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

Answer 1

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:

Answer 2

Puzzle 1

I solved it mostly by trial and error.