There are hundred statements.

Statement 1: At least one of these statements is false.
Statement 2: At least two of these statements are false.
Statement 3: At least three of these statements are false.
Statement 4: At least four of these statements are false.

Statement 100: At least a hundred of these statements are false.

What is the maximum number of statements that can be true?

4 criminals are caught and are to be punished. The judge allows them to be freed if they can solve a puzzle. If they do not, they will be hung. They agreed.

The 4 criminals are lined up on some steps (shown in picture). They are all facing in the same direction. A wall separates the fourth man from the other three.

So to summarise :
Man 1 can see Man 2 and Man 3.
Man 2 can see Man 3.
Man 3 can see none of the others.
Man 4 can see none of the others.

The criminals are wearing hats. They are told that there are two white hats and two black hats. The men initially don’t know what colour hat they are wearing. They are told to shout out the colour of the hat that they are wearing as soon as they know for certain what colour it is.

They are not allowed to turn round or move. They are not allowed to talk to each other. They are not allowed to take their hats off.

Who is the first person to shout out and why?

A farmer wanted to divide his 17 horses among his three sons. According to the farmer, the oldest son should get half of the horses,the middle son should get one third of the horses and the youngest son should get one ninth of the horses.

When their father died they were not able to divide the horses as the result was coming in fractions. As the sons were fighting on how to divide the horses a traveling mathematician came and heard their problem. He proposed a solution with which all the sons got their share in the property without harming any animal.

What was the advice given and how the group of horses were divided?