## Does Not Divide Another

How many numbers between 1 and 100 can you pick at most, so that none of them divides another?

You can choose at most 50 numbers: 51, 52, 53, …, 100.

In order to see that you cannot choose more than 50, express each number in the form 2ⁿ×m, where m is an odd number. Since no 2 numbers can have the same m in their expressions, and there are only 50 odd numbers between 1 and 100, the statement of the problem follows.

## Big on Saturday

I am big on Saturday and Sunday.
I am small on Tuesday, Wednesday, and Thursday.
I am not on Monday and Friday.
What am I?

The answer is the letter S.

## Surrounded by Rooks

White to play and mate Black in 20 moves.

The moves are as follows:

1. Qb7+ Rc5c6
2. Qa5+ Rc4c5
3. Qb3+ Rd4c4
4. Qd2+ Re4d4
5. Qf3+ Re5e4
6. Qg5+ e5
7. Qf7+ Rd6e6
8. Qd8+ Rc6d6
9. Qb7+ Rc5c6
10. Qa5+ Rc4c5
11. Qb3+ Rd4c4
12. Qd2+ Re4d4
13. Qf3+ e4
14. Qg5+ Re6e5
15. Qf7+ Rd6e6
16. Qd8+ Rc6d6
17. Qb7+ Rc5c6
18. Qa5+ Rc4c5
19. Qb3+ Rd4c4
20. Qd2x

## Murdered Wife

One night, a man received a call from the Police. The Police told the man that his wife was murdered, and that he should get to the crime scene as soon as possible. The man immediately hung up the phone and drove his car for 20 minutes. As soon as he got to the crime scene, the Police arrested him, and he got convicted for murder.

How did the Police know that the man committed the crime?

The police did not tell the man where the crime scene was.

## What Does the Liаr Do

What does the liar do when he dies?

He lies still.