Polysticks: Puzzles & Solutions

Author: David Goodger <goodger@python.org>
Date: 2013-09-02
Revision: 587
Web site:http://puzzler.sourceforge.net/
Copyright: © 1998-2012 by David J. Goodger
License:GPL 2
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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

These puzzles use the 1 monostick, 2 disticks, 5 tristicks, and 16 tetrasticks, for a total of 84 line segments.

Seven-Segment Digits

The pieces in this puzzle are modeled after the seven-segment display digits 0 through 9, as seen on digital watches, for a total of 49 line segments. Based on the "Digigrams" puzzle (AKA "Count On Me" or "Count Me In") by Martin H. Watson.

In the following puzzle, the digit pairs (2, 5) and (6, 9) are considered identical for the sake of counting solutions (preventing duplicate solutions). Also note that the 0 digit has a gap in one long side, allowing the 1 or 7 digit to intersect and occupy the 0 digit's otherwise enclosed central line segment.