Use the geometry of the cylinder. Start tilting the glass until the water surface gets either to the top or the bottom edge. If the glass is exactly half full, then the surface should touch both edges simultaneously.

The solution is shown below.

Cross out every other letter starting with the first one – N I N E L E T T E R S.
The remaining letters are – A S I N G L E W O R D.

2. People are sowing the crops, so it is early spring.
8. Since it is spring, birds are flying North.
1. Since birds are flying North, the shadows are pointing East, and therefore it is morning.
4. Judging by the water around the buoy, the river is flowing South.
3. Since there is a buoy, the river must be navigable.
5. The fishing line is long, so the river must be deep.
6. There would not be a ferry if there was a bridge nearby.
7. The guy on the left looks like a railroad worker, so probably the railroad is nearby.

No, it is impossible. Imagine you are placing the tetrominoes on a 7×28 chess board. All of them, except for the T-shaped ones cover exactly 2 black and 2 white cells. Each of the T-shaped tetrominos covers either 2 more black cells than white cells or 2 more white cells than black cells. Since there are 7 of them, combined they will cover either more black cells than white cells or more white cells than black cells. Therefore all pieces on the picture can not cover perfectly a rectangle, which contains an equal number of black and white cells.

The man travels one day, leaves one portion of bananas in the desert and returns back to his village. Then he leaves again with 3 new portions of bananas, picks the portion left in the desert on his way and ends up in the neighboring village on the sixth day.

This is the sequence 1, 2, 3, 4, 5… with all numbers stuck to their mirrored images.

The prisoner who gets a steak the first night should always vote 2, whereas the other two prisoners should vote 2 until the night they get a steak, and 1 every night after.

If there is any row or column in the grid with a negative sum, multiply it by -1. Since on every step the total sum of the numbers in the grid increases, we will be able to do this procedure only finitely many times. In the end, all row sums and column sums will be non-negative.

Because it is impossible for the covers to drop inside the holes, no matter how you position them on top. Also, when they have a circular shape, they are easier to roll.