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
To infinity and beyond! by Mark Rees)
The solution effectively 15+7.5+ (from n=2 to )(30/(2^(2n))), which comes out to 25. So you start a timer (doubled twice) for 15 min. When it finishes you do one doubled 3 times (7.5 min.) When that finishes, you run a timer doubled 5 times (1.875 min.) When that finishes you do a timer doubled 7 times, and so on. This will come out to 25.
I still think there might be a finite way to do this, though.

Posted by Oren
on 20040423 15:07:39 