Escaping the Tower

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 around it, and two identical baskets fastened at the ends of the rope. The queens weigh 195lbs, the daughter weighs 105lbs, and the son weighs 90lbs. If any of them gets in a basket and weighs 15lbs more than the contents in the other basket, he/she will fall too fast and will die upon impact with the ground. How can the three escape the tower, using the two baskets and one 75lbs stone they have in their room?

1. The stone is sent down in a basket.
2. The son goes down, the stone goes up.
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 son goes down, the stone goes up.
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.

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Domino and Chess

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.

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Population

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.

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Sequence 1, 11, 21, 1112

What follows next in the following sequence:

1, 11, 21, 1112, 3112, 211213, 312213, ?

Every term in the sequence describes how many 1s, 2s, 3s, etc. were there in the previous term. “11” means that in the previous term there was one 1. “21” means that in the previous term there were two 1s. “1112” means that in the previous term there were one 1 and one 2. “3112” means that in the previous term there were three 1s and one 2. “211213” means that in the previous term there were two 1s, one 2 and one 3. “312213” means that in the previous term there were three 1s, two 2s and one 3. Therefore, the next number in the sequence should be 212223.

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The Monty Hall Show

You are in Monty Hall’s TV show where in the final round the host gives you the option to open one of three boxes and to receive the reward inside. Two of the boxes contain just a penny, while the third box contains $1.000.000. In order to make the game more exciting, after you pick your choice, the rules require the host to open one of the two remaining boxes, such that it contains a penny inside. After that he asks you whether you want to keep your chosen box or to switch it with the third remaining one. What should you do?

This is the so called “Monty Hall” problem. The answer is that in order to maximize your chances of winning $1.000.000, you should switch your box. The reason is that if initially you picked a box with a penny, then after switching you will get a box with $1.000.000. If initially you picked a box with $1.000.000, then after switching you will get a box with a penny. Since in the beginning the chance to get a penny is 2/3, then after switching your chance to get $1.000.000 is also 2/3. If you stay with your current box, then your chance to get $1.000.000 will be just 1/3.

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Optical Illusions

If you count carefully the number of people before the tiles scramble and after that, you will see that one person disappears. Can you explain how this is possible?

Similarly, in this picture it looks like after changing the places of the tiles in the diagram, their total area decreases by one. Can you explain this?

If you look carefully, you will notice that every person in the picture of 12 people is slightly taller than the corresponding person in the picture of 13 people. Basically, we can cut little pieces from 12 different people without making noticeable changes and arrange them into a new person.

For the second question, none of the shapes before and after the scrambling is really a triangle. One of them is a bit curved in at the hypotenuse and the other one is a bit curved out. This is barely noticeable, because the red and the blue triangle have very similar proportions of their sides – 5/2 ~ 7/3.

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3 Men, 1 Woman

Warning: this puzzle involves mature themes that are inappropriate for younger audiences. If you are not an adult, please skip this puzzle.

3 men must have sex with 1 woman, but they have only 2 condoms. Each of the 4 people has some unique STD which they don’t want to transfer to the rest. What can they do?

They can start by putting the two condoms on top of each other and letting the first man use them. After that, the second man can take the inner condom out and use just the outer condom. Finally, the third man can take the removed inner condom, turn it inside out, and place it back inside the outer condom. Then he, he can use the two condoms simultaneously.

Water with Ice

You have a glass of water and an ice cube floating in it. When the ice cube melts, will the water level increase, decrease or remain the same?

It will remain the same. The amount of water that the ice cube displaces is equal to its mass. Since the mass does not change and the density of water is equal to 1, the extra water after melting will be the same amount as the displaced water before that.