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

As easy as you can get into me, it is as hard to get out of me.

Do you know what I am?

In this image, you can see three almost identical Doraemon images. Can you spot the odd one out from them?

Spelt forwards I’m what you do every day, spelled backwards I’m something you hate. What am I?

Find the next number in the series?
2, 12, 36, 80, 150, 252, 392, _ ?

In the image below, you can see two glasses and two matchsticks.You need to move four matchsticks in such a manner that the crosses come inside the glasses. Note: you cannot move the crossed.

The more of this there is, the less you see. What is it?

John is found dead in a bare field. Nobody killed John,
John did not commit suicide.

Inspector Jacob found a bag just a few meters away from John which could save his life. What was in the bag?

By using all numbers, i.e. 123456789 and subtraction/addition, operators number 100 can be formed in many ways.
Example: 98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100

But if we add a condition use of the number 32 is a must. Then there are limited solutions.
One of such solution is: 9 - 8 + 76 + 54 - 32 + 1 = 100

Can you tell me any other solution?

The square root of number 121 is "11". What is the square root of the number "12345678987654321."?