Thinking About A Puzzle
by Allen Rabinovich
I wrote these notes to remind myself how to solve puzzles. The ideas recited here were actually tested in battle — at least by me — and what’s perhaps even more important, is that there were times when I forgot them, and later regretted it.
I’ve tried to organize these in order by use, starting with what I think a puzzle constitutes, and continuing on through the steps that go into solving it. At the end, I’ve included some less connected, random ideas.
For starters, what is a puzzle?
A puzzle, in essence, is a problem. A problem starts with given conditions and asks you to derive a particular result. Finding the path from what’s given to what you are being asked for is problem solving, an ability driven by the highest functions of the human brain. (side note: did you know that “solve” means almost the same thing as “dissolve”? Both derive from Latin solvere, which stands for “to unfasten”). What’s even cooler is that problem solving is also a problem (“Given a problem, how do you solve it?”)—and that’s the one we want to look at here.
What’s special about a puzzle, as opposed to any old problem?
Well, a few things:
1. Minimalism. A puzzle is like a good boss: it doesn’t tell you what to do (unless it’s a duck konundrum). Most problems we encounter on the daily basis have predefined sets of steps that are almost guaranteed to lead to a solution (those steps were not always there: they were found by problem solvers who came before us). A puzzle is more like a research problem: there may be a few obvious steps you can take (if you have a crossword, solve it!), but the full path to the solution is still unwritten (and won’t be for months after the hunt ends!)
2. Obscurity of data. A puzzle is also like a car salesman: it’s hiding something from you. In some cases, getting to the hidden information is straightforward (this is what’s referred to as “data mining”: find the names of people whose photos appear in the puzzle; fill in the blanks in lines of song lyrics). In other cases, extracting the necessary data is a riddle on its own (You get a photo. What do you look for? The content depicted? CMYK values? Don’t ask me, I am just a set of notes.)
3. Human design. A puzzle creator is a human: just like you. They have similar notions of beauty and elegance, appreciation of rhymes in puzzle structure, cultural backgrounds, and, very importantly, similar constraints. Remembering that every puzzle has an author is crucial — I’ll talk about this further down.
So where do I start?
Before you can solve the problem that is your puzzle, you need to establish what’s given to you. As we just explained, what’s given is not likely to be given for free — you have to extract it. Here are some thoughts on data extraction:
1. A puzzle always comes to you on a medium. Look carefully and start by concentrating on the medium that carries the puzzle data. Is it a web page? A piece of paper? A disk? A plaster skull? A mysterious black box? Every medium has interesting properties that need to be explored. A web page has a source file. An image, in addition to its content, has multiple ways of representing its pixels. A sound may have some meta-information associated with it; it also has a graphical representation.
2. The data presented to you has a structure. Mindfully establish what it is. Do you have three columns of numbers? Do you have a 19x19 grid? Do you have pairs of something? Start thinking about what’s commonly associated with a particular structure. A 19x19 grid may be a game of Go. A set of binary data could be ASCII, or Morse, or a picture if you squint at it. The initial structure may not mean much, or it may mean everything. As you get “first hunch” ideas, write them down. “First glance” ideas are often good — you may want to give them a chance later. I’ll discuss structure some more, when we get to analyzing the data.
3. Do things that are straightforward first. If there is a set of word clues, solve them. If there are snippets of music, identify them.
4. Always be on the lookout not only for what’s there, but also for what is not. An ordinary looking paragraph may have missing letters that spell a word. A web page may have hidden text that completely changes the puzzle. A street-grid based game of chess might be missing a side street, in which case certain moves may be disallowed. Even things that look perfectly ordinary might be hiding something. “WISE” could be telling you to replace “W” with “E”; “MORE” could be suggesting that the letter you are looking for is either “M” or “E”.
5. In the same vein, take clues from strangeness. Strange things are usually a good sign that there’s treachery afoot. Are there strange words in otherwise regular sentences? Is the grammar awkward? Are there strange line breaks? Our minds are very good about detecting strangeness, so be vigilant and don’t throw away any suspicions.
6. Treat everything as data. The title of the puzzle is important. The flavor text—even more so. The fact that there are thumbnails leading to full images is also a potentially valuable piece of information. Even things that seem like errors could be important (unless they are actual errors, which are possible, but hopefully rare.)
7. Carefully organize all the data you find. Use spreadsheets, graph paper, magnets on a fridge, whatever it takes. If you have a sloppy handwriting, type it up, or let someone else write it down. This is so serious you cannot afford to forget it. Often just carefully organizing the data will make the path to the solution absolutely transparent.
8. Obscurity is a possibility. If you look at a piece of data, and have no idea what to do with it, it may just be you. If 5, 10, 15 people looked at it and had the same response, you may be dealing with something very obscure. Don’t just Google it. Yahoo it, Bing it, Ask.com it. Look for it in books that are very old. Ask your parents. Ask people who watch a lot of TV, and those who don’t watch it at all. Ask people of a different nationality, gender, age, ethnicity, and even sexual orientation (I once drafted a puzzle based on styles of Cher’s wigs; the poor souls who had to solve it took hours mining for data; I know at least 10 very gay people who could have cracked the whole thing in under a minute. She wears the shiny red one only for “Take Me Home”. Duh.) Ask John Smith or Jane Doe or Ben Bitdiddle. If they don’t know, you are fucked, but it’ll just make you feel better about your not knowing.
9. Treat the puzzle like a lemon. Keep squeezing it for data, then leave it alone for a bit, then come back and squeeze some more. You want to get every drop out.
10. If you are anywhere near a meta, look for missing pieces. What you have may simply be insufficient to get the data—so always keep in mind that there are other pieces either already found or waiting to be found. If you got numbers that look like FM frequencies, someone better remember that as a result of solving another puzzle, you got an FM radio. If you don’t, this may cost you a victory (true story).
I think I have all the data I can possibly get out of this thing, neatly arranged and prepared. What do I do next?
You analyze what you have and look for paths to the solution. Herein lies the heart of the dragon: the most interesting and groovy part of the puzzle. There isn’t a single strategy to approach this step, but here are some ideas and common points to keep in mind:
1. Patterns and structure. There is that word again—structure. To produce an answer, your data needs to be massaged and manipulated, until it spells out that magic word that clearly wants to be called in. The data frequently contains many hints on how to proceed, and pattern recognition is something we are good at, so you and puzzles make a great match. Ask yourself:
a. What is the relationship between individual elements in my data set? Do they have something in common? Is there something unique about each? Now ask the same question pairwise, triplewise, etc.
b. How can I group the data? Are there two or three-dimensional structures? Are there pairs of things arranged around a circle? 2x3 rectangles? Does the data contain any obvious delimiters?
c. How can I arrange the data? Alphabetically? Numerically? By color? By age?
d. Are there overlapping/hidden patterns? Say you have chess figures, but there are 26 of them left, so maybe they just represent letters of the alphabet.
e. Are there any “fractal” structures? If you have a puzzle where the key to data extraction was finding a list of singers from names of songs, and that list spelled out the name of a song, the answer better be the name of the artist.
f. Is there uniqueness? Does this maze have just one way to get through it? Is there only one way to play this game of Scrabble?
2. Always ask: “What data hasn’t been used yet?” In more than one case, this question helped me when I was pretty stuck.At the point when you are asking that question, some piece of data that wasn’t useful at the start could have easily been slightly forgotten—this will help you shake up the sand box and bring what you need to the surface.
3. Understand constraints. Data can be constrained by many different parameters, and it’s important to understand what those parameters are. Try to think about the data in terms of how it can conceivably be used. Do you have images of items? The names of those items, as well as their positions in the images could matter. Did you have seven snippets of song lyrics that mentioned colors? You can probably use these to arrange something else — but that’s about it. Also consider which constraints are important. If something is alphabetized, then the current order probably doesn’t matter; however, there may be an ordering based on some other aspect of your data. There exist other constraints: impossibility, for example. If you have a big batch of Morse data without delimiters, it’s practically impossible to decode it. Either you are missing delimiters, or you are not looking at Morse.
4. Think like the puzzle author. I find this technique very useful. When I am a little perplexed about a puzzle, I take a step back, and think: how would I write this puzzle? What’s the great idea that everyone on my writing team thought was good enough to go into the final set? Where is the elegant bit? What about the complex part? Is there something that may seem obvious to me and my team, but not to others? How can I provide clues to the solver to lead them to solution, but gently, without prodding?Most of these are things you will be thinking about anyway, but actually asking yourself how you would do them gets your gears going faster.
5.Keep all ideas on the table. Let’s say you had a good idea on how to go about the puzzle, but it doesn’t seem to pan out. That’s okay. Put it aside and try something else, but don’t throw it away. Log all ideas where everyone solving the puzzle can see them (e.g., the puzzle server!) If something else works, fine; but if you will go through many ideas and give up, keeping track of what you did would prove extremely useful, both for you and for someone else. In fact, things you’ve tried can lead you or someone else to the solution—sometimes all it takes is a brain that had a good night’s sleep.
Never let anyone tell you that “this just won’t work”. Pessimists tend to give up too early, but just saying something doesn’t make it true. It’s good to work in a team and listen to your teammates, but always use your own brain.
6. Is this a puzzle of some sort? (© Meepa) — look for humor. Sometimes the puzzle writer just really wants you to have fun. Don’t overcomplicate things without need. If you got “Rethponth/Tholution” as your data, you need to chuckle and call in the ANTHER.
7. Account for stupidity. There are three possible sources of stupidity:
a. Your own. CHECK YOUR WORK. A good friend of mine once said that if he were to write a guide on how to solve puzzles, that’s all he would say. So, let me say that again:
CHECK YOUR WORK.
Mistakes happen: it’s not a big deal. Anyone can misread, mistype, look up the wrong pope or see a cat and think they saw a tiger. It’s not stupid to make mistakes, but it IS stupid not to go back and check for them.
Of course, it helps not to make them in the first place. It helps to:
- Type rather than write (or write very neatly),
- Tabulate what you can,
- Use graph paper,
- Crosscheck multiple sources.
b. Another solver’s. Sometimes I do something stupid, get stuck on a puzzle, and then lose interest. Then, someone else takes over, and here’s what they should do: first, check my work. Then look at what I’ve already done and ask: “What did Allen do wrong? Oh wait, that’s not a ‘WOW’, that’s ‘MOM’ upside down. Your mom…”
c. The author’s. Sometimes, a puzzle is just badly written. It happens, especially if the author is a beginner, or has written too many puzzles and ran out of ideas. Here, it helps to go back to that advice about thinking like an author, and add this question: “If I were running out of ideas, what stupid thing could I invent that would have something to do with this data?” Try to do things that are painfully non-obvious: read in the direction nobody thought is reasonable to read in, remove all vowels, type the whole thing into Google, read the author’s blog, or, if this puzzle is really in the gutters, anagram.
8. Have fun. If you are not having fun with a puzzle, then move to a different one. If you are tired, take a break, or get sleep. But do not let yourself dread what you are doing. You win Mystery Hunt by having fun; if you are not having fun, you are not playing by the rules.