Bob and John form a team together. Bob is as old as John will be when Bob is twice as old as John was when Bob was half as old as the sum of their current ages. John is as old as Bob was when John was half as old as he will become over ten years.

How old are Bob and John?

A - B = B

B * C = A

D : B = E

C * C = E

C + E = A

For which numbers stand A, B, C, D and E?

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?