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.

That attorney is my brother, testified the accountant.

But the attorney testified he didn't have a brother.

Who is lying?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

Why did Buffon take the goal with him after every Juventus match?

What English word has three consecutive double letters?

Can you place three balls such that the equation shown in the picture holds true?

What has one letter and starts with an E?

In a guessing game, five friends had to guess the exact numbers of apples in a covered basket.
Friends guessed 22, 24, 29, 33, and 38, but none of the guesses was correct. The guesses were off by 1, 8, 6, 3, and 8 (in random order).

Can you determine the number of apples in a basket from this information?

Only one color, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?

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