science

Pentago

Pentago 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 Pentago rather than just read about it. In short: Pentago is a two-player abstract strategy game invented by Tomas Flodén. The game is played on a 6×6 board divided into four 3×3 sub-boards (or quadrants).

Key takeaways

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

Reference excerpt

Pentago is a two-player abstract strategy game invented by Tomas Flodén. The game is played on a 6×6 board divided into four 3×3 sub-boards (or quadrants). Taking turns, the two players place a marble of their color (either black or white) onto an unoccupied space on the board, and then rotate one of the sub-boards by 90 degrees either clockwise or anti-clockwise. This is optional at the beginning of the game, up until every sub-board no longer has rotational symmetry, at which point it becomes mandatory (this is because until then, a player could rotate an empty sub-board or one with just a marble in the middle, either of which has no real effect). A player wins by getting five of their marbles in a vertical, horizontal, or diagonal row (either before or after the sub-board rotation in their move). If all 36 spaces on the board are occupied without a row of five being formed then the game is a draw. There is also a 3-4 player version called Pentago XL. The board is made of 9 3×3 boards, and there are 4 colours (red, yellow, green and blue) instead of the basic 2. MindtwisterUSA has the rights of developing and commercializing the product in North America. The 6×6 version of Pentago has been strongly solved with the help of a Cray supercomputer at NERSC. With symmetries removed, there are 3,009,081,623,421,558 possible positions. If both sides play perfectly, the first player to move will always win the game.

Awards Game of the Year 2005 in Sweden Game of the Year 2006 in France Award winner in Mensa Mind Games 2006 Review So far Pentago has won 8 major awards, lastly Game of the Year 2007, by Creative Child Magazine.

References

External links Perfect play explorer online

Illustrations

Worked examples

Example 1 — a first encounter with Pentago

Start with the simplest possible case. Write down what Pentago 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 Pentago 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 Pentago 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 Pentago

In research: Pentago 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 Pentago 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: Pentago is common in secondary-school and first-year university syllabi. It links to neighbouring topics Abstract strategy games, Board game stubs, Board games introduced in 2005, so understanding it makes those chapters shorter.
In everyday life: Look for Pentago 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 Pentago in 20 minutes

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

Frequently asked questions

What is Pentago in simple terms?

Pentago is a two-player abstract strategy game invented by Tomas Flodén. The game is played on a 6×6 board divided into four 3×3 sub-boards (or quadrants).

Why does Pentago 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 Pentago?

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 Pentago.