You won't believe this. I worked all night to make a new 3D tetromino puzzle, and just as I was about to save the final version there was a power outage! Now I can't remember what the final clues were supposed to be, and I'm far too busy to try and figure it out myself. Can someone please help me?
The image above represents a $5 \times 5 \times 5$ cube. Insert any number of the pictured 3D-tetromino pieces into the cube at any orientation. The following conditions must be satisfied:
- Pieces cannot be adjacent to each other, but may touch at a corner or along edges.
- All uncoloured cells must be orthogonally connected.
- Cells with numbers must be uncoloured. The numbers give the total lengths of all runs of coloured cells, of the same colour, starting immediately adjacent to the number and extending outwards from it.
- A numbered cell cannot be orthogonally adjacent to a cell of a different colour.
Question marks represent clues which have an unknown colour and number.
Puzzle inspired by, and template taken from 3D Tetromino puzzle by jafe.
This has been hard work... may I not explain my approach?