One type of induction puzzle concerns the wearing of colored hats, where each person in a group can only see the color of those worn by others, and must work out the color of their own.
Part of a series on
Puzzles
Types
Guessing
Riddle
Situation
Logic
Dissection
Induction
Logic grid
Self-reference
Mechanical
Combination
Construction
Disentanglement
Lock
Go problems
Folding
Stick
Tiling
Tour
Sliding
Chess
Maze (Logic maze)
Word and Number
Crossword
Sudoku
Puzzle video games
Mazes
Metapuzzles
Topics
Brain teaser
Dilemma
Joke
Optical illusion
Packing problems
Paradox
Problem solving
Puzzlehunt
Syllogism
Lists
Impossible puzzles
Maze video games
Nikoli puzzle types
Puzzle video games
Puzzle topics
v
t
e
Induction puzzles are logic puzzles, which are examples of multi-agent reasoning, where the solution evolves along with the principle of induction.[1][2]
A puzzle's scenario always involves multiple players with the same reasoning capability, who go through the same reasoning steps. According to the principle of induction, a solution to the simplest case makes the solution of the next complicated case obvious. Once the simplest case of the induction puzzle is solved, the whole puzzle is solved subsequently.
Typical tell-tale features of these puzzles include any puzzle in which each participant has a given piece of information (usually as common knowledge) about all other participants but not themselves. Also, usually, some kind of hint is given to suggest that the participants can trust each other's intelligence — they are capable of theory of mind (that "every participant knows modus ponens" is common knowledge).[3] Also, the inaction of a participant is a non-verbal communication of that participant's lack of knowledge, which then becomes common knowledge to all participants who observed the inaction.
The muddy children puzzle is the most frequently appearing induction puzzle in scientific literature on epistemic logic.[4][5][6] Muddy children puzzle is a variant of the well known wise men or cheating wives/husbands puzzles.[7]
Hat puzzles are induction puzzle variations that date back to as early as 1961.[8] In many variations, hat puzzles are described in the context of prisoners.[9][10] In other cases, hat puzzles are described in the context of wise men.[11][12]
^Stuhlmüller, A.; Goodman, N.D. (June 2014). "Reasoning about reasoning by nested conditioning: Modeling theory of mind with probabilistic programs". Cognitive Systems Research. 28: 80–99. CiteSeerX 10.1.1.361.5043. doi:10.1016/j.cogsys.2013.07.003. S2CID 7602205.
^Lucci, Stephen; Kopec, Danny (2015). Artificial Intelligence in the 21st Century. Stylus Publishing, LLC. ISBN 978-1-944534-53-0.
^Tagiew, Rustam (2008). "Simplest Scenario for Mutual Nested Modeling in Human-Machine-Interaction". KI 2008: Advances in Artificial Intelligence. Lecture Notes in Computer Science. Vol. 5243. Springer. pp. 364–371. doi:10.1007/978-3-540-85845-4_45. ISBN 978-3-540-85844-7.
^Fagin, Ronald; Halpern, Joseph Y.; Moses, Yoram; Vardi, Moshe Y. (March 1999). "Common knowledge revisited". Annals of Pure and Applied Logic. 96 (1–3): 89–105. arXiv:cs/9809003. doi:10.1016/S0168-0072(98)00033-5. S2CID 59551.
^van der Hoek, Wiebe; van Ditmarsch, Hans (2007). Dynamic epistemic logic. Springer. ISBN 978-1-4020-5838-7.
^"Google Scholar "Muddy Children Puzzle"". scholar.google.com. Retrieved 11 February 2020.
^Fagin, Ronald; Halpern, Joseph Y.; Moses, Yoram; Vardi, Moshe (2004). Reasoning about knowledge. MIT Press. ISBN 978-0262562003.
^Hardin, Christopher; Taylor, Alan D. (2008). "An introduction to Infinite Hat Problems" (PDF). Mathematical Intelligencer. 30 (4): 20–25. doi:10.1007/BF03038092. S2CID 24613564. Archived from the original (PDF) on 2012-04-05.
^"The Prisoners' Hats – Puzzles And Riddles". www.puzzlesandriddles.com.
^"Prisoners and Hats Puzzle". CrazyforCode. 13 August 2013.
^"Robots pass 'wise-men puzzle' to show a degree of self-awareness". techxplore.com.
^Leite, João (2005). Computational Logic in Multi-Agent Systems: 5th International Workshop, CLIMA V, Lisbon, Portugal, September 29–30, 2004, Revised Selected and Invited Papers. Springer Science & Business Media. ISBN 978-3-540-28060-6.
Inductionpuzzles are logic puzzles, which are examples of multi-agent reasoning, where the solution evolves along with the principle of induction. A puzzle's...
puzzle. There are different genres of puzzles, such as crossword puzzles, word-search puzzles, number puzzles, relational puzzles, and logic puzzles....
tour puzzles, a sliding block puzzle prohibits lifting any pieces off the board. This property separates sliding puzzles from rearrangement puzzles. Hence...
Disentanglement puzzles (also called entanglement puzzles, tanglement puzzles, tavern puzzles or topological puzzles) are a type or group of mechanical puzzle that...
traditional flat, two-dimensional puzzles, three-dimensional puzzles have entered large-scale production, including spherical puzzles and architectural recreations...
puzzles related to the Monty Hall problem is Bertrand's box paradox, posed by Joseph Bertrand in 1889 in his Calcul des probabilités. In this puzzle,...
Double entendre Language game List of puzzle video games Phono-semantic matching Puns Puzzles Rebuses – picture puzzles representing a word Verbal arithmetic...
dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Inductionpuzzles Trust game Princess and monster game Rendezvous problem Theorems Aumann's...
Combination puzzles Jeu de taquin, an operation on skew Young tableaux similar to the moves of the 15 puzzle Klotski Mechanical puzzles Pebble motion...
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...
Puzzle video games make up a broad genre of video games that emphasize puzzle solving. The types of puzzles can test problem-solving skills, including...
Situation puzzles are often referred to as minute mysteries, lateral thinking puzzles or "yes/no" puzzles. Situation puzzles are usually played in a group...
it. While puzzles of this type have been in use by humanity as early as the 3rd century BC, one of the most well-known mechanical puzzles of modern day...
1000 playthinks: puzzles, paradoxes, illusions & games. Workman. ISBN 978-0-7611-1826-8. Petković, Miodrag (2009). Famous Puzzles of Great Mathematicians...
This is a list of puzzles that cannot be solved. An impossible puzzle is a puzzle that cannot be resolved, either due to lack of sufficient information...
different combinations by a group of operations. Many such puzzles are mechanical puzzles of polyhedral shape, consisting of multiple layers of pieces...
distance Hamming weight Hash collision Hash function Hash list Hash tree Inductionpuzzles Integrity check value Interleaving ISBN ISMN LM hash Lexicographic...
Magical Drop Magnetica Money Puzzle Exchanger Puzzle League series Poker Smash Puzzle Bobble (a.k.a. Bust-a-Move) Puzzle Link, Puzzle Link 2 Wordle Unlimited...
Tiling puzzles are puzzles involving two-dimensional packing problems in which a number of flat shapes have to be assembled into a larger given shape...
The puzzles saw a major increase in general popularity in the late 19th century when newspapers and magazines began running dissection puzzles. Puzzle creators...
want, as you will have solved the puzzle. Sam Loyd's Book of Tangram Puzzles (ISBN 0-486-22011-7) Mathematical Puzzles of Sam Loyd (ISBN 0-486-20498-7):...
typically fixed, but puzzles in which the walls and paths can change during the game are also categorised as mazes or tour puzzles. Mazes have been built...
Another popular examples of the usage of the construction are the inductionpuzzles. And so is Robert Aumann's construction of common knowledge. Jean...
Global Information
