When you call my name, I will be gone.

What is my name?

A peasant is convicted in China. He gets the death penalty. The judge allows him to say a last sentence in order to determine the way the penalty will be carried out. If the peasant lies, he will be hanged, if he speaks the truth he will be beheaded. The peasant speaks a last sentence and to everybody surprise some minutes later he is set free because the judge cannot determine his penalty.

What did the peasant said?

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?