Puzzle Theory

The following theory is entirely my own work, including the example puzzles… for which I apologize.

Past efforts to classify puzzles have focused on the few specific puzzle types that have been given names (cryptogram, lipogram, anagram) or the context of the puzzle (dialogue puzzle, timing puzzle, machinery puzzle, escape puzzle). Instead I focus on core puzzle mechanics that are common to a wide variety puzzles.


A puzzle, for our purposes, is a word, phrase, object, image or concept which is hidden in such a way that it may be uncovered, with the intention that the process of uncovering it will be entertaining.

All puzzles are based on facets of the human psyche in which we are prone to misinterpreting our environment. For instance, many words with different spellings and meanings sound alike when spoken. This confusing inconvenience can be used to create a puzzle:

Unscramble “Knot – Oar – Weather.”

Puzzles play on those niches in the day to day human experience between certainty and the unknown where frequent errors occur. Any error common to humans in general can be turned into a puzzle. Illusions work in the same way, illusions trigger those aspects of the human interpretation of the senses that consistently fail to correctly convey reality. Puzzles are a catalog of the limitations and weaknesses of the human mind. Perhaps the reason solving puzzles is enjoyable is because we are hardwired to receive pleasure when we overcome our weaknesses.


Quantitative Puzzles: 99.9% of all puzzles are quantitative, that is to say, they have a specific, verifiable solution. When the solution is found the finder instantly knows it.

Example: A showy city slicker just now has moved in to his timber-built lake home. 4 – 3 – 2 – 1 – What is his name?

Qualitative Puzzles: A rare few puzzles are qualitative, or open-ended. The puzzle itself doesn’t define the solution, merely the general parameters of the solution. Once a solution is found, it may be improved upon or another solution found.

Example: You have to retrieve a bundle of bananas hanging loosely from a hook twelve feet off the floor using only three items, none of which may weight more than 2 ounces. Which items do you choose? How do you do it?

Interpretive Puzzles: Rarer still, are interpretive puzzles. These puzzles have a specific solution, however that solution is a concept, and therefore must be interpreted by the solver. By nature concepts have a range of acceptable ways of capturing the idea. So several fairly different descriptions of the solution may all be correct in capturing the gist of the concept.

Example: In a room on a table is a clean place setting including a fork, a knife, a cup, a glass, and a bowl. On the wall is a sign that says, “No shoes, no shirt, no service,” and another says, “Tuesday: Oysters on the half shell.” Also on the table are three receipts, the top one is labeled “Monte Carlo Hotel” and has handwritten on it “Card declined.” On a counter behind the table is a glass bowl with a tiger on it. In the bowl are 31 gumdrops. Behind the table is a man with a roll of money in his hand.


[While Christopher Manson makes use of every form of puzzle mentioned here, he makes masterful and frequent use of interpretive puzzles. While it is likely that he is not the first person to make use of interpretive puzzles, MAZE is the only example I have come across so far - with the possible exception of some of the metaphorical elements of Chris Consani's paintings.]


While there are an infinite variety of puzzles, almost all appear to be based on seven core principles: commonality, majority/minority, similarity exchange, similarity conjoin, progressive sequence, disrupted sequence, and blank disguise.

Collective commonality:

The goal of this kind of puzzle is to find the common denominator between several seemingly disparate items that (unlike majority/minority) is not present in the items by themselves. Usually this commonality can be described in a word or phrase, though occasionally (in the case of some video games) it is a physical object or symbol.

Example: Hot ___ Ice ___ Out ___ Boat ___

Similarity exchange: 

The basic idea is to replace an item with another with which it has a similarity. This most often appears in word puzzles. The similarity can be classically defined such as a homophone, homonym, homograph, heterograph, heteronym, heterophone, or any of the twenty defined but yet unnamed types of word similarities.

Example: Two people are assessing some macaroni. One says, “Too sticky.” The other agrees. One says, “Too slimy.” The other agrees. One says, “Too tubey.” The other says, “Tubey? It is not!” “Yes,” says the first, “it is!” “Is not!” “Is too!” “Is not!” Etc.

In a word based similarity exchange puzzle the similarity must be within certain bounds or the “puzzle” is reduced to gibberish. But in a visual, virtual, or descriptive similarity exchange puzzle the similarity may take a more conceptual form. The following example is, obviously, a descriptive similarity exchange puzzle:

Example: A short time-lapse movie shows people making boxes when it is light outside (as visible through the windows) but at night the factory lays dormant. The movie is looped to show the passage of night and day continually.

Similarity conjoin:

In this type of puzzle items that share a commonality are linked to form a solution (unlike in collective commonality) not based the that commonality. In this kind of puzzle the various items are in some manner pieces of the solution. These pieces are identified as being pieces of the puzzle by some common factor, though this commonality need not be more complicated than the items being grouped together.

Example: On a desk is a book that says, “Learn your letters A to Z!” Next to this is a safe whose combination you need. Also on the table is bowl of fruit, in particular a pineapple, an  apple, and a pear.

Pattern recognition – disruption or repair: The point of a pattern recognition puzzle is to, you guessed it, recognize a pattern. These kinds of puzzles are sometimes referred to as logic puzzles. This is somewhat of a misnomer since all the puzzles require some degree of logic to solve.

At a minimum a pattern involves three items but has no maximum (“1…3″ is not a pattern, “1…3…5″ is a pattern). Pattern recognition puzzles have two kinds of solutions, those in which the solver must fill in the missing portion of the pattern (usually at the end), and those in which the solver must disrupt the pattern in some way.

For instance whenever you try to open a door, it barely moves causing clanking noise behind you. Behind you are a series of gears attached to a wall. Seeing the gears as the cause and following the series of gears back to the problem involves recognizing the pattern. Fixing the problem mechanism will involve repairing the pattern. The newly repaired pattern allows the gears to move freely. Conversely the gears may be functioning normally and thus keeping the door shut. In this case the task is to disrupt the pattern.

In word puzzles pattern recognition almost always involves repairing the sequence. For instance, words that leave out letters (transdeletion), words that add bogus letters (transinsertion) or words in which the letters are mixed up (anagram). Since language is by its very nature a pattern, any puzzle that involves repairing a word or sentence from available letters or words is a pattern recognition puzzle.

Example: Two keep you safe – “PSAESCSUWROIRTDY”

Majority/Minority: A simple version of the pattern recognition puzzle in which the answer is either “these not those” or “yes versus no.” The solution to this kind of puzzle is based on either the majority (odd-one-out) or the minority (odd-one-in) being the correct choice. Which of these is correct is based the context/rules of the puzzle.

Odd-one-in – When the goal is the minority item the puzzle is akin to the classic game of Sesame Street fame, “Which one of these is not like the other, which one of these is not quite the same.”  There are four sandwiches with various toppings but one sandwich has mustard and the others have mayonnaise. The mustard sandwich is the correct choice.

Odd-one-out – The inverse of odd-one-in, in the odd-one-out the majority items are the correct choice.

Example: You need to hire some writers for your newspaper. You have narrowed it down to three applicants. When asked to write as sentence to describe themselves, they wrote, ”Sturdy, hardworking, and determined.” “Hangs loose and goes with the flow.” “Takes, chances, and risks.” Which ones do you offer to hire?

Blank disguise: A blank disguise puzzle involves masking the prize with a veiling substance. The goal of a blank disguise puzzle is to find the hidden item(s).

The “Where is Waldo?” puzzle books are based blank disguise. Finding Waldo in the picture is a challenging because of the vast amount of “not Waldo” flotsam on every page. Hidden object puzzles are one of the oldest and also most common puzzles in world. Hidden object drawings frequented advertisements in the mid to late 1800′s, and were also sold in Europe and the U.S. on greeting card size prints.

Word puzzles based on blank disguise a fairly new invention and are far less common. Words can be masked by inverting letters, making letters look like parts of the background, darkening the word so that it is barely view-able, hiding the word in a pile of letters, etc. (Note: If any part of the word is omitted or its sequence interrupted then it is a pattern recognition puzzle as well.)

Example: \\/|-||73 2/-\\/3^


Almost all puzzles can be described using combinations of these core principles. Puzzles often include non-puzzle aspects which change the experience, such as shooting a basketball through a hoop or learning to operate a machine. These inclusions are not new types of puzzles but do expand and often enhance the experience of solving the puzzle. Having a count down to a bomb going off adds drama to a puzzle, but being able to tell time, or having to hurry does not change the core principle of the puzzle.

While I have found that the vast majority of puzzles can helpfully be described using these principles, there are no doubt core principles I am missing. Feel free to suggest additions.


Puzzle Answers:

Answer to first riddle above: “Whether or not.”

Answer to quantitative puzzle above: “Justin Timberlake.” (Four words omitted) “just” (three words omitted) “in” (two words omitted) “timber” (one word omitted) “lake.”

Answer to qualitative puzzle: Could be anything. Personally I would go with bubble gum and string. I would put a wad of bubblegum on the end of the string and toss it at the banana stem. When it stuck I would walk in a circle to loop the string around the top of the bundle, and then yank. My third item would be a little cool whip, it tastes good on bananas.

Answer to the interpretive puzzle: The man is some kind of con artist. Here is the evidence: Monte Carlo Hotel + card denied + three receipts = Three card monte, a card game scam. Tiger + 31 gumdrops + counter = A card game con called “scat” or “31.” Tiger droppings are called “scat.” The goal of scat is to count to 31 (“counter” + 31 gumdrops). Oysters on the half shell + Tuesday (3rd day of the week) + empty bowl, cup, glass + no shoes, no shirts, no service = the shell game con. Three empty vessels, three “no”s, half shells on the 3rd day of the week.

Answer to the collective commonality puzzle: “House.”

Answer to the word similarity exchange puzzle: “To be or not to be?” (“Tubey” sounds like “To be.”)

Answer to the similarity conjoin puzzle: The combination is “5 – 4 – 9.” When you order the three fruit in alphabetical (“A to Z”) order and count the letters you get 5 “apple” 4 “pear” and 9 “pineapple.”

Answer to the visual similarity exchange puzzle: “Boxing Day.”

Answer to the pattern recognition puzzle: “Security password.” The words are mixed every other letter. P s A e S c S u W r O i R t D y

Answer to the majority/minority puzzle: The first two get the job since the last one misused a comma, disrupting the intended meaning of the sentence.

Answer to the blank disguise puzzle: “White Raven.” The word was disguised using a variant of an alphaic substitution known as “Leet” (“1337″).  \\/=W  |-|+H  |+I  7=T  3=E   2=R  /-\=A  \/=V  3=E  ^=N