Behold a maze of fuses (the black dotted lines) laid out on a grid:
The fuses can be lit, causing sparks to burn along them at a perfectly uniform rate: one segment per second. Your goal is to light the fuses in exactly four (4) places so that all sparks extinguish at exactly the same time.
- fuses may only be lit on the corners of grid squares (that is, the "gaps" between the fuse segments); all fuses must be lit at the same time
- if $n$ spark(s) meet at an $n$-way intersection, they extinguish; this includes the case of a single spark reaching a dead-end
- if $n$ spark(s) meet at a $k$-way intersection, with $k > n$, they do not extinguish; instead, they split or merge if necessary and continue to follow all outgoing branches (all branches that sparks didn't come in on)
Can you figure out which four places to light the fuses?
Hint: See http://i.stack.imgur.com/lu4qO.png
The four colours (red, purple, blue, and green) correspond to fuses burned by sparks spreading from the first, second, third, and fourth spark origins, respectively.
As an example, consider one part of the grid:
Lighting the fuse at D5 is a potential solution. It will start burning north and south, reaching B3 in 4s and B6 at 3s, splitting at both. The B3 north spark and B6 south spark will continue burning (exiting the grid). The B3 south and B6 north sparks will reach B4 at exactly the same time (5s) and merge, continuing to burn along the western branch.
Lighting the fuse at D4 is not a potential solution. We see that in this case, two sparks will meet and extinguish at B5 after 5s, but other sparks (at A2 and A4, and possibly B7) will still be burning, meaning all sparks do not extinguish at the same time.