Transform the word THINK into BRAIN while changing only one letter at a time in a manner that each of the word in the process is a real word!!!

What can you deduce from the following BrainBat?

CRY
LMKI

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

You have a roll of cloth 1km long. You have a machine which cuts this roll into pieces of 10-meter-long cloth.

How long would it take for the machine to cut the roll if each cut took 4 secs?

Can you find a number that lies one third of the distance between 1/3 and 2/3?

Its something that each of us devours,
Not just us but birds, beats, trees, and flowers,
Frets iron and nibbles steel,
Toil hard stones to meal,
Exterminates king, collapse town,
And blows the mountains down.

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

In the picture that is attached with this question, you can find a square which comprises of four little squares inside it. Consider this square to be made with matchsticks. You have to remove two matchsticks such that only two squares remain instead of five.How will you do it ?

Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?

In two decks of cards, what is the least amount of cards you must take to be *guaranteed* at least one four-of-a-kind?