Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

Which number should replace the question mark?

Rahul decided to meet Simran so he boards a local train from Bombay station. Just after the station, there is a 1km long tunnel. The train starts and is now accelerating. Rahul is a claustrophobic guy, so what is the best position for him to sit?

I come in different shapes and sizes.
Parts of me are curved, other parts are straight.
You can put me anywhere you like,
but there is only one right place for me.
What am I?

Most people think of me as money. But when they find me in the water, they won’t get any money out of me. What am I?

I cannot talk, but I always reply when spoken to. What am I?

I am the beginning of the end, and the end of time and space. I am essential to creation, and I surround every place. What am I?

A finger goes in me. You fiddle with me when you're bored. The best man always has me first. What am I?

Christina has four daughters, and each of her daughters has a brother. How many children does Christina have?

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?