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 just a thought
i've tried that... and I still come up with some issues... i've got a ton of work i need to finish, but give this a thought... des cartes tried to prove calculus by approximating the area under a curve with reimann sums... Newton and Leibniz simultaneously saw his problem... as he increased the number of his summation, he could approach an answer, but never quite arrive at a finite solution. However, Leibniz and Newton assumed that the intervals of summation were infinity, and SHAZAM... Calculus was born. I think this answer is going to require an infinite number of clocks much like the aforementioned example of integration. There is a way to come close to the answer in a finite manner, right? Take it there, and then incorporate the philosophy of integration using the principle of infinity.
Posted by AD
on 2003-09-11 14:35:57