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

which number am I?

100 prisoners are stuck in the prison in solitary cells. The warden of the prison got bored one day and offered them a challenge. He will put one prisoner per day, selected at random (a prisoner can be selected more than once), into a special room with a light bulb and a switch which controls the bulb. No other prisoners can see or control the light bulb. The prisoner in the special room can either turn on the bulb, turn off the bulb or do nothing. On any day, the prisoners can stop this process and say "Every prisoner has been in the special room at least once". If that happens to be true, all the prisoners will be set free. If it is false, then all the prisoners will be executed. The prisoners are given some time to discuss and figure out a solution. How do they ensure they all go free?

All of Jacob's shoes are red except two.
All of Jacob's shoes are green except two.
All of Jacob's shoes are yellow except two.

How many shoes does Jacob have?

You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

I have branches, but no fruit, trunk or leaves. What am I?

A man looks at a painting in a museum and says, “Brothers and sisters I have none, but that man’s father is my father’s son.” Who is in the painting?

Using mathematical symbols like +, -, and x in order to make the equations correct. Replace # with the above-given symbols.

9 # 8 # 7 # 6 # 5 # 4 = 91

A man is found dead in his bathroom naked with blood scattered all around him. The bathroom was locked from the inside and there is no trace of any struggle. There is nothing in the bathroom except his pant with the belt still around and his shirt. Also, the medic team can't find any incision in his body that may have been the reason behind so much blood loss.

The Police department is clueless regarding this murder mystery.
Can you?

Let's play a word game. Following are some meaningless words that can be completed by adding random letters on either side of the word.

For example, the word "rdo" can be formed into "pardon".

Using the same technique, can you complete the given words?
ecalc
airb
rinci
tibac
uidel
gorit
igna
eyho

The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member ?