Small cube packing puzzle collection

I wanted some small puzzles to entertain people post-Christmas lunch, and thought it'd be really handy if there were a collection all on one build plate to avoid searching around for interesting ones, and kicking off multiple builds.  The four puzzles here each pack in to a 3x3x3 cube, and all four fit on a single build plate.  There is one with just three pieces, one with four, one with five and one with six.

The three piece puzzle is known as the Bucolic Cube, designed by Yasuhiro Hashimoto; you can find many videos on how to solve it via Google, if you get stuck.  The other three puzzles come from a book by Stewart T. Coffin.  He says:

The four piece puzzle has the intriguing property of being serially interlocking, meaning that it can be assembled in one order only.  It also doesn't tend to fall apart once you tip it out the box.

The five piece puzzle is described as surprisingly difficult.

The six piece one has one unique solution.

I'll admit that I managed to solve the three and four piece ones myself, but to solve the five and six piece ones I turned to AI and got Claude.ai to write some code to solve them!

You can find the solution to the 3 piece puzzle by googling “bucolic cube”.  The solutions for the others are included in the attached photos.  The numbers in the cells tell you which piece occupies those cells in each layer; then you just have to figure out which piece matches that pattern of cells.

Enjoy!