Monumental – Markus’ Tetrahedron

Only the passing of the great ones are marked by a pyramid.  And a pyramid it was to remind us of the loss of puzzle master Markus Götz to the puzzle community in 2018.  His puzzle legacy lives on through his many designs generated over the years and I’m always happy to run across a new one that I’ve yet to discover.

Markus’ Tetrahedron was designed by Markus Götz and used by Stan Isaacs as his exchange puzzle at last years International Puzzle Party (IPP).  The 4 identical bright shiny green 3D printed pieces can be used to construct a tetrahedron in 2 different ways.  And since these exchange puzzles were made by George Bell, the pieces are constructed from conjoined spheres.

Don’t let the small number of pieces lull you into a sense of complacency.  It took me some time to find the first of the two solutions.  Each piece consists of 5 spheres and the pieces don’t seem to want to go together.  And each piece consists of a string of 3 spheres and another of 2 spheres that are connected by a cube.  Keep track now – identical pieces of conjoined strings of spheres connected by cubes that form a tetrahedron.  I don’t usually give clues on how to solve puzzles but just this once I’ll let you know that the solution uses Face-Centered Cubic (FCC) Packing.  Your welcome!

It doesn’t take long to determine that each of the 4 tetrahedron edges will consist of 4 spheres with each corner sphere belonging to 3 of the edges.  4 edges, 4 corners, 4 pieces, maybe there’s some kind of correlation going on here.  And lo-and-behold, the first solution emerges.

When solving this puzzle, you can ignore the cubes that connects the strings of spheres like I did.  Or you can realize before you solve it that each cube has a sphere connected to 2 of its faces and maybe this is a clue to where the spheres of the other pieces have to go.

It took some effort to find the second solution.  I kept getting the first solution and couldn’t see past it.  I had to step back to give it a good think and I’m getting a bit long in the tooth for that.  Eventually, I thunk (I know, it’s less of a process and more of a sound that my aging brain makes, k-thunk, k-thunk, k-thunk) my way to the other solution, which unlike the first, snaps closed when you get all the pieces together.  Looking at the final assembly, I could easily see why the second solution is much more difficult to find than the first.  I basically needed to jettison all those great ideas that lead to the first solution. 

Of course, once both solutions are discovered, the next challenge is to pack the 4 pieces back into the rather non-tetrahedralish box.  However, this was a much easier challenge than the other 2.

Receiving this monumental puzzle at IPP last year reminded me just how much I miss seeing that energetic, smart, and entertaining puzzle genius at IPP.  He always make everything seem a bit more special.

Markus Götz (1974-2018) attended 17 IPPs, participated in 16 exchanges and hosted IPP31 in Berlin.  He invented over 100 puzzles and authored six CFF articles.  He wrote about this puzzle in CFF 66 (2005).  He is greatly missed!
        - From the Markus’ Tetrahedron Puzzle Insert

RIP Markus!