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# Mechanical puzzle design

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### Mechanical puzzle design

1. 1. Mechanical Puzzle Design as a Man-Machine Collaboration Pavel Curtis Pavel’s Puzzles http://www.pavelspuzzles.com
2. 2. Overview • Explore development of my puzzle design process • How I did (or would) design three specific puzzles • Lessons I’ve learned along the way
3. 3. On the Problem of Spoilers • How to describe my process without spoiling puzzles? • Approach #1: Some designs are hard to spoil! • #2: Spoil somebody else’s puzzles!  • #3: Spoil a puzzle that’s currently unavailable! • And hope you’ll have forgotten by the time it is available…
4. 4. Birth of a Puzzle Design • Summer 2000: International Puzzle Party • To be held in Tokyo, Japan • The Japanese flag is very simple, elegant: dissect it? • Break it up into 12 ‘domino’ shapes • A 4×6 tray yields 12 pieces: that’s a good number • Feels way too easy… • Make the pieces double-sided? • It should have a unique solution, right?
5. 5. Hinomaru: The Japanese Flag Puzzle
6. 6. Good Idea! Now What? • Is it possible to design pieces with a unique solution? • Time for software! • Compute all possible ways to dissect a 4×6 rectangle into twelve 1×2 domino shapes • Answer: something like 261 distinct dissections • Manually select the one that looks most ‘random’ • Assign faces to the backs such that solution is unique • Lots and lots of assignments work: how to choose? • Try to use each face design the same number of times?
7. 7. Design Complete! On to Test Solving… • I abuse my friends. • A lot. • The prototype: • First tester (a genius): 2 hours and 30 minutes! • Second tester (super-genius): 45 minutes! • Making it hard enough was not the problem… • Can it be solved without exhaustive, brute-force search?
8. 8. Lessons Learned I: Pavel’s Three Laws • It’s easy to design a hard puzzle. • It’s hard to design a good puzzle. • It’s good to design an easy puzzle. (At least sometimes)
9. 9. Lessons Learned II: One Useful Design Process • Imagine an interesting puzzle ‘story’ • Use software to search for puzzles that tell that story • Almost always, only two possible outcomes • No such puzzles? ‘Open up’ the story • Too many puzzles? Add more detail to the story
10. 10. Example #2: ‘Four Sleazy Pieces’ • Designed by Stewart Coffin • American ‘elder statesman’ of puzzle design • Let’s pretend that I designed this puzzle • A non-spoiling analogue for my ‘Sleazier’ puzzle • It was inspired by my (failing at) solving Stewart’s puzzle!
11. 11. First, the Story • Pack a square tray with polyominoes • Polyominoes = shapes made of multiple squares
12. 12. Make the Tray a Weird Size • Not an integral side-length: ~5.8 units • Experienced puzzlers know what this means • Anything weird is that way for a reason
13. 13. Then Double-Cross Them! • Pieces do go in at an angle, but not that one! • (It is called ‘Four Sleazy Pieces’…)
14. 14. Time for Software! • Find all ways to dissect the goal shape • Reusable module #1: shape partitioning algorithm • For each possible dissection, perform solving tests • Reusable module #2: shape solving algorithm • Must solve goal shape in exactly one way • Must solve these shapes in no ways:
15. 15. Drowning in an Ocean of Puzzles! • Thousands or even millions of dissections work! • Add more constraints to the story: • No straight pieces • No duplicate pieces • All pieces about the same size • Still too many? Talk to my wife! • a.k.a, my ‘sadism consultant’ • “Can you make it almost solve 5×5?” • Pieces must solve these shapes:
16. 16. Puzzles that are Stories • A ‘story puzzle’ is solved in ‘chapters’ • Goal of first chapter is (fairly) obvious • Solving that chapter leads to a new puzzle • Welcome to Chapter Two! • Final chapter yields a satisfying conclusion • Typically an appropriate word or phrase • Story puzzles usually have 3 to 5 chapters
17. 17. Example #3: Holiday Discount Puzzle 2012 • Genesis: Can this shape make a puzzle? • Eight square pieces, each with or without certain corners • Need solution to be unique • Ensures a consistent ‘next chapter’ • Answer: create some kind of picture • Pieces must have ambiguous placements
18. 18. Chapter One • Eight pieces: • Goal: make a solid diamond: • Each piece could fit at two corners and two edges
19. 19. Chapter Two • Somehow read a message off the assembly • Thus, need letters on the pieces: A R P L I E S S E S E R T H R A N O E T R E E D W T A C E • Solver must infer: read clockwise around the diamond, ignoring other letters
20. 20. Chapter Three • Message suggests reading the other letters • But doesn’t explain exactly how • Solver must infer: read left to right, top to bottom • Result: “ANSWER IS _______” • Only three chapters here • Want the discount puzzle to be on the easy side
21. 21. When Software Can’t Help • Many puzzle searches can’t be automated: • Disentanglement / topological puzzles • Trick-opening boxes • My “Get a Clue!” puzzle • This category is growing for me • Still lots of design lessons to learn!
22. 22. Story-First Design • Craft a pleasing solving story • Use whatever tools work to search for puzzles that tell that story • Revise or refine the story as indicated • Treat test-solvers as story critics
23. 23. What Story Would You Like to Solve Today? Thank you. Pavel’s Puzzles http://www.pavelspuzzles.com High-quality mechanical puzzles, direct from the designer!