Two Lips Are Better Than One – Tulip 1

What do you call a puzzle with a large square corner opening that incorporates 2 lips constructed from triangular half-squares?  Perhaps 2 Lips or maybe even better Tulip.  And if there is more than one design like that, maybe they can be called Tulip 1 and Tulip 2.

Tulip 1 was designed by Osanori Yamamoto in 2019.  It is a 3D apparent cube packing puzzle where the objective is to assemble 3 pieces within a frame such that there appears to be a 3x3x3 cube within the frame although there may be unseen holes within the frame.  Spoiler/No Spoiler – there are vacant voxels when the pieces are packed in the frame.  The frame has a very large and very obvious open corner to add and remove pieces and a single voxel opening in the opposite corner.  My version was made by Pelikan with a Padouk frame and Wenge pieces.  It looks and feels fantastic and is a fun little puzzle with 13 moves to take the first piece out.  Of course, since I consider it an assembly puzzle, it’s really 13 moves to get the last piece in.

As already mentioned, the large opening in the frame has 2 lips.  Why is this of interest?  I would argue that each lip makes its corner open so that the adjacent internal voxel needs to be occupied to satisfy the apparent cube criteria while at the same time being closed so that pieces are barred from being removed there.  Open and closed.

To solve Tulip 1, my initial attempt was to find an assembly of the pieces that would fit within a 3x3x3 space but I ended up with too many assemblies that obviously wouldn’t satisfy the apparent cube requirement.  So I looked for assemblies with a solid corner to fill the large opening while simultaneously having cube in the opposite corner to fill the smaller opening.  This didn’t quite do it for me either, so I instead focused on ways to use the smaller opening.  Now sure, that opening could be there just to force a cube in that corner but I was going on the premise that one of the pieces would eventually have to stick out of that hole.

And thus I found a good candidate assembly that permitted a nice sequence of a few moves.  And if I’ve learned anything from these types of puzzles, if it makes a few nice moves, it’s probably the start of the solution path.  There were a couple of times that I thought I had it solved but there was a move in my path that was not realizable when actually in the box.  I could get it to what I estimated was the half-way point but I couldn’t free the first piece.   Eventually, I realized that the first piece to be removed was not the one I was trying to liberate.  With that new perspective, I completed the solve.

Tulip 1 is another great puzzle from Osanori.  Now to track down Tulip 2.