Can you find a pattern and the missing number in the series given below?

100, 155, 258,? , 584, 819.

If I remove one from eleven it becomes Ten and if I remove one from nine also becomes Ten. How?

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?

John: "Hi Teacher, What is your favourite movie ?".
Chemistry Teacher: "Indium Cerium Platinum Iodine Oxygen Nitrogen".
Ten seconds later... John replied I got it.

Do you?

4 fathers, 2 grand-fathers and 4 sons went to watch the movie.What is the minimum number of tickets they need to buy ?

What word begins and ends with an E, but has only one letter?

You find yourself in a strange place guarded by two guards.One of the guard always say truth while other always lies.You don't know the identity of the two.You can ask only one question to go out from there. What should you ask?

Check out the number list below and find what number comes next in the sequence.

111 , 113 , 117 , 119 , 123 , 137 , ?

Andrew sees a very rare bird named "Ruppell's vulture". Soon Andrew was dead. Can you explain the mystery, Mr. Sherlock?

John gave half of the apples he had plus one more to Jacob. He gave half of the remaining ones plus one more to James. Now, John was left with just one apple.

Can you find out how many did he have in the beginning?