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?

25 is indivisible by 3. Here we are dealing with numbers such as 60, 30, 15, 7.5....all divisible by 3. Notice that the question says we can set the timer to double speed at any time, but even so, we are still dealing with arithmetric calcutions of addition and subtraction. The results of these calculations at any time would give a number which is divisble by 3.

I sure hope someone could prove me wrong, and would be extremely delighted to learn something new if there is an answer to this question.

Posted by tan on 2004-02-20 00:22:09