We have specified number of light bulbs. In addition to the array there are buttons. Pressing the button changing state of light bulbs which are connected to the switch. It is known that for each set of lamps exist button that is connected with the odd-number of bulbs from this set. Prove that properly pressing the buttons we can turn off all bulbs.
Very nice task, but hard. I think that I can make a $Z^n$ space of bulbs, but how to prove that we have a basis of it? Or that's not a correct way?
I'm looking for hints.