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

The host of a game show, offers the guest a choice of three doors. Behind one is a expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

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?

You are given four tennis balls and asked to arrange those balls in a manner that the distance between each one of them is exactly equal. How will you do it?

Count the number of lines in the image below ?

It can be easily calculated that the digits 0 to 9 can be arranged into 3628800 distinct ten-digit numbers.

But do you know how many of these numbers are prime?

Can you decipher the following common phrase?

T M C
A U O
H S M
W T E

It's a protector.
It sits on a bridge.
One individual can see directly through it, while others wonder what it hides.

What is it?

Can you find the ages of a son, father and grandfather based on the following facts?
The sum of the ages of grandfather, father and son is 140 years.
The age of the son in months is the same as the grandfather in years.
The age of the son in days is the same as the father in weeks.

As shown in the picture below, we can see a boy hanging on the tree branch to save his life. There are various ways in which he can die like1. A snake hanging toward the right waiting to bite the boy.2. A roaring Lion near the tree.3. Two crocodiles are ready to attack if the boy reaches near water. The tree is chopped to some extent, so can fall as if he moves a lot. Can you give this boy an escape plan?