ftp.cs.arizona.edu/ftp.cs.arizona.edu.tar/ftp.cs.arizona.edu/icon/newsgrp/group93b.txt/000118_icon-group-sender _Tue May 25 04:39:09 1993.msg

Internet Message Format | 1993-06-16 | 2KB

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Date: 25 May 93 04:39:09 GMT
From: dog.ee.lbl.gov!network.ucsd.edu!munnari.oz.au!titan!trlluna!bruce.cs.monash.edu.au![e-mail]  (Lloyd Allison)
Organization: Computer Science, Monash University, Australia
Subject: Re: Yet another variation on queens (was Icon vs Prolog)
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[e-mail] (Boris Borcic) writes:
 ...
>3) Write a 3D version of 1+2, e.g. N^2 queens in N^3 cubic "board"
>   (are there any 3d solutions to N^2 queens ? should one use plane
>    diagonals, 3d diagonals, or both ?)
 ...

In general there are lots of solutions for N^2 queens on an N*N*N "board",
but none if N<11, N=12 or N=14.
For n=11 and N=13, all solutions are also solutions of the toroidal
version, and they are all "linear" solutions.
Conjecture that there are solutions to the toroidal problem
iff the smallest factor of N is > 7.
Q: what is the smallest N with a non-linear solution?

%A L. Allison
%A C. N. Yee
%A M. McGaughey
%T Three-dimensional queens problems.
%R TR 89/130
%I Dept. Computer Science, Monash University, Australia
%M AUG
%D 1989
%K n-queens, queen, chess, 3D, TR 89 130 TR130 TR89/130

Lloyd Allison, Dept. Comp. Sci., Monash University, Australia 3168.
[e-mail]