Mathematical puzzle

This article is about puzzles that require mathematics to solve them. Often mathematical puzzles are referred to as mathematical games, but here mathematical games such as tic-tac-toe are multiplayer games whose rules, strategies, and outcomes can be studied and explained by mathematics. Note that the players may not need to use mathematics to play mathematical games.

Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules as do multiplayer games, but they do not usually involve competition between two or more players. Instead, to solve such a puzzle, the solver must find a solution that satisfies the given conditions.

Mathematical puzzles require mathematics to solve them. Logic puzzles are a common type of mathematical puzzle.

Conway's Game of Life and fractals, as two examples, may also be considered mathematical puzzles even though the solver interacts with them only at the beginning by providing a set of initial conditions. After these conditions are set, the rules of the puzzle determine all subsequent changes and moves.

List of mathematical puzzles

The following categories are not disjoint; some puzzles fall into more than one category.

Numbers, arithmetic, and algebra

• Cross-figures or Crossnumber Puzzle
• Dyson numbers
• Four fours
• Feynman Long Division Puzzles
• Pirate loot problem
• Verbal arithmetics

Combinatorial

• Cryptograms
• Fifteen Puzzle
• Rubik's Cube and other sequential movement puzzles
• Sudoku
• Think-a-Dot
• Tower of Hanoi

Analytical or differential

• Ant on a rubber rope

See also: Zeno's paradoxes

Probability

• Monty Hall problem

Tiling, packing, and dissection

• Mutilated chessboard problem
• the generic Packing problem
• tiling Pentominoes
• Tangram
• Slothouber–Graatsma puzzle
• Conway puzzle
• Bedlam cube
• Soma cube
• T puzzle

Involves a board

• Life
• Sudoku
• Mutilated chessboard problem
• Peg solitaire

Chessboard tasks

• Eight queens puzzle
• Knight's Tour
• No-three-in-line problem

Topology, knots, graph theory

The fields of knot theory and topology, especially their non-intuitive conclusions, are often seen as a part of recreational mathematics.

• Disentanglement puzzles
• Seven Bridges of Königsberg
• Water, gas, and electricity

Mechanical

Main article: Mechanical puzzle

• Rubik's Cube
• Think-a-Dot
• Many others

0-player puzzles

• Flexagon
• Life
• Polyominoes

External links

• Historical Math Problems/Puzzles at Convergence