I am soft and cuddly that soothe your heart. But, If you pick my last name I am going to tear you all apart. Who am I?

Begin with a word, five letters to my name,
Remove the first and last but I am the same
Take out my middle and still, I remain.
What word am I?

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 had an infinite supply of water and 5 litres and 3 litres jars.

How would you measure exactly 4 litres in the least number of steps?

Can you solve the tricky chess rebus puzzle below by ciphering the hidden meaning?

I am thinking of a five-digit number such that:
The first and last digits are the same, their submission is an even number and multiplication is an odd number and is equal to the fourth number. Subtract five from it and we obtain the second number. Then divide into exact halves and we get the 3rd number.

What number I am thinking of?

You have 10 balls with you. A friend of yours out of nowhere asks you to place those ten balls in five lines such that each of the lines has exactly 4 balls on them. He needs to check your intelligence. Prove him by doing the task.

As easy as you can get into me, it is as hard to get out of me.

Do you know what I am?

As we know that white starts the game of chess. Can you find the scenario shown in the picture below is possible when all the white pieces are at the original place while the black pawn is not as in the below picture?

Outside a tattoo artist's shop, there was a signboard which read 'I make tattoos on only them who do not tattoo themselves'.

Reading it what do you think, does the tattoo artist tattoo himself?