A Physical Manifestation Of An Ethereal Concept – T Pack

Haym Hirsh, a professor of computer science for 100100 years, presents us with the Technological Pedagogical Content Knowledge (TPACK) framework.  This educational model describes the intersections between technology, pedagogy, and content for the effective integration of technology within teaching.  It consists of 3 contextual knowledge categories: content knowledge, pedagogical knowledge, and technological knowledge, the 3 pairwise intersections of these categories, and the overall 3-way intersection representing the entire framework.  Realizing that such a conceptual frameworks would not capture much interest, Haym transformed this abstract concept into something more physical albeit somewhat still cerebral.  The framework has become a box frame, and the 3 knowledge categories and 3 pairwise intersections have each been embodied in a T.  He has anointed this physical construction with the name T Pack.  Note the introduction of the critical space to distance it from the original ethereal concept.

T Pack is a 3D apparent cube packing puzzle designed by Haym Hirsh and made by Wood Wonders.  It consists of 6 wood T-shaped pieces that need to be packed within a 3D printed box made with wood infused filament.  And the box has been specifically constructed so that each side presents a smooth 3D printed plate-side finish.

Each side of the box has a square opening in each corner except for 1 side that has a corner shifted to the middle of a side to merge with the adjacent corner.  The edge of the new opening has also been removed to provide a full 2x1 voxel opening for inserting and removing the Ts.  And even though you can’t pass the Ts through the square windows, they are large enough for the pieces to poke out of them.

The goal is to pack 6 Ts in a box.  What a great concept!  I’m quite partial to 6 T puzzles (Shhhh! She Just Turned – 6T and Not A Box For Tea, A – T-Box).

Since all the pieces are the same T shape,  you only need to investigate how that one piece can enter the box and how it can manipulated once inside.  After looking for possible 3x3x3 assemblies outside the box, it quickly becomes apparent that some of the pieces will need to be rotated.  And although there’s not a lot of room within the box, all those windows facilitate the rotation of pieces.

Since not all the voxels within the box will be occupied by the Ts, the first piece removed from the solved configuration does not necessarily need to come out in the first move.  In fact with all those windows, there could possibly be a lot of movement before the first piece comes out.  I focused on the removal of this first piece as a starting point of how the pieces would be configured.  Of course, I didn’t start with the correct way to remove this piece and spent quite a bit of time unnecessarily cajoling pieces into positions to no avail.

It’s always fun when you get half the pieces in, decide it’s not going to work, and then have to figure out how to get them back out for another think.  Sometimes its because I naively thought I could do something undoable or sometimes its because I simply lose my way.  I’ve recently noticed a strong correlation between puzzle experience and losing the thread of a solution.

After discovering an infinite number of ways that the Ts can’t be rotated within a partially filled box, I finally manged to get everything aligned and had an apparent cube of Ts within the box.  The solution entails a nice sequence of moves with rotations and I really enjoyed this one.  At the time of this posting, T Pack was still available at Wood Wonders.