3D Statue Park: U shapes

This is a three-dimensional Statue Park puzzle.1 The five squares in the below image depict the five levels of a $$4\times4\times5$$ cuboid. The goal is to fit inside it the four three-dimensional pieces shown in the picture, so that the resulting space satisfies the following conditions:

• The pieces can be rotated or reflected along any axis.
• No piece can be orthogonally adjacent to another piece.
• The cells not occupied by pieces must all be orthogonally connected.
• Cells marked with a black circle must be part of a piece, and cells marked with a white circle cannot be part of a piece.

1 The Statue Park puzzle type was invented by Palmer Mebane. The original rules can be found on his blog.

• How do the sides fit together? Jul 26, 2019 at 20:24
• Do you mean a 4x4x5 cuboid?
– Deusovi
Jul 26, 2019 at 20:28
• Yeah, just realized it's not a cube at all. Just a second, fixing the description...
– Jafe
Jul 26, 2019 at 20:29
• Should be fixed now? That's what I get for reusing old templates instead of starting from scratch.
– Jafe
Jul 26, 2019 at 20:31

Step 1:

The two black dots on the top layer tell us that two Us must be placed vertically, going downwards into the the puzzle.

Step 2:

The two remaining black dots cannot be part of the same shape. The dot on layer 4 cannot be part of a U that is entirely on layer 4. There cannot be a dot above it. Using the left given white dot on layer 2, the only way for a U to be placed is to be parallel to the two other Us, with the given dot at the very bottom.

Step 3:

This resolves the orientation of the left U-shape on layer 1 (as well as the right U-shape, which could have been resolved earlier using the right white dot on layer 2). The final U-shape then must be placed entirely on layer 5, and there is only one way to place it (since it cannot occupy any of column 2 except for the bottom cell).

• Yup, this is correct.
– Jafe
Jul 26, 2019 at 21:09

Deusovi beat me but here's the solution in Minecraft:

Top to Bottom:

• That's a very creative way of answering the question +1 Jul 26, 2019 at 21:32