Although there are many types of puzzles, most aim to bring order out of chaos, or to find the underlying sense in what appears to be nonsense. Puzzles can be generally grouped into word puzzles, math puzzles, and mechanical puzzles, but that leaves out a number of puzzles that don't fit neatly into a particular type.
Logic problems mix math and language, because the first order of business is for the solver to figure out just what a solution requires and to understand the puzzle's language. Once translated, the solver will likely use a mathematical sort of elimination to find a solution.
Picture puzzles are a type of puzzle that doesn't involve words or math, or don't involve math as most people understand it.
Lateral thinking puzzles depend on psychology for their difficulty, utilizing human blind spots to hide a solution. Therefore, solving a lateral thinking puzzle may bring considerable insight. Interesting, the solver may think. But then, most puzzles are.
Here are some of the main types of puzzles:
Crosswords, double acrostics, and clever British crosswords (in which solving the clues depends on wordplay) are tests of vocabulary. Although they come in varying degrees of difficulty, solvers may also challenge themselves by doing only the across clues, or by working in pen.
Riddles and conundrums are word puzzles that play with meaning. A conundrum, for example is a word puzzle to which the solution is a pun: When is a door not a door? When it's ajar.
Codes and logic problems
Ciphers and codes, like logic problems, are somewhere between math and language, at least at the puzzle-page level, because hobby solvers will often rely on the frequency of the letter "e," for example, or the probability of a certain word's appearance to speed their solution, as well as on their vocabulary. Cracking codes in Mastermind, on the other hand, involves logic, but no words. Higher-level codes, though, are entirely reliant on math.
Logic is math, and people who succeed at logic problems are better at math than they may know. Logic problems are one of the most popular forms of puzzle, and happily keep solvers up at night.
Many math puzzles resemble the word problems of grade school. Solved with algebra or perhaps a bit of logic, the first step is translating the word problem into the language of math.
Puzzles that require a boater to get her cats and birds across the river without any creature escaping or being eaten, are also plainly math. Because these problems ask the solver to work out a path, they resemble an abstract maze.
Geometry also comes into play with puzzles that ask solvers to divide up land, or to share dinner or an inheritance.
Mechanical puzzles are some of the most pleasurable toys. Puzzle boxes delight children, and Rubik's Cubes entertained a generation. The Hanoi Tower, which requires solvers to move sets of rings, has fascinated people for centuries.
Sliding puzzles, in which pictures or sentences are scrambled within a frame, are mechanical puzzles as well.
Jigsaws can appeal to the sense of order of small children, or can frustrate vacationers for days. The difficulty seems to grow exponentially as the number of pieces increases. Jigsaws can be solved upside down if they seem too easy, or without reference to the picture on the box.
Mazes are picture puzzles too, because solvers map out a visible path. So are connect-the-dots, and puzzles that ask solvers to spot the differences in pairs of pictures.
Lateral thinking puzzles
These are almost always logic problems, but can be anti-logic too. The puzzle's inventor means to subvert the form, to make the familiar processes of abstraction and deduction useless to the solver. The intention is to get the solver to cut the Gordian knot of the problem.
While most puzzles encourage the solver to aim for the solution, discarding answers that don't work, a lateral thinking puzzle encourages the solver to think about a problem in new ways, perhaps creating many solutions that might work rather than arriving at The Answer.
Whether based in words, math, mechanical contrivances, pictures, or some hybrid, all types of puzzles delight those who enjoy discovering a hidden pattern. Ancient puzzles were often wrapped in legend because of the way they seemed to expose and explain the secret order of the world.
Modern solvers who spend hours working on their favorite types of puzzles may learn nothing, not even the solution, but they certainly can have all kinds of fun trying.
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