Polysticks: Puzzles & Solutions

Author: David Goodger <goodger@python.org>
Date: 2012-10-07
Revision: 573
Web site:http://puzzler.sourceforge.net/
Copyright: © 1998-2012 by David J. Goodger
License:GPL 2
images/puzzler.png

Contents

Polysticks of Order 1 Through 3

These puzzles use the 1 monostick, 2 disticks, and 5 tristicks, for a total of 20 line segments on the square grid.

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.

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 2 vertical or horizontal line segments (H, J, L, N, or Y), symmetrical shapes can be formed.

  • 6x6 grid: 1795 solutions

    In this solution, the "Y" piece is omitted:

    images/sticks/tetrasticks-6x6.png
  • Aztec Diamond of order 3: 3 solutions

    In this solution, the "J" piece is omitted:

    images/sticks/tetrasticks-aztec-diamond.png

One-Sided Tetrasticks

9 of the 16 tetrasticks are asymmetrical, therefore there are 25 one-sided tetrasticks.

Polysticks of Order 1 Through 4

This puzzle uses the 1 monostick, 2 disticks, 5 tristicks, and 16 tetrasticks, for a total of 84 line segments.