Suppose we have 50 light bulbs in one room of a big house and 50 switches at a switchboard close to the entrance, far away from the room and without visual contact with it. Each of the switches corresponds to one light bulb. We can only see the status (on, off) of each light bulb by walking to the room.

We want to find out which switch goes to each bulb. What is the minimum number of times we will need to walk to the bulbs room?

I don't know how to solve these types of problems but I assume it has to do with divisors and modulos of 50.

Any clues?