In which direction should the missing arrow point?

A rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different. How do you measure 45 minutes?

With pointed fangs I sit and wait; with piercing force I crunch out fate; grabbing victims, proclaiming might; physically joining with a single bite. What am I?

John can fit six large chocolate boxes or nine small chocolate boxes into a carton. How many cartons will he require to put sixty-six chocolate boxes into?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

One night, a woman receives a call from the police. They tell her that her husband was murdered and that she should come to the crime scene as soon as possible. The woman drops the phone, shocked, and drives 20 minutes to the crime scene. As soon as she reaches the crime scene, the police arrest her and she is convicted of murder. How do the police know she committed the crime?

A man embarked on a questionnaire game. He kept asking the same question to whomever he found. The answer each time was different.

Can you guess what the question was?

The chance of Mr John winning the lottery is 10%. All participants lined up and Mr John is 4th in the row. The first three participants lose the lottery.

What is the chance of Mr John now?

For an extra income, John decided to work at a Hotel for one hour daily. The manager offers him that they will pay him $11 after every 11 days.
However, John offered a different proposition to the manager. The offers stand as:
He will be paid just a penny on his first day.
Two pence will be paid on the second day,
Four pence will be paid on the third day.
And so on till the 11th day.

Should the Hotel manager accept his offer?