Apparently Packing Puzzles - Corner Cube, Edge Cube, Angle Cube

The latest fad for packing puzzles is to pack a few puzzle pieces into a box with one or more restricted openings such that the box appears completely full.  Usually, the pieces dance around each other within the box to acquire their final resting position.  It is surprising how many moves some of them take to solve.

The 2 most popular sizes for these puzzles are 3x3x3 and 3x3x2.  The solved appearance, making it look like a complete cube (or squat cube) within a box, has led to these puzzles being referred to as Apparent Cube Puzzles.  

These types of puzzles are very approachable and a great way to introduce puzzles to non-puzzlers.  They are clever little conundrums that can be enjoyed without requiring a large intricate attack strategy.

Recently, I had the opportunity to play with 3 of these types of packing puzzles from Andrew Crowell: Corner Cube, Edge Cube, and Angle Cube.  All 3 were 3D printed by Andrew in a variety of colors. All the cubes are of the squat 3x3x2 format and each of the puzzles has the name nicely debossed on the outside.  Everything is perfectly sized so that the pieces move extremely well within the boxes.  Occasionally, a piece will rotate out of alignment, but this is easy to remedy and not a real problem.

There has been some debate recently on whether it is obvious that the box should look completely filled instead of simply getting all the pieces within the box.  For those that don’t apparently get it, Andrew has addressed this issue by providing the following message on the inside bottom of the box: COMPLETELY FILL THE OPENING.  I’m sure that this will be followed by photos of pieces crammed in the openings and hanging out at all sorts of angles.


Corner Cube

 

 

 

 

 

 

Corner Cube consists of a brown box and 4 yellow pieces.  The opening of the box is in the corner and is unusual in the fact that it is not an integral number of voxels (think of voxels as the cubies used to construct the pieces).  It is 1.5 voxels in each direction.  I hope you weren’t thinking that the extra half voxel in each direction was to help you get the pieces in.  It’s there to provide a larger area that needs to be filled by the apparent cube within.

The 4 pieces look rather innocuous with 2 of them being simple di-cubes.  Don’t let that fool you however.  It takes 8 moves to get the first piece out once it’s assembled.  The solving procedure is very satisfying, and as with many packing puzzles like this, there is a lot of box tilting to get the pieces to move where you want them.  And yes, there is a rotation involved.  I hope you weren’t surprised by that.


Edge Cube

 

 

 

 

 

 

Edge Cube was made with a dark green box and 5 black pieces.  With the 2 dark colors, the contrast isn’t as striking as the with the other 2 puzzles.  I think that swapping the dark green with the lighter green of the Angle Cube might be a better choice.  

Like Corner Cube, the opening is 1.5 voxels in each direction.  The difference is that it is on the edge instead of the corner.  Are you grokking the naming scheme yet?

This one took me the longest to figure out even though it is the easiest one to repeat.  I had a good idea early on what the first piece to be removed was but couldn’t find a way to make it work. I tried a couple of other assumptions but in the end, I went back to the first assumption and finally found out how to make it work.  There is a very nice movement required and once that is figured out, the rest falls into place.  And yes, rotations are required.


Angle Cube

 

 

 

 

 

 

Angle Cube has a shiny light blue box with shiny gold pieces.  Don’t you just love the sound of that - A box full of gold pieces.  Is anyone else thinking that there should be a treasure chest puzzle available sometime in the future.  I have to say that the filament used to make the gold pieces is awesome!  They really stand out.

The box for Angle Cube is missing an entire edge.  But to make up for taking a piece of the bottom out, a 1x1 triangular wedge has been added back on to the top and bottom to provide an opening with an angle.

Only 3 pieces to pack in the box.  Should be easy!  However, 7 moves are needed to remove the first piece when they are all in the box.  At this point do you even have to wonder whether rotations are required?  Of course they are!  And this one has the most unusual use of rotations in the series so far.

In summary, Andrews’s Apparent Cubes are nicely designed and clever.  I highly recommend them.  As a puzzle designer myself, I appreciate the effort required to come up with a good design and, for the Andrew’s Apparent Cubes in particular, the design considerations concerning the shape of the box openings.