The Elusive 13-Piece Complete Set Puzzle Design for G4G13

Designing a puzzle related to Martin Gardner and the number 13, this project aims to create shapes with 13 members exhibiting specific edge flipping and matching rules. Through careful testing and exploration, a unique family of hexagonal pieces with two edge types was discovered, presenting an intriguing challenge for puzzle enthusiasts.

• Puzzle Design
• Martin Gardner
• G4G13
• Shapes
• Edge Flipping

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Uploaded on Sep 30, 2024 | 2 Views

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1. The Elusive 13 Piece Complete Set Puzzle Designing a puzzle for G4G13 By Peter Knoppers April 15 2016 The Elusive 13 Piece Complete Set Puzzle 1

2. A Puzzle for G4G13 Should be related to Martin Gardner and/or 13 I ll leave the martingardner 13 letter based puzzles to others I want a puzzle with shaped pieces that naturally exhibits the number 13 Thirteen is an uncommon number April 15 2016 The Elusive 13 Piece Complete Set Puzzle 2

3. The Shape Enumerator A long time ago I wrote a PERL program that enumerates the number of possible regular polygons with N edges, K edge styles with or without flipping Flipping requires specifying a translation that describes wether a flipped edge looks like itself, or like another edge. e.g. 01 01, or 01 10, or 012 021 April 15 2016 The Elusive 13 Piece Complete Set Puzzle 3

4. Edge Flipping rules Straight edge stays straight (0 0) Rotational symmetrical edge inverses (1 2) (12 21) Mirror symmetrical edge stays the same (34 34) (3 3) April 15 2016 The Elusive 13 Piece Complete Set Puzzle 4

5. Edge Matching Rules Straight edge always matches a straight edge Rotational symmetric edge matches itself, except when the piece is flipped Mirror symmetric edge does not match itself, but it will match the inverted shape April 15 2016 The Elusive 13 Piece Complete Set Puzzle 5

6. Search I tested all regular polygons from 2 up to 8 sides Using up to 7 edge types With and without flipping The number 13 appears exactly once April 15 2016 The Elusive 13 Piece Complete Set Puzzle 6

7. Results I found precisely one reasonable family of shapes that has 13 members Hexagonal pieces with two edge types, Flipping translates 01 01 000000 000001 000011 000101 000111 001001 001011 001111 010101 010111 011011 011111 111111 April 15 2016 The Elusive 13 Piece Complete Set Puzzle 7

8. Making a Puzzle from the Set Interlocking edges make a nicer puzzle Most somewhat convex shapes using 13 hexes have thousands or millions of solutions Specifying the entire outline can reduce that number considerably April 15 2016 The Elusive 13 Piece Complete Set Puzzle 8

9. 13-Piece Complete Set Puzzle This shape has only 5 solutions Beware There is a catch I won t tell you what the catch is April 15 2016 The Elusive 13 Piece Complete Set Puzzle 9

10. 13-Piece Complete Set Puzzle The set can also be used to play domino- like games You ll have to work out the rules for those domino-like games yourself You ll find a physical set of the pieces and some puzzle outlines in your goody bag The Shape Enumerator can be downloaded from http://buttonius.com/g4g13 April 15 2016 The Elusive 13 Piece Complete Set Puzzle 10