science

Futoshiki

Futoshiki is a science 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 Futoshiki rather than just read about it. In short: Futoshiki (不等式, futōshiki), or More or Less, is a logic puzzle game from Japan. Its name means "inequality".

Key takeaways

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

Reference excerpt

Futoshiki (不等式, futōshiki), or More or Less, is a logic puzzle game from Japan. Its name means "inequality". It is also spelled hutosiki (using Kunrei-shiki romanization). Futoshiki was developed by Tamaki Seto in 2001.

The puzzle is played on a square grid. The objective is to place the numbers such that each row and column intersection contains only one of each digit. Some digits may be given at the start. Inequality constraints are initially specified between some of the squares, such that one must be higher or lower than its neighbor. These constraints must be honored in order to complete the puzzle.

Strategy Solving the puzzle requires a combination of logical techniques. Numbers in each row and column restrict the number of possible values for each position, as do the inequalities. Once the table of possibilities has been determined, a crucial tactic to solve the puzzle involves "AB elimination", in which subsets are identified within a row whose range of values can be determined. Another important technique is to work through the range of possibilities in open inequalities. A value on one side of an inequality determines others, which then can be worked through the puzzle until a contradiction is reached and the first value is excluded. A solved futoshiki puzzle is a Latin square.

Futoshiki in the United Kingdom A futoshiki puzzle is published in the following UK newspapers:

The Daily Telegraph — Saturdays Dundee Courier — daily i — Mondays through Fridays The Guardian — Saturdays The Times — daily

Notes

Illustrations

Worked examples

Example 1 — a first encounter with Futoshiki

Start with the simplest possible case. Write down what Futoshiki claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 Futoshiki 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 Futoshiki 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 Futoshiki

In research: Futoshiki appears in science 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 Futoshiki 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: Futoshiki is common in secondary-school and first-year university syllabi. It links to neighbouring topics Japanese board games, Latin squares, Logic puzzles, so understanding it makes those chapters shorter.
In everyday life: Look for Futoshiki 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 Futoshiki in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Futoshiki 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 Futoshiki out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Futoshiki in simple terms?

Futoshiki (不等式, futōshiki), or More or Less, is a logic puzzle game from Japan. Its name means "inequality".

Why does Futoshiki matter?

Because it connects several science 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 Futoshiki?

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 Futoshiki.