Puzzles: Solving and Writing Tips

ΣUMS talk - 5/4/12Sean Gardiner

Introduction

• Puzzles are presented as a bunch of words and/or pictures, and little else

• The goal is always to extract a word or phrase– Done by searching for patterns and identifying and

utilising themes (cf. solving maths problems)• The crux is the intuitive leap(s)– Always motivatable, but rarely obvious

• Different categories (based on appearance)

Word Puzzles

• Words can have multiple properties:– Meaning (double meaning, “cryptic” definitions)– Letter/constituent properties (too many to list!)– Sound (rhymes, phonetics, ...)

• Varied forms of presentation: – List – Hidden (e.g. in a paragraph/poem)– Codes (Caesar cypher, Morse, Braille, alphanumeric...)– Clues (straight, cryptic)

Solving Word Puzzles

• Huge range of word puzzle mechanics

• Expect puzzles to use at least two properties

• Always look for patterns (in letters/meanings)

• Numbers => convert or index (usually)

Recapitulation – Corey Plover (MUMS 2010)

Recapitulation – Corey Plover (MUMS 2010)

Wockyjabber – Sean Gardiner (ΣUMS 2010)

Headless Snake – Steven Irrgang (CiSRA 2009)

Kangaroo Jack – Corey Plover (MUMS 2011)

Picture Puzzles

• Pure picture puzzles rely only on image interpretation

• Usually employ different perspectives as a mechanic

• Sometimes drawing/adding to the picture is required

Solving Picture Puzzles

• Be artistic! – Think visually (or know someone who can)

• While puzzle type can vary wildly, the answer extraction (last step) is very restricted:– Find/construct letters that spell out the answer– Find/construct an easily and uniquely-identifiable

image or set of images (more likely)

Smilies – Andrew Shellshear (CiSRA 2008)

Smilies – Andrew Shellshear (CiSRA 2008)

Concyclicity – Ivan Guo (ΣUMS 2009)

Concyclicity – Ivan Guo (ΣUMS 2009)

Meet Your Match – Andrew Coker (CiSRA 2009)

Logic Puzzles

• “Logic” puzzles are self-contained and often original ideas:– Follow a series of steps (usually disguised)– Identify/determine a rule set – Reinterpretations (e.g. board games)

• All puzzle types overlap with this one in one way or another

Solving Logic Puzzles

• An inherent property of logic puzzles is that everything needed to solve one is already on the page in some capacity (and usually there’s only just enough information)– In some cases new rules/steps might be implied

from old ones (mechanic repetition is common)

• Using deduction can often prove just as useful as induction

Art – Andrew Shellshear (CiSRA 2010)

The Drover – Sam Chow & Stephen Muirhead (MUMS 2011)

Characterisation – Sean Gardiner (ΣUMS 2010)

Latin Pipes – David McLeish (CiSRA 2010)

Latin Pipes – David McLeish (CiSRA 2010)

Construction Puzzles

• Basically a mix of picture and logic types

• Involve cutting/folding/pasting– The construction rules are usually made clear

• Most basic construction ideas have already been exhausted

Solving Construction Puzzles

• First step: Always cut everything out!

• Expect the construction step to be relevant to the overall puzzle:– If cutting is involved, there ought be a reason the

pieces were originally separated– If folding is involved, you’ll want to use the 3D

property at some point

Shapeshifter – Duncan Sutherland & Sean Gardiner (ΣUMS 2011)

Shapeshifter – Duncan Sutherland & Sean Gardiner (ΣUMS 2011)

Shapeshifter – Duncan Sutherland & Sean Gardiner (ΣUMS 2011)

Continuity – David Morgan-Mar (CiSRA 2007)

Duplex – Ivan Guo (ΣUMS 2010)

Research Puzzles

• These tend to contain very specific descriptions/jargon/pictures/themes:– Rarely solvable without doing some research

• Can involve retrieving facts/stats, recognising pictures/music, etc.

Solving Research Puzzles

• Research!– Wikipedia/Google/specialist websites– Ask around – the topic might be someone’s field

of expertise

• Try to identify the puzzle’s theme as early as possible, as this will greatly help narrow down the research

Super Effective – Scott Mooney (ΣUMS 2010)

Kingfisher – Sam Chow (MUMS 2008)

Identikit – Andrew Shellshear (CiSRA 2010)

Identikit – Andrew Shellshear (CiSRA 2010)

General Solving Tips

• Practise! – Lots of puzzles in archives• Work with friends – Multiple perspectives• Pay close attention to hints – Sometimes

there’s more to a hint than its surface meaning• Don’t be afraid to guess• Keep a checklist of what elements of the puzzle

you have/haven’t used yet (not foolproof)• Try to think from the writer’s perspective

The ΣUMS Commandments

• Minimal extraneous information• Minimal ambiguities (in clues, answers, etc.)• No specialist knowledge required• No repeated mechanics (i.e. from other puzzles)• All steps should be motivatable• Hints should ideally be written such that they

help solvers stuck at any step• Meta should require majority of puzzles solved

More ΣUMS Commandments

• Puzzles solvable without using title/story• Everything needed is contained in the PDF (static)• Minimise number of research/casebash puzzles• Meta: disallow backsolving and involve story• Range of puzzle types and difficulties• Thematic mechanics/presentation/title/answer• Enjoyable intuitive leap – if solving the puzzle

wasn’t fun, we’ve failed

Bad Example: Disc – Julian Assange (MUMS 2004)

Bad Example: Disc – Julian Assange (MUMS 2004)

Writing Puzzles

• Start with an idea/theme and build the puzzle naturally around it

• Test every iteration with new people• Write good hints (difficult!)• Be aware of the other puzzles – Is your mechanic or theme too similar to another?– Does the Meta enforce any requirements?

Example: Porcus – Sean Gardiner (ΣUMS 2010)

• Idea: Pig Latin pairs (e.g. wrecks X-ray)• Theme: Pigs! • Expand: Pigpen cypher –

• Restrictions: – Not many Pig Latin pairs– Can only use letters A-R to avoid cheating– Want the answer to be pig-related

Example: Porcus – Sean Gardiner (ΣUMS 2010)

Example: Porcus – Sean Gardiner (ΣUMS 2010)

• Refinement: – Adjusted some of the clues to be fairer– Removed the alphabetic ordering restriction to

include a better hint– Changed black/white to pink/green (to avoid

people trying to mix colours – minimise confusion)– Changed rocks to “biscuits” (more thematic)

Example: Porcus – Sean Gardiner (ΣUMS 2010)

References

• CiSRA Puzzle Competition:– http://puzzle.cisra.com.au/

• MUMS Puzzle Hunt: – http://www.ms.unimelb.edu.au/~mums/puzzlehunt/

• ΣUMS Puzzle Hunt: – http://www.maths.usyd.edu.au/u/sums/puzzlehunt