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
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$\begingroup$ left top corner is top, right top corner 3rd layer, right? +1! $\endgroup$– Omega KryptonCommented Jul 15, 2019 at 11:54
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$\begingroup$ @OmegaKrypton That's correct, although in this case I think it doesn't matter. $\endgroup$– JafeCommented Jul 15, 2019 at 11:56
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$\begingroup$ @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. $\endgroup$– JafeCommented Jul 15, 2019 at 12:08
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$\begingroup$ Your rules do not say what the numbers are for. $\endgroup$– LeppyR64Commented Jul 15, 2019 at 12:12
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$\begingroup$ @LeppyR64 Wow, how'd I miss that? Missing rule added. Thanks! $\endgroup$– JafeCommented Jul 15, 2019 at 12:15
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1 Answer
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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…
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$\begingroup$ Wow, that was fast. Everything's correct. $\endgroup$– JafeCommented Jul 15, 2019 at 12:43
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3$\begingroup$ The answer would be even better, if the logical deduction for the solution would be present. $\endgroup$– BmyGuestCommented Jul 15, 2019 at 13:47
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$\begingroup$ @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 IvanCommented Jul 15, 2019 at 14:13
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$\begingroup$ 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... $\endgroup$– JafeCommented Jul 15, 2019 at 14:27
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$\begingroup$ 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. $\endgroup$– BmyGuestCommented Jul 15, 2019 at 14:39