What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

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?

I make two people out of one. What am I?

It walks on 4 when its young, walks on 2 when it's older, and walks on 3 when its very old?

You see a mathematical expression in the picture. Can you think of a movie that this expression refers to?

Can you place three balls such that the equation shown in the picture holds true?

Irene killed hundreds of people mercilessly and yet the police were not able to put her behind the bars. Why?

As shown in the image, the nine Dogs are square fenced. By constructing just two square fences can you make sure that two Dogs cannot meet each other without crossing the fence?

For an extra income, John decided to work at a Hotel for one hour daily. The manager offers him that they will pay him $11 after every 11 days.
However, John offered a different proposition to the manager. The offers stand as:
He will be paid just a penny on his first day.
Two pence will be paid on the second day,
Four pence will be paid on the third day.
And so on till the 11th day.

Should the Hotel manager accept his offer?

I came first on earth but second on the heaven.
I also came twice in a week but found just once in a year.
I stay away from months but you can find me in February.

What am I?