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

Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?

Look at the picture and find out which square is not linked with any of the other squares.

Replace each alphabet with the number (1-9) to make the below equation correct.

AB * C = DE - F = GH / I

What's the only room from which no one can enter or leave

A man and a dog were going down the street. The man rode, yet walked. What was the dog’s name?

The warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another.

"In the prison is a switch room, which contains two light switches labeled 1 and 2, each of which can be in either up or the down position. I am not telling you their present positions. The switches are not connected to anything.

"After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must flip one switch when he visits the switch room, and may only flip one of the switches. Then he'll be led back to his cell.

"No one else will be allowed to alter the switches until I lead the next prisoner into the switch room. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back. I will not touch the switches, if I wanted you dead you would already be dead.

"Given enough time, everyone will eventually visit the switch room the same number of times as everyone else. At any time, anyone may declare to me, 'We have all visited the switch room.'

"If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will all die horribly. You will be carefully monitored, and any attempt to break any of these rules will result in instant death to all of you"

What is the strategy they come up with so that they can be free?

Find three numbers such that

* When we multiply three numbers, we will get the prime numbers.
* The difference between the second and the first number is equal to the third and second.

Rearrange the letters in "new door" to make one word.

Eight of us go fourth, not back, to protect our king from an attack. What are we?