My "conjecture" is, that some depositions could be excluded by comparing two shapes: e.g. if they are back to back, side by side, nob on nob. Here I have in mind two shapes where one is just a rotation around the long axis of the other and shifted by only one unit perpendicular to the axis of rotation.

With some "random" changes the time for computation on my computer went down from 1534s to 67s. What I did is exclude some pieces I found suspicious. Therefore I introduced basically the function exclude and had to do some bookkeeping of already places pieces.

  ```haskell
  len :: V3 Int -> Float
  len (V3 x y z) = sqrt (x'*x' + y'*y' + z'*z')
                where
                    x' = fromIntegral x :: Float
                    y' = fromIntegral y :: Float
                    z' = fromIntegral z :: Float
  exclude :: Shape -> Shape -> Bool
  exclude [a1, _, _, d1, _]  [a2, _, _, d2, _] = len (a2 - a1) < 1.1
                                                && len (d2 -   d1) < 1.1
  ```

  ```haskell
  conflict :: Shape -> Shape -> [Shape] -> Bool
  conflict occs piece oldPieces = any (\voxel -> elem voxel piece) occs ||
                any (\o -> exclude o piece) oldPieces
  ```

  ```haskell
  subsolutionsSmart :: Int   -- ^ How many pieces should be in the subsolution we're looking for?
                  -> Shape -- ^ Unavailable voxels, already occupied by some piece
                  -> [Shape]
                  -> [[Shape]]
  subsolutionsSmart 0 _ _ = [[]]
  subsolutionsSmart n occupiedVoxels oldPieces = do
    let freeVoxel = pickFreeVoxel occupiedVoxels
    newPiece <- filter
                  (\piece -> elem freeVoxel piece &&
                             not (conflict occupiedVoxels piece oldPieces)
                  )
                  allValidPieces
    let updatedOccupiedVoxels = newPiece <> occupiedVoxels
    let updatedOldPieces = (newPiece:oldPieces)
    otherPieces <- subsolutionsSmart (n - 1) updatedOccupiedVoxels updatedOldPieces
    return $ newPiece : otherPieces
  ```

  ```haskell
  allSolutionsSmart :: [[Shape]]
  allSolutionsSmart = subsolutionsSmart 25 [] []
  ```