*Adam M.
Costello* :
*Puzzles*
### Fuse Solution

To measure 45 minutes, ignite both ends of one fuse and one end of
the other. When the first fuse disappears, ignite the remaining end of
the second. When the second disappears, 45 minutes have elapsed since
the start.

To measure 40 minutes, ignite three flames and maintain three flames
until both fuses are gone. 120 minutes worth of fuse divided by three
is 40 minutes. Whenever two flames go out together (when a piece of
fuse burning from both ends disappears) you must ignite two more to
replace them, which you can do by cutting a piece in the middle and
igniting both of the new ends (or just ignite the middle, which performs
the cut for you). Whenever a single flame goes out (when a piece of
fuse burning from one end disappears), you must ignite one end of
another piece, which might require first cutting a piece if all pieces
are burning from both ends. Notice that a potentially infinite number
of operations may be required, so it's especially important that you
move infinitely fast.

To measure any fraction `n`/`d` of an hour, where
0 < `n`/`d` <= 1, maintain `d` flames
on the first fuse and `d`-`n`+1 flames on the second.
When the first fuse is gone, extinguish all but one of the flames on
the second, and maintain one flame. When the second fuse is gone,
`n`/`d` of an hour has elapsed since the start.