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?
It is impossible. 25 min = 60*(5/12), and all possible fractions that result in the manipulation of the timers are of the form 60*(x/2^k) – where both x and k are positive integers – thus any addition of the fractions will always give a denominator that is a power of 2, thereby eliminating the possibility of having a 5/12 fraction of an hour.

Posted by Eric
on 20031107 17:57:49 