1. Mechanical Puzzle Design
as a
Man-Machine Collaboration
Pavel Curtis
Pavel’s Puzzles
http://www.pavelspuzzles.com
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. 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. 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?
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. 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. 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. 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. 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. First, the Story
• Pack a square tray with polyominoes
• Polyominoes = shapes made of multiple squares
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. Then Double-Cross Them!
• Pieces do go in at an angle, but not that one!
• (It is called ‘Four Sleazy Pieces’…)
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. 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. 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. 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. Chapter One
• Eight pieces:
• Goal: make a solid diamond:
• Each piece could fit at
two corners and two edges
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. 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. 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. 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. 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!
