Generally speaking, a puzzleis any task which satisfies two properties:

- It is designed to entertain the solver.
- There is a well-defined solution.

This can be accomplished through many methods!Here are a few such categories of puzzle types that I’ve come acrossin my work.

*By the way, thanks for checking this page out and not one of the dozenknock-offs folks have written (or generated via AI) after this pagehappened to get popular in search results. You can check out my ownpuzzle projects at the link above, or contact me directlyif you’re looking for a consultantto create puzzles for your next project.*

## Cryptic puzzles

Example: the first two puzzles on my puzzle homepage.

These are the most common type of puzzles found in quality puzzlehunts andescape rooms, and enthusiasts consider these challenges to be simply “puzzles”Such puzzles might alternatively be called “designer” puzzleswhich are meant to be solved at most once by a given person, since part of thepuzzle is the epiphany required to see an extraction technique. Note that“cryptic crosswords” (often just called “cryptics”) are a type of word puzzle that doesn’t really fit thisdefinition (although the overlap of cryptic puzzle and cryptic crosswordfans is non-trivial!).

In a cryptic puzzle, the ultimate goal/answer typically should bewell-defined (i.e. enter a certain word or phrase into an online form which isaccepted; find a clue to a location where a previously designated token can be found).However, the mechanics of extracting this solution are left partially or completely vague,and it’s up to the solver to guess at several interpretations of what the puzzlecould mean until one fits. Often the puzzle’s title or its flavortext canhide clues to this extraction: “you’d be **blind** to not know how to solve this”might be a (not-so) subtle clue to look for a way to find **Braille letters**in the puzzle.

Designing such puzzles takes a lot of practice, in addition to knowledge ofyour audience. Different communities expect different levels of difficulty,and different players will have different levels of “genre savviness”.These are by far my favorite type of puzzle to design and solve, but it’s hard to tell at a quick glance if such a puzzle is a high-quality difficult cryptic puzzle, or just badly written.

## Logic Puzzles

Examples include Sudoku,nonogram,calcudoku,Masyu, andlogic grid puzzles.

A logic puzzle is typically characterized by a grid which must be completed byfollowing some well-defined rules. Generally such puzzles have a unique solution(a property which itself helps the solver filling the grid). Often thesepuzzles may be made easier by partially filling out the puzzle for the solver.I’m a particular fan of picross puzzles (also called nonograms) because the solutionpaints a picture (i.e. gives the solver new information unrelated to the propertiesof the puzzle itself).

## Math Puzzles

Arguably, these come in two varieties.

### Explicit

Given \(xy=6\), \(xz=10\), and \(yz=15\), find the value of \(xyz\).

What distingishes these from math *problems* in that a mathpuzzle is meant to be recreational, orperhaps competitive. These puzzles typically don’t lend themselves to algorithmicsolutions; at least, not algorithms which are traditionally taught in school, anyway.See also: AMC comeptitions, Putnam problems, and other traditional math competitions.

By the way, the trick in the example is to not try to solve for `xyz`

, but first tryto solve for `x^2y^2z^2`

… It’s a fun puzzle the first time you hear it, but thetop competitors in these competitions memorize hundreds of tricks just like that.So ironically, while these puzzles are typically designed to challenge students’mathematical abilities, the optimal strategy for solving such puzzles is tomemorize a large backlog of tricks and gimmicks, and figure out what slight variationis required for the puzzle at-hand.

### Implicit

You’ve developed a new social networking platform, and you plan to support100 users for your beta release. Each user can be “friends” with every otheruser. How many “friendships” does your social network’s database need to beable to store?

Rather than explicitly asking a mathematical “solve for \(x\)” question,a modern math puzzle paints a narrative, and leaves the application ofmathematics up to the solver.

For instance, since the first user could haveup to 99 friends, the second user could have up to 98 *other* friends,and so on, we find that the answer is:

\[99+98+\dots +2+1=4950\]

But that might be hard (and we could make it completely infeasible byupping the number to a thousand, or million users).In that case, players are forced into making the clever observation that each of the 100 users can have 99 other friends, but sincethat’s double-counting friendships we should divide this product by two:

\[\frac{100\times 99}{2}=4950\]

Of course, if you know some graph theory, you could also approach this problem by expressing it as agraph and asking yourself “how many edges are in the complete graph with 100vertices?”. This illustrates that a good modern math puzzle can both challenge and teachmathematics,without explicitly being posed as a “solve for \(x\)” math problem.

It’s worth noting that this puzzle is very close to being a mathematical “word problem”.And if it was given in the context of a course on combinatorics, it would be!But unless you were taught about triangular numbers in class just yesterday,the point of the challenge isn’t to test your memorization of the formula\(\sum_{k=0}^n k=\frac{n(n+1)}{2}\),but to challenge your problem-solving and mathematical modeling abilitiesto come up with your own patterns and formulas.

## Mechanical Puzzles

Examples include jigsaw puzzles, nail puzzles, Rubik’s Cubes.

Probably the most common variant of puzzle; I expect most puzzlers consider ajigsaw piece as the “logo” for puzzling. These can be solved through trial-and-error,but particularly for Rubik’s cube-type puzzles there can be mathematical/logicalmethods for a solution as well.

## Trivia puzzles

Similar to cryptic puzzles, trivia puzzles usually have custom designs (otherwise,they’re just plain trivia). While trivia puzzles often have cryptic elements, such a puzzlemay also be explicit (in which case, it might also be a type of word puzzle). In any case, the player must have some domain knowledge to solve such puzzles,or the ability to learn about the topic.

Novice escape room designers often fall into the trap of including trivia puzzlesin their challenges, which would be very disappointing for a player stuck in a roomfor 60 minutes just because they were rusty on (say) ABBA’s discography!However, I often find myself enjoying trivia puzzles even when they involve domainsI’m not very familiar with: just make sure I have a way to look up the solutions asneeded, and preferably have a secondary challenge beyond the trivia once I’veincorporated the solutions.

## Word puzzles

Examples include crosswords, Boggle.

Word puzzles are puzzles which require knowledge of a language. Most word puzzles areactually mathematical in nature assuming a dictionary is available; for example,there are 120 ways to permute the letters in a five-letter word without repeated letters,and there are 104 possible three-letter words in a 4 by 4 grid of letters.

The line gets blurred a bit with crossword puzzles; technically (as was pointed outby fellow puzzler Christopher Night) crosswords may have multiple answers and areup to interpretation (like pattern puzzles). In general, word puzzles which are basedon defintions have a bit of flexibility (unless there’s a way to check the solution),so designing them takes finesse.

On the other hand, puzzles like Places Pleaseare actually logic puzzles, even though they use words! This is because no priorknowledge of words is required, as they are all provided. Instead, players mustsimply use logic to find how these words can be used to fill out the grid.

A couple related concepts:

## Pattern Guessing

Example:

What comes next in the list? 1, 2, 4, …

These is not typically well-defined puzzles. Especially egregious are“which picture comes next in the pattern” Mensa-type questions.I’ll point out that in the example,both \(f(n)=2^n\) and \(g(n)=\frac{n^2+n+2}{2}\)satisify the requirements\(f(0)=g(0)=1,f(1)=g(1)=2,f(2)=g(2)=4\), yielding equally reasonable guessesof \(f(3)=8\) and \(g(3)=7\), respectively.

## Riddles

Example:

A man and his son are involved in a car accident. The father dies, but the sonis taken to the hospital. The doctor refuses to operate, saying “I cannotoperate on my son!” How can this be?

Riddles don’t fit my definition of a puzzle since there’s no definite logically-deduced solution. Note that there are a few answers to the above riddle:“The doctor is the mother!” “The son has two fathers!” etc. etc. These may be fun to ponder in a low-stakes environment, butare bad form in any sort of competition such as puzzlehuntsor escape rooms.

To learn more about me or my work with puzzles,please visit my Aboutand Puzzle pages, or you can learn more about myBooks.