I am a type of room you cannot enter or leave. Raised from the ground below, I could be poisonous or a delicious treat. What am I?

What is the fastest way to double your money?

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

which number am I?

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

Can you write down eight eights so that they add up to one thousand?

On a certain day, John celebrated his birthday. Two days later, his older twin brother Jacob celebrated his birthday.

Is this even possible? How can it be?

What goes up but never comes down?

What is in seasons, seconds, centuries and minutes but not in decades, years or days?

For this puzzle, you might have to find logic in something illogical. But hey, it's fun and a healthy little break from your strenuous puzzle-solving sessions.

Can you decipher the meaning in the following cluster of letters?

ITIT,NCENTCENT

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?