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

After teaching his class all about Roman numerals (X = 10, IX=9 and so on) the teacher asked his class to draw a single continuous line and turn IX into 6. The teacher's only stipulation was that the pen could not be lifted from the paper until the line was complete.

I have a clock(12-hour format) and both the needles of the clock overlap at 12:00.
After how much time, they will overlap again?

Can you replace the X (both small and big x) with the numbers between 1 to 19 such that all the rows of 3 numbers between X (big x) sum to 23?

Through your logical capabilities, can you make 7 an even?

They came out at night, without being called.
They lost at day, without being stolen.
Who are they?

A man plots the murder of his wife. His plan is full proof. Nobody saw them leaving their house. He stabbed her with a knife while driving. She died on the spot. He threw her body in a valley. He threw the knife carefully wiping his finger prints on a random garbage bin. Then he went back to his home and no one was watching him this time as well.

After an hour, he was called by the local police department who informed him that his wife was murdered. They asked him to reach the scene of crime immediately. But as soon as he arrived at the crime scene, he was arrested by them.

How did the police know that he himself is the murderer?

An explorer goes on an exposition in the jungle. He sets up camp in the middle of the jungle. The next morning he sees something with a head and a tail, but he is not afraid. What did he see in his bag?

Imagine a box with two cogwheels, one big with 24 teeth and one small with 8 teeth. The big one is firmly attached to the center of the box which means it does not turn or move while the small one rotates around the big one.

How many times do you think that the smaller wheel will turn compared to the box when it turns once around the big one?

I am a normal creature, but I have five hands. I can even have more but even then I will be considered normal.

Who am I?