Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.

If "P" means "-", "Q" means "/", "R" means "+", and "S" means "*" then find the value of the following:

21 Q 7 R 9 S 10 P 13

You have to put a letter on the following to make it a meaningful word. The only challenge is that you can't use 'E'.

S E Q U E N C _

A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?

Three men in a cafe order a meal the total cost of which is $15. They each contribute $5. The waiter takes the money to the chef who recognises the three as friends and asks the waiter to return $5 to the men.

The waiter is not only poor at mathematics but dishonest and instead of going to the trouble of splitting the $5 between the three he simply gives them $1 each and pockets the remaining $2 for himself.

Now, each of the men effectively paid $4, the total paid is therefore $12. Add the $2 in the waiters pocket and this comes to $14. Where has the other $1 gone from the original $15?

A prisoner is told: "If you tell a lie, we will hang you and if you tell the truth, we will shoot you." What did the prisoner say to save himself?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

Solve The below Equation:

ALFA + BETA + GAMA = DELTA

A man stands on one side of a river, his dog on the other. The man calls his dog, who immediately crosses the river without getting wet and without using a bridge or a boat. How did the dog do it?

I am a mother. However, I never give birth.

I am a father. However, I never nurse my children.

Wandering is not possible for me, but standing still happens occurs rarely.

Who am I?