What has hands, but can’t clap?

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

Can you solve below mathematical equation?

2^1234 - 2^1233

Here is a Swiss Cross. You have to make two straight cuts in the figure so that it is divided into four congruent pieces. Also, you should be able to join these pieces into a square then. Can you accept this challenge?

What can run but never walks, has a mouth but never talks, has a head but never weeps, has a bed but never sleeps?

2 ladies and 2 girls need to cross a river in a boat big enough for 1 LADY or 2 girls. How do they do it?

What can you serve, but never eat?

Why is the longest human nose just 11 inches?

I am green and found in the forest and have needles instead of leaves. What am I?
Hint 1: It can be used for Christmas decorations.
Hint 2: I have a strong, scent that is used in air fresheners.

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)