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.

Man in the Elevator

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.

$5 Bill

Bern tells Sandy, “This isn’t the $20 bill you left on the table. It is mine – I was keeping it between pages 15 and 16 of my textbook.”
Sandy retorts, “You are lying and I can prove it.” How does she know?

Pages 15 and 16 are on the same sheet of paper in the textbook (just like pages 1 and 2 are) and therefore the bill couldn’t be between them.

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.

Heads Up, Heads Down

You are blindfolded and on the table, in front of you, 50 coins are placed. You are told that X of them are heads up and the rest are heads down. Then you are asked to separate the coins into two groups and optionally flip some of them so that the number of heads in both groups becomes the same. How can you do this?

Separate the coins in one group of X coins and in another group of 50-X coins, then flip every coin in the first group. If in the first group there were Y heads up initially, then after flipping there will be X-Y – exactly the number of heads up in the second group.