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?
If you look at it as fractions, there is no possible way to get 12 on the denominator (bottom part of fraction) and 1, 5, 7 or 11 on the numerator (top) by adding without resorting to approaching to infinity with only 2^n values available on the denominator.
So, I believe that makes it impossible to time it EXACTLY.
Posted by Dacre
on 2003-09-22 10:09:37