Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

Detective Rockford was jogging near the beach at 4:30 am.
He hears a sound near the shack "No Michael, Please Do not shoot me".
Next instance he heard the sound of gunfire. Rockford rushes to the shack where he finds women lying dead and a gun in close proximity of three "Doctore Lawyer and a Teacher".

Rockford immediately knew that the Lawyer has committed the crime. How?

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

I shave every day, but my beard stays the same. What am I?

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

I have lakes with no water, mountains with no stone and cities with no buildings. What am I?

Can you find a number that lies one third of the distance between 1/3 and 2/3?

Below, you can see some coding:
January = 1017
February = 628
March = 1335
April = 145
May = 1353
June = 1064
July = 1074
August = 186

Now deciphering the way it has been coded, can you find out how September will be coded?

Can you name some countries which do not have the alphabet 'A' in them?

I am beautiful, up in the sky. I am magical, yet I cannot fly. To people I bring luck, and to some people, riches. The boy at my end does whatever he wishes. What am I?