Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

There are three light switches outside a room. One of the switches is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.

You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)

Your task is to then determine which switch controls the bulb?

You have a thousand Re. 1 coins with you. You have ten bags with you and you can put any number of coins in each of the bags. The condition is that if someone asks you for any amount between 1 and 1000, you must be able to give that amount by just giving the bag (you are not allowed to open the bag and give coins).

How will you do it?

Two fathers and two sons went fishing one day. They were there the whole day and only caught 3 fish. One father said, that is enough for all of us, we will have one each. How can this be possible?

Create a number using only the digits 4,4,3,3,2,2,1 and 1. So i can only be eight digits. You have to make sure the ones are separated by one digit, the twos are separated by two digits the threes are separated with three digits and the fours are separated by four digits

A boy and his father are caught in a traffic accident, and the father dies. Immediately the boy is rushed to a hospital, suffering from injuries. But the attending surgeon at the hospital, upon seeing the boy, says 'I cannot operate. This boy is my son.' How is this situation explained?

Why do people go to bed?

A gardener planted the Lemon trees in a mathematical ordered way (i.e. he planted a tree in rows).
He created a total of 19 rows of trees.

Note: There should be more than 2 trees to count as a row.

What is the minimum number of trees required by the gardener to have 19 rows of trees?

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?

You can hear me, but you can't touch or see me.

What am I?