I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

What seven-letter word has hundreds of letters in it?

Spot 5 differences in two Christmas tree below:

The doctor prescribed you to take one pill from the bottle every half an hour. The bottle is now left with only three pills.

How long do you think you have before you run out of pills?

You have three orange, two pink and five purple balls in the drawer beside your bed. There is no electricity and the room is entirely dark. How many balls must you take out to ensure at least one ball of each colour at least?

There are six people in a family namely M, N, O, P, Q and R.

R and O are brother and sister.

N is the brother of Q's husband.
P is the father of M and grandfather of R.

How many male members are in the family?

A woman lives in a Tall building thirty-six floors high and served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?

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