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?
Given we need infinitely many clocks, the question is how do we use them. Getting 1/4 hour + 1/8 hour is the easy start, with three timers started simultaneously with the first one on immediate double speed, doubling the second timer when the first expires, and doubling the third when the second expires. Starting the timed interval at the halfhour mark, when the first timer expires, gives us the 1/4 + 1/8 when the third timer expires.
The problem is that an interval of 1/32, rather than 1/16, must begin immediately after the 1/4+1/8. Can anyone see how?
Edited on September 10, 2003, 2:15 pm

Posted by Charlie
on 20030910 14:15:01 