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If you have two spheres, you can always make a loop with some wire, such that it fits both of them (for example you can shape it as a circle). If you have any two potatoes, can you do the same?
Yes, you can. Just take the two potato surfaces and intersect them. Their intersection will give you the shape of a wire which fits them both.
One man who lives on the 12th floor every day takes the elevator to go to work. When he comes back in the evening, unless it is raining or there are other people in the elevator, he goes with it just to the 8th floor and then uses the stairs for the last 4 floors. Why does he do this?
The man is very short. Unless he has an umbrella or can ask other people to press the button for him, he can’t make the elevator go to the 12th floor.
A Queen is captured in the top room of a very high tower, along with her son and daughter. Outside their window, there is a pulley with a rope
1. The stone is sent down in a basket.
2. The
3. The daughter goes down, the son goes up.
4. The stone is thrown back down.
5. The queen goes down, the daughter and the stone go up.
6. The stone goes down.
7. The
8. The daughter goes down, the son goes up.
9. The stone is thrown back down.
10. The son goes down, the stone goes up.
Can you cover the chess board with 31 domino pieces, such that only two opposite corners are left uncovered?
The answer is NO. Every domino piece covers exactly one black and one white square on the chess board. Since initially you start with a different number of available white and black squares on the chess board, it is impossible to cover it with domino pieces.
Can you arrange 6 new identical pencils in space such that every two of them touch each other? What if you have 7 pencils?
Remark: The construction doesn’t need to be stable.
Below you can see solutions for 6 and 7 pencils. The construction with 6 pencils is stable, the construction with 7 pencils – not.
Move only 2 matchsticks, so that the fly will escape from the trap. The shape of the trap must remain the same.
The solution is shown below.
You have unlimited number of knights, bishops, rooks and kings. What is the biggest number of pieces (any combination) you can place on a chessboard, so that no piece is attacked by another one?
If we put 32 knights on all black squares, then no two pieces will attack each other. Now let’s see that if we have more than 32 pieces, then there will be two which attack each other. Split the chessboard in 8 rectangular sectors of size 2×4. It is not hard to see that if we have more than 4 pieces in the same 2×4 sector, then 2 of them will attack each other. Therefore we can place at most 4 × 8 = 32 pieces on the chessboard.
In certain society all parents stop having children right after they get their first boy. After 1000 years, approximately what will be the percentage of the women in the society?
The answer is 50%. The reason is that no matter what birth plan the society comes up with, the chance for having a boy or a girl during every birth is 50/50.
In what countries a man can not marry his widow’s sister?
In no country, a man can marry his widow’s sister, because he would be dead.
A man stands in the center of a circular field which is encompassed by a narrow ring of water. In the water there is a shark which is swimming four times as fast as the man is running. Can the man escape the field and get past the water to safety?
Yes, he can. Let the radius of the field is R and its center I. First the man should start running along a circle with center I and radius slightly less than R/4. His angular speed will be larger than the angular speed of the shark, so he can keep running until gets opposite to it with respect to I. Then, the man should dash away (in a straight line) towards the water. Since he will need to cover approximately 3R/4 distance and the shark will have to cover approximately 3.14R distance, the man will have enough time to escape.
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