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?

I can see only ways of producing powers of 2 fractions of an hour. That would mean being able to produce time intervals that are expressed as a terminating binary fraction. However, 25/60 is a non-terminating binary fraction: 0.0110101010101.... This represents
1/4+1/8+1/32+1/128+1/512+1/2048+...

It would seem, depending on how close to 25 minutes you want, there would be ever more complex timings that could be done, but none would give exactly 25 minutes.

Posted by Charlie on 2003-09-10 11:26:48