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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.

enter image description here

1 Paraphrased from the original rules on Nikoli

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  • $\begingroup$ left top corner is top, right top corner 3rd layer, right? +1! $\endgroup$ – Omega Krypton Jul 15 at 11:54
  • $\begingroup$ @OmegaKrypton That's correct, although in this case I think it doesn't matter. $\endgroup$ – jafe Jul 15 at 11:56
  • $\begingroup$ @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. $\endgroup$ – jafe Jul 15 at 12:08
  • $\begingroup$ Your rules do not say what the numbers are for. $\endgroup$ – LeppyR64 Jul 15 at 12:12
  • $\begingroup$ @LeppyR64 Wow, how'd I miss that? Missing rule added. Thanks! $\endgroup$ – jafe Jul 15 at 12:15
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Like that?

Red = light bulb, yellow = light Solution 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…

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  • $\begingroup$ Wow, that was fast. Everything's correct. $\endgroup$ – jafe Jul 15 at 12:43
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    $\begingroup$ The answer would be even better, if the logical deduction for the solution would be present. $\endgroup$ – BmyGuest Jul 15 at 13:47
  • $\begingroup$ @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. $\endgroup$ – Jan Ivan Jul 15 at 14:13
  • $\begingroup$ 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... $\endgroup$ – jafe Jul 15 at 14:27
  • $\begingroup$ 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. $\endgroup$ – BmyGuest Jul 15 at 14:39

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