What is next number in the pattern below:

131 517 192 123 ?

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

which number am I?

Can you complete the sequence puzzle?

AR TA GE CA LE VI LI _

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?

Lifeless eyes on my smiling face and watch your child's sleeping place. In their dreams they hold me tight. What am I?

What have one eye but still cannot see?

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

In a Society, there are over 100 flats.

Flat 1 is named the first flat.
Flat 2 is named the second flat.
Flat 3 is named the third flat. And So On.....

A visitor decides to walk through all the flats, and he finds all the flats except flat 62.
Anmol later founds that the locals of the town have given it another name.

What is the name of the Flat?

By including only four matchsticks in below picture, you have to make "Four Triangles And Two Squares"

Give it food and it will live; give it water and it will die.