Four-dimensional light bulbs

Question

In reaction to Three-dimensional light bulbs - rules are same (almost)

This is a four-dimensional Akari puzzle (also known as Light Up). The nine squares represent the layers of a $3\times3\times3\times3$ hypercube, top to bottom (… or something like that). The objective is to add light bulbs into any number of cells so that the resulting grid satisfies the following rules:

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 or along the 4th-axis).

A light bulb illuminates its own cell as well as every cell visible from it in all eight directions (up/down, right/left, and along the Z-axis and 4th-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: I'm almost sure solution is unique and solvable by logic alone. Always had same result with 14 light bulbs (and 34 on second puzzle). If you start wrongly, you will quickly run into contradictory rules. But on the right track no guesswork or trial-and-error is necessary here. And I guess I will offer hints soon.
Puzzle 1:

Once you finish it, you can keep up going.
Puzzle 2:

Hint 0:

Hint 0

Hint 1:

You can put two zeros to 4x3 without changing solution (to empty walls, not rewriting "3").

Hint 2:

Hint 2 - added some numbers

i have no idea where the breakthrough for puzzle 2 is. +1ed tho! — Omega Krypton, Jul 17 '19 at 15:36
I feel like the best hint would be explaining how you solve puzzle 1. Kruga used "trial and error" but you said that wasn't necessary. I can't even get started on it... hence my interest. — Skosh, Jul 22 '19 at 13:34
@DarkThunder Lets say I want to start Puzzle 1 - I focus on 2x3, 2x2, 1x3 and 3x3. There can't be many lights around in 2x3 because of "0" in 3x3. So there are 4 possibilities for each "2" in 2x3. If I place one light next to "1" in 2x2 - for every possibility, it will always illuminate lot of space inside 1x3, no matter "what I try" so only two possibilities for "2" will left in 1x3, which is awesome start and then I can "try" something. Well, I can make some pictures with animation "how to start" second puzzle (seems harder). — Jan Ivan, Jul 22 '19 at 13:49
That's... hard to follow. Placing bulbs in 2x2 doesn't seem to conclude anything for me. Maybe I'm still missing something? I'm trying to keep an open mind, but it sounds like you use "trial and error" so much you go multiple levels deep... which is nuts. — Skosh, Jul 22 '19 at 15:44

score 9 · Answer 1 · answered Jul 17 '19 at 08:16

9

Puzzle 1

I solved it mostly by trial and error.

answered Jul 17 '19 at 08:16

Kruga

3,662
17
30

score 3 · Accepted Answer · answered Jul 22 '19 at 13:43

For puzzle $2$, I'm able to solve after seeing Hint $1$:

You can start to deduce the lights which are on the first $2$ on $4 \times 4$, then the second $2$, and you move to $3 \times 4$, and so on. There are always at least one number which enables us to make deductions.

However:

There are $2$ possible solutions (after Hint $1$ -- if no hint is provided, there may be more than $2$).

And this is the final grid:

Four-dimensional light bulbs

2 Answers2