What occurs twice in a week, once in a year but never in a day?

Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?

One is to three as three is to five and five is to four and four is the magic number.
What is the pattern?

What does this Rebus Picture mean?

I got a bee but no honey.
got an eye but am still blind.
got a sea but no water.
got a tea but no coffee.
got a why but no answer.

What Am I?

There is a square piece of paper with a hole that is denoted by the circle on the top right side in the given picture. You have to cut the paper in a manner that it forms two and only two separate pieces of paper and then rearrange the pieces in a manner that the holes come in the centre of the paper.

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

What number comes next in the series?

5 15 5 18 5 24 14 20 _

A man was found murdered on Sunday morning. His wife immediately called the police. The police questioned the wife and staff and got these alibis: The Wife said she was sleeping. The Cook was cooking breakfast. The Gardener was picking vegetables. The Maid was getting the mail. The Butler was cleaning the closet. The police instantly arrested the murderer. Who did it and how did they know?

Imagine a box with two cogwheels, one big with 24 teeth and one small with 8 teeth. The big one is firmly attached to the center of the box which means it does not turn or move while the small one rotates around the big one.

How many times do you think that the smaller wheel will turn compared to the box when it turns once around the big one?