From dik@cwi.nl Mon Aug 2 20:52:23 1993 Return-Path: Received: from charon.cwi.nl by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA05478; Mon, 2 Aug 93 20:52:23 EDT Received: from boring.cwi.nl by charon.cwi.nl with SMTP id AA19947 (5.65b/3.8/CWI-Amsterdam); Tue, 3 Aug 1993 02:52:21 +0200 Received: by boring.cwi.nl id AA23253 (4.1/2.10/CWI-Amsterdam); Tue, 3 Aug 93 02:52:19 +0200 Date: Tue, 3 Aug 93 02:52:19 +0200 From: Dik.Winter@cwi.nl Message-Id: <9308030052.AA23253.dik@boring.cwi.nl> To: cube-lovers@life.ai.mit.edu Subject: Fitting puzzle solved 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. Briefly: 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) solved. 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: gm@phys.uva.nl.) dik -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland home: bovenover 215, 1025 jn amsterdam, nederland; e-mail: dik@cwi.nl