mathematics

Mathematical puzzle

Mathematical puzzle is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Mathematical puzzle rather than just read about it. In short: Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules, but they do not usually involve competition between two or more players.

Key takeaways

Mathematical puzzle belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Mathematical puzzle to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Mathematical puzzle from memory before moving on to harder problems.

Reference excerpt

Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules, 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. Many of the puzzles are well known because they were discussed by Martin Gardner in his "Mathematical Games" column in Scientific American. Mathematical puzzles are sometimes used to motivate students in teaching elementary school math problem solving techniques. Creative thinking – or "thinking outside the box" – often helps to find the solution.

List of mathematical puzzles

Numbers, arithmetic, and algebra Cross-figures or cross number puzzles Dyson numbers Four fours KenKen Water pouring puzzle The monkey and the coconuts Pirate loot problem Verbal arithmetics 24 Game

Combinatorial Cryptograms Fifteen Puzzle Kakuro Rubik's Cube and other sequential movement puzzles Str8ts a number puzzle based on sequences Sudoku Sujiko Think-a-Dot Tower of Hanoi Bridges Game

Analytical or differential Ant on a rubber rope See also: Zeno's paradoxes

Probability Monty Hall problem

Tiling, packing, and dissection Bedlam cube Conway puzzle Mutilated chessboard problem Packing problem Pentominoes tiling Slothouber–Graatsma puzzle Soma cube T puzzle Tangram

Involves a board Conway's Game of Life Mutilated chessboard problem Peg solitaire Sudoku Nine dots problem

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 Slitherlink

Mechanical

Rubik's Cube Think-a-Dot Matchstick puzzle

0-player puzzles Conway's Game of Life Flexagon Polyominoes

References

External links Historical Math Problems/Puzzles at Mathematical Association of America Convergence

Worked examples

Example 1 — a first encounter with Mathematical puzzle

Start with the simplest possible case. Write down what Mathematical puzzle claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Mathematical puzzle before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Mathematical puzzle ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Mathematical puzzle

In research: Mathematical puzzle appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Mathematical puzzle in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Mathematical puzzle is common in secondary-school and first-year university syllabi. It links to neighbouring topics Mathematical puzzles, Recreational mathematics, so understanding it makes those chapters shorter.
In everyday life: Look for Mathematical puzzle outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Mathematical puzzle in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Mathematical puzzle means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Mathematical puzzle out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Mathematical puzzle in simple terms?

Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules, but they do not usually involve competition between two or more players.

Why does Mathematical puzzle matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Mathematical puzzle?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Mathematical puzzle.