We have a lamp and a chronometer. The lamp is initially turned off. Then, we start running the chronometer. When it marks 30 seconds, we turn on the lamp. When the chronometer marks 45 seconds, we turn it off. When it marks 52.5, we turn it on. I think you see where am I going. The next interval of time is half of the previous one. The question is: After a minute, how will be the lamp (turned on or turned off)? Does the result depend on the initial state of the lamp? Thanks.