12.Feb.22

We can first agree that each wick will burn all the way through in one minute.

If this is the case, then we can agree that if we light a wick from both sides at once it will burn through in 30 seconds.

This is the first part of the puzzle, but it only gets us 30 seconds, and we're after 45 seconds.

Let's assume for a moment that the wicks burn evenly instead of at random rates throughout. If this were the case, then we could light one end of one wick and both ends of the other.

Once the wick burning at both ends has burnt out (after 30 seconds), we have 30 seconds worth of wick for the second wick; and then lighting that one from the other end will make it last only an additional 15 seconds: 30 + 15 = 45 seconds.

That leaves the question: Does this method still work when the wick is burning at unpredictable rates throughout?

We don't need to worry about the first wick that we burned from both ends at the same time. That will work no matter what.

For the second wick, I am going to create a sample wick of known burn rates. This wick will be made from four even-length segments. The ratio of the times these segments burn for are 6 : 12 : 18 : 24 seconds (totaling 60 seconds).

We light the "left" side of this wick, and it will burn for 30 seconds. The first of the four even segments burns up in 6 seconds. The second burns up in 12 (total of 18 seconds). The third segment burns for another 12 seconds, leaving it with 6 seconds of burntime remaining when we hit the 30 second mark and light the other side.

In the six remaining seconds of the third segment, we burn through an equal six seconds of the "right" side's 24-second segment, leaving it with 18 seconds. However, it is now burning from both sides, meaning it will last only half that time: nine seconds. 6 + 9 = 15 seconds.

IT WORKS!