers went to town for a meal. They all chose the menu of the day, which cost ten pounds. After the meal they each paid the waitress 10 pounds. Back in the kitchen, the owner told her that the total price was only 25 pounds. Before the waitress went back to the farmers, she put 2 pounds in her own pocket. She explained that they had paid too much and refunded each farmer 1 pound. Happily, everything turned out fine, because each farmer had paid 10 minus 1, i.e. nine pounds. Three times nine plus the two pounds in the waitress's pocket makes exactly 29 pounds.

Where has the one pound gone?

The next day the same three farmers decided to sell apples. The first man decided to sell his apples at the price of three for a dollar. The second man decided to sell his apples at the price of two for a dollar. It was getting late and both men each had 30 apples left to sell (sixty total). They had prior engagements, so they asked the third man to sell the remaining apples for them. The third man didn't want to bother with two prices, so he sold the apples at the price of five for two dollars (which he reasoned was the same as three apples for one dollar plus two apples for one dollar). He sold all of the remaining apples for twenty-four dollars. The next day the first two men asked for their money. The first felt he should get ten dollars, since his thirty apples sold at three for a dollar. The second man wanted fifteen dollars, since his thirty apples sold at two for a dollar. The third man was perplexed, he only had twenty-four dollars, not twenty-five dollars ($10+$15). What happened to the other dollar?

It is not the arrow that moves, it is our mind which presumes movement. To prove this, take a bow and arrow, shoot it and try to come eye to eye with the arrow. At every point the moving arrow is where it is and where it is not. The arrow cannot be where it is not. Therefore, it must be where it is. So because it is where it is, the arrow does not appear to move.

A true revelation.

What came first: the chicken or the egg? This question still keeps people busy, even now that we know Darwin's Evolution theory. Can it be answered? Can you answer it?

1. A similar hypothetical question to "the chicken and the egg problem" is the following:
What would happen if an unstoppable force collided with an immovable object?

2. God, being omnipotent, can create what he wants.
Can he create an object that he can't move?

The clever Zeno (appr. 490-430 BC) proved that the 10 times faster Achilles could never catch up with a slower tortoise, even if it had a 10-meter head start. He argued: By the time Achilles reaches the 10-meter mark, the tortoise will be at 11 meters. By the time Achilles gets there the tortoise will be at 11.1 meters, and so on. This process of looking at where the tortoise will be when Achilles catches up to where he WAS can be repeated indefinitely, creating an infinite sequence of snapshots all showing the tortoise still ahead. Therefore, Achilles, even though he runs ten times as fast as the tortoise, will never catch up the tortoise. What do you think?