Correct the equation above by inserting one straight line.

A very big building in which thousand monkeys are living is lighted by thousand lamps. Every lamp is connected to a unique on/off switch, which are numbered from 1 to 1000. At some moment, all lamps are switched off. But because it is becoming darker, the monkeys would like to switch on the lights. They will do this in the following way.

Monkey 1 presses all switches that are a multiple of 1.
Monkey 2 presses all switches that are a multiple of 2.
Monkey 3 presses all switches that are a multiple of 3.
Monkey 4 presses all switches that are a multiple of 4.
Etc., etc.

How many lamps are switched on after monkey 1000 pressed his switches? And which lamps are switched on?

In a group of 200 people, everybody has a non burning candle. On person has a match at lights at some moment his candle. With this candle he walks to somebody else and lights a new candle. Then everybody with a burning candle will look for somebody without a burning candle, and if found they will light it. This will continue until all candles are lit. Suppose that from the moment a candle is lit it takes exactly 30 seconds to find a person with a non burning candle and light that candle. From the moment the first candle is lit, how long does it take before all candles are lit?