11

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

Jafe
  • 78,615
  • 8
  • 162
  • 614

1 Answers1

11

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…

Jan Ivan
  • 5,196
  • 14
  • 31
  • Wow, that was fast. Everything's correct. – Jafe Jul 15 '19 at 12:43
  • 3
    The answer would be even better, if the logical deduction for the solution would be present. – BmyGuest 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. – Jan Ivan 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. – BmyGuest Jul 15 '19 at 14:39
  • Even if I spotted this right when it posted I wouldn't have beaten your time. Well done! Knowing what I know now I wouldn't have bothered trying to add so many X's everywhere like I do in 2D. – Skosh Jul 19 '19 at 16:48