Which is the rope you never skip with?

I know a 5-digit number having a property that With a 1 after it, it is three times as large as it would be with a one before it.

Guess the number?

If,

A = 1

B = 2

C = 3

...

...

Z = 26.

Based on above rule, you need to find an eleven letter word whose letter sum is equal to 52.

A man who was outside in the rain without an umbrella or hat didn’t get a single hair on his head wet. Why?

Can you solve below mathematical equation?

2^1234 - 2^1233

Replace the question mark with the correct number below.

Your last good ping-pong ball fell into a narrow metal pipe embedded one foot deep in concrete.
How can you get it out undamaged, if all the tools you have are your tennis paddle, shoe laces, and plastic water bottle, which does not fit into the pipe?

Can you fill the blank with the correct number?

6 30 870 756030 _____

There is an English word that can be used up to four times in a row without modifying the spelling and form a valid grammatical sentence.

Do you know what word is that?

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?