There are two cogwheels in a box. The bigger one has 24 teeth and it is tightly attached to the center of the box (it doesn’t turn or move). The smaller one has 8 teeth and it rotates around the bigger wheel. How many times does the smaller wheel turn compared with the box when it turns once around the bigger wheel?

You are sentenced at court.

Judge is a fair guy so he offers you following:

“You can say one sentence to defend yourself. If you lie we will hang you. If you tell us the truth we will shoot you.”

What will you say?

A river. Three cannibals and three missionaries are standing on one bank. There is a boat with maximum capacity of two people. How do they get to the other side so that missionaries are never outnumbered by cannibals on any bank?

Can you cut and reassemble a square so that you create a red cross of the same volume?

You are standing next to three switches. You know these switches belong to three bulbs in a room behind a closed door – the door is tight closed, and heavy which means that it’s absolutely impossible to see if any bulb is on or not. All three switches are now in position off.

You can do whatever you want with the switches and when you are finished you open the door and go into the room. While in there you have to tell which switch belongs to which bulb.

How will you do that?