You have an infinite amount of timers, each is an hour long (they do not have dials on telling you how long they've been going - they just beep when the time is up). You can set it to double speed at any time, but you cannot set it back to normal speed (eg if you set it to double speed at the start it will last 30 minutes.
Using each timer only once, is it possible to time exactly 25 minutes?
If it is, what is the smallest number of timers you need to do this, and the quickest time you can acheive it?
(In reply to Answer
I'm confused. If I understand you correctly, the times you get will converge to 20 minutes, not 25. Also, the error only goes down by half each time, so even after N clocks (N = any finite number) there will still be some error (5/2^N minutes, +/- 1 on the N here, I'd have to check)
In any case, you get neither 25 minutes, nor an EXACT measure of 20 minutes.
Or did I completely misunderstand what you are saying?