# Three-dimensional light bulbs

This is a three-dimensional Akari puzzle (also known as Light Up). The six squares represent the layers of a $$6\times6\times6$$ cube, top to bottom. The objective is to add light bulbs into any number of cells so that the resulting grid satifies the following rules:1

• Black cells are walls and cannot contain light bulbs.
• Numbers in black cells indicate how many light bulbs are directly adjacent to that cell (vertically, horizontally or along the Z-axis).
• A light bulb illuminates its own cell as well as every cell visible from it in all six directions (up/down, right/left, and both ways along the Z-axis), continuing until a wall comes in the way.
• Every white square must be illuminated by at least one light bulb.
• No light bulb may be illuminated by another light bulb.

Note: The solution is unique and solvable by logic alone. No guesswork or trial-and-error is necessary here.

1 Paraphrased from the original rules on Nikoli

• left top corner is top, right top corner 3rd layer, right? +1! Jul 15 '19 at 11:54
• @OmegaKrypton That's correct, although in this case I think it doesn't matter.
– Jafe
Jul 15 '19 at 11:56
• @OmegaKrypton Hmm, correction: Actually the order does indeed matter (even though top vs bottom doesn't). Sorry about that. Better add in the layer numbers.
– Jafe
Jul 15 '19 at 12:08
• Your rules do not say what the numbers are for. Jul 15 '19 at 12:12
• @LeppyR64 Wow, how'd I miss that? Missing rule added. Thanks!
– Jafe
Jul 15 '19 at 12:15

Like that?

Red = light bulb, yellow = light Start from bottom
1 because you can't place light bulb above (in z) "2" and next to "1" can be only one, so it has to be there.
2 because you can't place light bulb above (in z) "2" and there is already light from first light bulb
3 since second light bulb eliminates one solution
4 because 1st and 3rd light bulbs eliminates rest
5 because of 4th and so on…

• Wow, that was fast. Everything's correct.
– Jafe
Jul 15 '19 at 12:43
• The answer would be even better, if the logical deduction for the solution would be present. Jul 15 '19 at 13:47
• @BmyGuest oh come on, it is too easy :P But added first few moves. Solution took me something under 20 mins, I would be happy for harder. Jul 15 '19 at 14:13
• Didn't realize it turned out that easy. My intention was to leave a "unique" starting point, but turns out there was another way to start which you found. (The idea was to begin with row 1 col 1 on #6.) Let's see if I can come up with a "hard mode" follow-up...
– Jafe
Jul 15 '19 at 14:27
• See? Giving your description helped jafe... I think in the spirit of the site, it's always a good idea to describe the answer better. +1 from me now. Jul 15 '19 at 14:39