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?
Can't find a finite solution but it's clear that you can get 60, 30, 15, 7.5, 3.75 etc minutes and the infinite sum of every other term starting after 15+7.5 is 25. ie 15+7.5+1.875+0.46875+..., however you would not only need infinite clocks but you would have to set infinite number going at the beginning and then later set an infinite number going infinitely often!