An analytic framework forestimating puzzle quality

Scott Blomquist @ GC Summit (Feb 12, 2009)

(Shoutout to Shark Bait: Hoo ha ha!)

Agenda

• Introduction to Puzzle Theory framework• Apply it to a sample• How you can use it to improve your

puzzlecraft

Introduction to Puzzle Theory

• Unexplored branch of mathematics– (mathematicians help me figure out where it

fits in the math family tree)

• Scope– Provides a framework for decomposing

information reduction puzzles into component information streams and transformation steps

• Possibly in scope, but not covered here– How to solve constraint puzzles (such as

Sudoku, Battleships, even crosswords to some extent)

Definitions

• Information Reduction Puzzle (IRP)– Describes most Game puzzles (as well as

Mystery Hunt, Puzzle Hunt, etc.)– Solver is provided with an initial set of data

and the goal to reduce the information content of this data to a word or short phrase

Definitions (cont’d)

• Information Stream (or just “Stream”)– A single related set of information in an IRP– May be provided explicitly or derived through

a transformation step– Example: A CD puzzle may have information

streams consisting of track listings, track times, actual audio, cover art, etc.

• Transformation Step (or “Transform”)

– A step used in an IRP to transform initial or derived data into another form

– Examples: order by X, use X as an index into Y, convert from clock hands into semaphore

Sample analysis

Sample analysis (cont’d)

• Obvious information streams– Set of car manufacturer badges

• Candidate transformation steps– Identify manufacturer names

– Describe the location of each badge– Count occurrences of each badge type

Sample analysis (cont’d)

• Current information streams– Still have badges– Also have names, counts, locations (?)

• Candidate transforms– Index name by count– Index name by location

Sample analysis (cont’d)

Manufacturer name Count Name[count]

Porsche 7 E

Infiniti 6 I

Saab 3 A

Toyota 5 T

Ferrari 2 E

Mercedes 8 S

Lexus 4 U

BMW 1 B

• Candidate transforms• Order Name[count] by count

Sample analysis (cont’d)

• Answer: BEAUTIES– (GC, wand, SHARC, Leon, etc. confirms)

Sample analysis (cont’d)

• Analysis tree– (nodes are streams, edges are transforms)

Applications in puzzle quality

• Signs of a bad puzzle– Analysis tree is very broad– Good paths are not strongly confirmed– Bad paths are not strongly discouraged– Long time req’d for a bad path to seem bad

– Obvious streams are never used– A stream is reused for inconsistent purposes– Transforms are not robust against mistakes– Unfair transforms are employed– Abuse of the “aha!” transform

First puzzle theory “discovery”

“__ __ __ __ __ __ __ __”

More information

• http://groups.google.com/group/puzzletheory• http://puzzletheory.pbwiki.com

• Contact me– scott@blomqui.st

– http://www.puzzlehunters.com

– QUESTIONS?