- You must add red, green and blue light bulbs to the grid to satisfy these rules.
- Each white hex must contain either a red, green or blue light bulb, or an X. You can't add Xs yourself.
- Light bulbs of the same color cannot be in neighboring hexes.
- Each white hex must be lit by all three colors of light. This includes those that started with lights or Xs.
- Light travels away from light bulbs in six rays, one each through the six sides of the hex.
- Light continues in a straight line until it is blocked by a black wall hex. Xs do not block light.
We start by filling all hexes that are forced to one color by adjacency. Then let's work in the bottom left corner. The two hexes between the given green and red hexes must pairwise been green and blue, forcing the hex adjacent to the given green to be red. Then, the bottom corner has to be blue to ensure the given green has a blue light on it, forcing the hex northeast of it to be green. Finally, the remaining hex in the corner needs a green light on it, forcing it to be green itself. The grid thus far:
In the bottom middle where there is a set of three mutually adjacent Xs, the lower right of three Xs is currently only lit green, meaning the two adjacent hexes to it must be red and blue, in some order. In the tunnel in the bottom right corner, the middle hex is lit only by this row, so the two blank hexes must be blue and green in some order. These two criteria force this corner, and we get a couple more hexes via adjacency. Then we look at the triangle of Xs in the bottom right, and notice that the bottom of these three is only lit green and red, forcing the hex to its bottom right to be blue. The grid thus far:
We continue in this vein for a while, identifying hexes where a color is missing and can only be illuminated by one open hex. This finishes about half of the grid as below:
Our next deductive step is in the upper right corner. The given green is adjacent to two hexes, which must be red and blue, in some order. But then we see that in the set of Xs to the bottom right of the given green, the top X is only shaded red and blue, forcing the hex to its upper right to be green. We can then chase colors around the handle at the top. Now looking at the Xs to the upper left of the given green, we see the bottom one is only lit red and green, forcing the rest of this corner of the grid. This gives:
Now looking to the bottom left in the triangle of Xs, the bottom X is only lit green, so the two hexes to its right must be red and blue, forcing the hex above these two to be green. In this same triangle, the upper left X is also only lit green, so the two hexes to its upper right must be red and blue, forcing the hex to which both are adjacent to be green as well. Now looking at the triangle of Xs in the upper left, which will be let red and blue when the rest of this cavern is filled, we see the hex to its left must be green. The grid thus far:
At this point, I realized I missed a fairly obvious chance to turn the remaining unshaded square in the upper left corner green. Once you stop making rookie mistakes, the rest falls out easily :-)