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?
Rats, got to run, so don't have time to work out a full solution. Obviously the trick is to start by having two timers starting together, one ot normal speed and one at double speed. Then you can start third timer after half an hour, and set it to go fast after another half hour. Otherwise you are always stuck with increments of half an hour.
The third timer will go off 15 minutes after the first. If a fourth timer was started when the second one was, and set to fast when the third one goes off, it will go off 7.5 minutes after the third, and 22.5 minutes after the first.
That's all I've got for now, I expect this will all be solved next time I look.
Posted by Sam
on 2003-09-10 10:22:21