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?
(In reply to re: thoughts
by Brian Wainscott)
Indeed, I was confused when I was trying it earlier in a hurry the way that I kept on just stepping over 25, getting closer but never quite hitting it. Indeed, I still can't see the exact algorithm to use, but intuitivley I'm sure you're right, the time we will be measuring will tend towards 25 minutes, never hitting it with a finite number of clocks.
However, I'm almost certain that it can be done in a finite amount of time, because most of the clocks will be starting at the same time, I think. We'll have to see.
Posted by Sam
on 2003-09-10 12:36:06