A Doctor always sneezes before the rain. Doctor sneezes, Will it rain?

Open a Laptop which is password protected. Hint for the password is given as below:

1 mobile 3 books 2 Boards 1 night 4 balls 2 lighters 1 ghost 1 hat 3 watches

Find The Next Number in this series.
1, 2, 6, 42, 1806 ?

There are hundred red gems and hundred blue gems. The blue gems are priceless while the red gems equal wastage. You have two sacks one labeled Heads and the other Tails. You have to distribute the gems as you want in the two sacks. Then a coin will be flipped and you will be asked to pick up a gem randomly from the corresponding sacks.

How will you distribute the gems between the sacks so that the odds of picking a Blue gem are maximum?

Replace the question mark with the number below given a simple math problem.

John Went to the nearby store in a Mall to buy something for her home. Below is the conversation between the two:

John: How much for the one?
Shopkeeper: It is $2
John: How much for the Eleven?
Shopkeeper: It is $4
John: How much for the Hundred?
Shopkeeper: It is $6.

What is John buying?

You are driving down the road in your car on a wild, stormy night, when you pass by a bus stop and you see three people waiting for the bus

An old lady looks as if she is about to die.
An old friend who once saved your life.
The perfect partner you have been dreaming about.
Knowing that there can only be one passenger in your car, whom would you choose?

Replace the question mark with the correct number.

2 + 2= 4
3 + 3= 18
4 + 4= 48
5 + 5= ?

Detective John was investigating a murder in China.
It was a difficult case, and John was completely stumped until he noticed a message sent to him by the killer cunningly hidden in a newspaper advertisement selling Car Licence Plates.
Detective John thought about it for a while, and when he had solved the puzzle, immediately arrested the guilty man.

Q1) How did John know the advert was a clue for him?

Q2) Solve the code and tell me who John arrested.

This is the newspaper advert (Car licence plates for sale) that Detective John saw.

Plates For Sale;

[W 05 NWO]
[H 13 HSR]
[O 05 EBM]
[D 08 UNE]
[U 10 HTY]
[N 04 BRE]
[N 16 TTE]
[I 26 LHC]
[T 10 AEE]
[I 26 CNA]
[X 22 VDA]

What are the 50th, 63rd and 100th numbers in the sequence below?
4, 5, 8, 8, 9, 9, 12, 13, 13, 13, 17, 18, ...