Some time ago I posted an article (c.q. mailed a message) describing
the contents of Cubism For Fun, the newsletter published by the Dutch
Cubists Club (NKC). In that article (message) I gave a more elaborate
description about a problem involving fitting pieces.
The base problem is as follows. Build a tetrahedron consisting of balls,
8 balls on an edge. When you look at the lattice induced by this
tetrahedron after some thinking you will find there are 25 ways to pick
4 connected balls. Now take those 25 ways and make "pieces" from it.
Again, go back to the tetrahedron and inside it create a hollow
tetrahedron with 4 balls on an edge. The remainder requires 100 balls
to fill. Try to do that with the 25 "pieces" you just created.
This has been a fairly long-standing problem but it is now (partly)
I just had word that Jan de Ruiter from Purmerend (the Netherlands)
found a number of solutions. Details will likely be presented in
a forthcoming issue of CFF.
An amusing side-note. Between the 25 pieces there are two that can
be created interlocked. It is not clear whether it is possible to
separate those two pieces by hand when interlocked, so it is not
clear whether a solution that has those two pieces interlocked
really is a solution. The first solutions Jan de Ruiter found
*had* those two pieces interlocked. But after some time he found
a solution with those two pieces far away from each other, so there
is really a true solution.
Remaining questions: How many solutions are there? How many do not
have those two pieces interlocked? Is it possible to separate those
two pieces when interlocked? (The last puzzle resembles one of those
chinese metal separation puzzles.)
(Information about CFF can be obtained from Anton Hanegraaf,
Heemskerkstraat 9, 6662 AL Elst, The Netherlands. E-mail is
now also possible: firstname.lastname@example.org.)
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland
home: bovenover 215, 1025 jn amsterdam, nederland; e-mail: email@example.com