mathematics

Jan Rusinek

Jan Rusinek 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 Jan Rusinek rather than just read about it. In short: Jan Rusinek (born 2 December 1950) is a Polish mathematician and chess composer, particularly noted for his brilliant endgame studies. He was editor of the study section of Szachy (Chess) from 1971 to the magazine's closure in 1990.

Key takeaways

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

Reference excerpt

Jan Rusinek (born 2 December 1950) is a Polish mathematician and chess composer, particularly noted for his brilliant endgame studies. He was editor of the study section of Szachy (Chess) from 1971 to the magazine's closure in 1990. Rusinek became an International Judge of chess composition in 1983, and a Grandmaster of chess composition in 1992. He won over 30 first prizes in composing tourneys. The Oxford Companion to Chess opines that "his achievements are likely to rival those of his greatest predecessors".

Endgame studies

To the left is one of Rusinek's better known studies. Black threatens Nb5-d6# or Ne4-d6# and 1.Kb7 Bd5+ does not help, so 1.a7 is necessary. Now 1...Bd5 can be answered with, among other lines, 2.g8Q Bxg8 3.a8Q Nxb6+ 4.Kb7 Nxa8 5.Kxa8 Be6 6.Kb8 and Black must give up a piece for the c pawn, so instead 1...Ba6+ 2.b7. Now 2...Nb5 threatens 3...Nd6# but is met with 3.g8N+ Ke8 4.Nf6+ when 4...Nxf6 loses to 5.a8Q. Instead, therefore, Black plays 2...Ne4 3.g8N+! Ke8 4.Nf6+ and now 4...Nexf6 is possible. This seems to put White in a dilemma, since 5.a8Q loses to 5...Nd5 with 6...Ne7# next move. But instead there is 5.a8B!! when 5...Nd5 is stalemate, so therefore 5...Ne5 6.Kb8 Nc6+ 7.Kc8 Bf1 and again White has a problem because 8.b8Q will lose to 8...Ba6+ 9.Qb7 Ne4 10.Qxa6 Nd6#. 8.b8N is no better: 8...Ne7+ 9.Kb7 Bg2+ 10.Ka7 (10.Nc6 Bxc6+ 11.Ka7 Bd7) 10...Nc8+ 11.Ka6 Bxa8. However, white can draw with a third underpromotion: 8.b8R!!. Now after 8...Ba6+ 9.Rb7, 9...Ne4 is stalemate, and there is no useful way for Black to avoid this. White draws.

White's being required to make all three underpromotions in order to draw is exceptionally unusual. In Endgame Magic (Batsford, 1996), John Beasley and Timothy Whitworth comment that it "represents a very much greater feat of composition than might at first appear. That it was accomplished with the use of only nine men adds still more to the composer's achievement." Beasley and Whitworth also comment that "It is quite easy to construct a position in which White must promote to a rook or bishop in order to avoid giving stalemate," but "It is much more difficult to create a position in which White must underpromote to create a stalemate," which is done on two occasions in this study.

Rusinek subsequently (64, 27 July 1978) added an introduction to this study which added a promotion to queen to the already existing underpromotions, thus creating an Allumwandlung. This later version is shown to the right. 1.h8R+ is insufficient, since 1...Ke7 will mate quickly. 1.h8Q+ is therefore necessary, and after the forced continuation 1...Qxh8 2.g7+ Qxg7 3.hxg7+ Ke7, the initial position of the original study is reached. Rusinek himself considered this version inferior to the original (aesthetics versus task).

Articles by Rusinek "Stalemate by pinning in the middle of the board", in EG No. 51 (June 1978) "Studies in the FIDE Album 1986-88", in EG No. 105 (May 1992) "Grzegorz Grzeban, 1902-1991", in EG No. 106 (October 1992)

References David Hooper and Kenneth Whyld, The Oxford Companion to Chess (Oxford University Press, 1992)

External links Jan Rusinek at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Jan Rusinek

Start with the simplest possible case. Write down what Jan Rusinek 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 Jan Rusinek 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 Jan Rusinek 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 Jan Rusinek

In research: Jan Rusinek 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 Jan Rusinek 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: Jan Rusinek is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1950 births, Chess composers, Grandmasters for chess composition, so understanding it makes those chapters shorter.
In everyday life: Look for Jan Rusinek 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 Jan Rusinek in 20 minutes

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

Frequently asked questions

What is Jan Rusinek in simple terms?

Why does Jan Rusinek 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 Jan Rusinek?

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 Jan Rusinek.