self Maths Puzzle

A light bulb is hanging in a room. Outside of the room there are three switches, of which only one is connected to the lamp. In the starting situation, all switches are 'off' and the bulb is not lit. If it is allowed to check in the room only once to see if the bulb is lit or not (this is not visible from the outside), how can you determine with which of the three switches the light bulb can be switched on?

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self Other Question

Here is a sequence of numbers: 1 11 21 1211 111221 It seems to be a strange sequence, but yet there is a system behind it... What is the next term in this sequence? You are a landscape designer and your boss asked u to design a landscape such that you should place 4 trees equidistance from each other.