Can you find out which number multiplied by itself will give the output as 12345678987654321?

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

In an office's desk, you find a unique method that shows the current day of the month. Two numbered cubes are used to depict the current date.

Can you find out the numbers on both the cubes so that each date can be mentioned using them?

Please note that you have to use both the cubes to display any date. Thus the 1st day must be represented by 01 and so on.

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?

I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?

A man is found unconscious in front of a store at two in the morning. His head is bleeding and there’s a brick laying next to him. When the police arrive, they carry the man to jail. Why did they arrest him?

It's pretty hard to give up.
If you remove a part of it, you will be left with a bit.
Even if you remove another part, the bit still remains.
Remove one more and it still remains.

What is it?

What number divided by 4 is the same as that number minus 4?

Which statement is true out of the following?
One statement here is false.
Two statements here are false.
Three statements here are false.

Decode below three cipher riddles:

26 L of the A
7 D of the W
1000 Y in a M