Three 3 x 3 x 3 Polycube Dissections

Question

The Soma cube is perhaps the most well-known polycube dissection. Here are three more dissections to be assembled into 3x3x3 cubes.

The best answer will provide:

• the first correct solution for all three puzzles. Excluding rotations and reflections, puzzles 1 and 3 have only one solution. Puzzle 2 has 13 possible solutions.
• a format similar to the example below. Colors or numbers or both can be used to indicate the location of each piece.
• a few words about your methodology (ie. simple deduction, used some code or calculations, found some help on the web...)

Note that all pieces for these 3 puzzles have a thickness of 1 unit.
Here is an example format for the Soma cube solution that is shown on the Wikipedia page.

These 3 puzzles do not have copyright restrictions. The puzzle names are in this spoiler:

1) Slothouber-Graatsma puzzle
2) Diabolical cube
3) ZZZLLL cube

Answer 1

Puzzle 1:

Puzzle 2:

Puzzle 3:

All solved by deduction. In most cases you can promptly rule out a large portion of possible solution spaces by considering the most awkward shapes e.g. the light blue piece in the second puzzle can only have one of two positions. If we place it in those we limit where the orange piece may go, etc...