Polysticks Puzzles & Solutions
| Author: | David Goodger <goodger@python.org> |
|---|---|
| Date: | 2008-10-19 |
| Revision: | 240 |
| Web site: | http://puzzler.sourceforge.net/ |
| Copyright: | © 1998-2008 by David J. Goodger |
| License: | GPL 2 |
Also see:
Contents
Tetrasticks
One-Sided Welded Tetrasticks
The "welded" tetrasticks are those that contain junction points, or welds, and therefore do not form simple connected paths (in other words, they branch). There are 6 welded tetrasticks, 4 of which are asymmetrical, therefore there are 10 one-sided welded tetrasticks.
5x5 grid: 3 solutions
15 of 16 Tetrasticks
Due to an imbalance in horizontal/vertical parity, the 16 tetrasticks cannot be formed into a symmetrical shape. But by omitting one of the five tetrasticks that have an excess of vertical or horizontal line segments (H, J, L, N, Y), symmetrical shapes can be formed.
6x6 grid: 1795 solutions
In this solution, the "H" piece is omitted.
One-Sided Tetrasticks
9 of the 16 tetrasticks are asymmetrical, therefore there are 25 one-sided tetrasticks.
5x5 diamond lattice: 107 solutions (none calculated yet though)
All 107 non-isomorphic solutions are listed in "Covering the Aztec Diamond with One-sided Tetrasticks, Extended Version", by Alfred Wassermann, University of Bayreuth. The solution above is number 9 in Wassermann's paper. (Wassermann, and Knuth before him, mistakenly called the shape an "aztec diamond", but an aztec diamond is a subtly different shape. This puzzle actually corresponds to a centered square number.)
8x8 grid with center hole: solutions incomplete
8x8 grid with one clipped corner: solutions incomplete
8x8 grid with two clipped corners 1: solutions incomplete
Polysticks of Order 1 Through 4
This puzzle uses the 1 monostick, 2 disticks, 5 tristicks, and 16 tetrasticks.
7x7 grid: solutions incomplete
3x7 diamond lattice: solutions incomplete
