A camper needs to cook something on the stove for exactly 45 minutes, but has no watch or any of the usual means of telling time. The only available items are two mosquito coils, each of which will burn from one end to the other in an hour. Can the camper reliably determine when 45 minutes have elapsed?
Suppose I counted the steps I took while one coil burned up?
I suppose then that if you took, say, 6,000 steps during the burning
of the first coil, you could then cook your meal while taking
4,500 steps? And we wouldn't even need the second coil! But no,
let's assume that there is no reliable source of regular motion
that you could calibrate using one of the coils.
What's a mosquito coil anyway?
You can think of it as just some sort of string that burns at a slow
and steady rate. The fact that it's coiled is not significant.
Can I straighten out the coil and figure out where its middle is?
No, and the solution does not require that the coil be cut, marked,
folded, measured, or altered in any way (except, of course, for burning
it!).
You are given two "hourglasses", one of which will empty in 9 minutes, and one in 13. You need to measure a time interval of exactly 30 minutes. You can almost do it by using the 13 minute hourglass, then when it empties, turning it over to measure another 13 minutes, and then running the 9 minute hourglass, to measure 35 minutes exactly. But is there a strategy that will measure 30 minutes?
I give up, show me the solution.