Logic puzzle
Encyclopedia
A logic puzzle is a puzzle
deriving from the mathematics
field of deduction
.
. In his book The Game of Logic he introduced a game to solve problems such as confirming the conclusion "Some greyhounds are not fat" from the statements "No fat creatures run well" and "Some greyhounds run well". Puzzles like this, where we are given a list of premises and asked what can be deduced from them, are known as syllogism
s. Dodgson goes on to construct much more complex puzzles consisting of up to 8 premises.
In the second half of the 20th century mathematician Raymond M. Smullyan
has continued and expanded the branch of logic puzzles with books such as The Lady or the Tiger?
, To Mock a Mockingbird
and Alice in Puzzle-Land. He popularized the "knights and knaves
" puzzles, which involve knights, who always tell the truth, and knaves, who always lie.
There are also logic puzzles that are completely non-verbal in nature. Some popular forms include Sudoku
, which involves using deduction to correctly place numbers in a grid; the nonogram, also called "Paint by Numbers", which involves using deduction to correctly fill in a grid with black-and-white squares to produce a picture; and logic maze
s, which involve using deduction to figure out the rules of a maze.
s dedicated to the subject, is a format in which the set-up to a scenario is given, as well as the object (for example, determine who brought what dog to a dog show, and what breed each dog was), certain clues are given ("neither Misty nor Rex is the German Shepherd"), and then the reader fills out a matrix with the clues and attempts to deduce the solution. These are often referred to as "logic grid" puzzles. The most famous example may be the so-called Zebra Puzzle
, which asks the question Who Owned the Zebra?.
Common in logic puzzle magazines are derivatives of the logic grid puzzle called "table puzzles" that are deduced in the same manner as grid puzzles, but lack the grid either because a grid would be too large, or because some other visual aid is provided. For example, a map of a town might be present in lieu of a grid in a puzzle about the location of different shops.
This type of puzzle is often included on the Law School Admissions Test (LSAT).
Puzzle
A puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to put together pieces in a logical way in order to come up with the desired solution...
deriving from the mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
field of deduction
Deductive reasoning
Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...
.
History
The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the author of Alice's Adventures in WonderlandAlice's Adventures in Wonderland
Alice's Adventures in Wonderland is an 1865 novel written by English author Charles Lutwidge Dodgson under the pseudonym Lewis Carroll. It tells of a girl named Alice who falls down a rabbit hole into a fantasy world populated by peculiar, anthropomorphic creatures...
. In his book The Game of Logic he introduced a game to solve problems such as confirming the conclusion "Some greyhounds are not fat" from the statements "No fat creatures run well" and "Some greyhounds run well". Puzzles like this, where we are given a list of premises and asked what can be deduced from them, are known as syllogism
Syllogism
A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...
s. Dodgson goes on to construct much more complex puzzles consisting of up to 8 premises.
In the second half of the 20th century mathematician Raymond M. Smullyan
Raymond Smullyan
Raymond Merrill Smullyan is an American mathematician, concert pianist, logician, Taoist philosopher, and magician.Born in Far Rockaway, New York, his first career was stage magic. He then earned a BSc from the University of Chicago in 1955 and his Ph.D. from Princeton University in 1959...
has continued and expanded the branch of logic puzzles with books such as The Lady or the Tiger?
The Lady or the Tiger?
"The Lady, or the Tiger?" is a much-anthologized short story written by Frank R. Stockton for publication in the magazine The Century in 1882. "The Lady, or the Tiger?" has come into the English language as an allegorical expression, a shorthand indication or signifier for a problem that is...
, To Mock a Mockingbird
To Mock a Mockingbird
To Mock a Mockingbird and Other Logic Puzzles: Including an Amazing Adventure in Combinatory Logic is a book by the mathematician and logician Raymond Smullyan. It contains many nontrivial recreational puzzles of the sort for which Smullyan is well-known...
and Alice in Puzzle-Land. He popularized the "knights and knaves
Knights and knaves
Knights and Knaves is a type of logic puzzle devised by Raymond Smullyan.On a fictional island, all inhabitants are either knights, who always tell the truth, or knaves, who always lie. The puzzles involve a visitor to the island who meets small groups of inhabitants...
" puzzles, which involve knights, who always tell the truth, and knaves, who always lie.
There are also logic puzzles that are completely non-verbal in nature. Some popular forms include Sudoku
Sudoku
is a logic-based, combinatorial number-placement puzzle. The objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 sub-grids that compose the grid contains all of the digits from 1 to 9...
, which involves using deduction to correctly place numbers in a grid; the nonogram, also called "Paint by Numbers", which involves using deduction to correctly fill in a grid with black-and-white squares to produce a picture; and logic maze
Logic maze
Logic mazes, sometimes called 'mazes with rules', are logic puzzles with all the aspects of a tour puzzle that fall outside of the scope of a typical maze. These mazes have special rules, sometimes including multiple states of the maze or navigator...
s, which involve using deduction to figure out the rules of a maze.
Logic grid puzzles
Another form of logic puzzle, popular among puzzle enthusiasts and available in magazineMagazine
Magazines, periodicals, glossies or serials are publications, generally published on a regular schedule, containing a variety of articles. They are generally financed by advertising, by a purchase price, by pre-paid magazine subscriptions, or all three...
s dedicated to the subject, is a format in which the set-up to a scenario is given, as well as the object (for example, determine who brought what dog to a dog show, and what breed each dog was), certain clues are given ("neither Misty nor Rex is the German Shepherd"), and then the reader fills out a matrix with the clues and attempts to deduce the solution. These are often referred to as "logic grid" puzzles. The most famous example may be the so-called Zebra Puzzle
Zebra Puzzle
The zebra puzzle is a well-known logic puzzle. It is often called Einstein's Puzzle or Einstein's Riddle because it is said to have been invented by Albert Einstein as a boy; it is sometimes claimed that only 2% of the population can solve it....
, which asks the question Who Owned the Zebra?.
Common in logic puzzle magazines are derivatives of the logic grid puzzle called "table puzzles" that are deduced in the same manner as grid puzzles, but lack the grid either because a grid would be too large, or because some other visual aid is provided. For example, a map of a town might be present in lieu of a grid in a puzzle about the location of different shops.
This type of puzzle is often included on the Law School Admissions Test (LSAT).
See also
:Category:Logic puzzles, a list of different logic puzzlesExternal links
- Hankies, Snarks, and Triangles – Ivars PetersonIvars PetersonIvars Peterson is an award-winning mathematics writer.He is currently Director of Publications for Journals and Communications at the Mathematical Association of America....
's MathTrek - Logic grid numbers and pictures puzzles by Quisoft