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Problemist Diary 5: A merry-go-round tale of problems

by Satanick Mukhuty - 05/07/2019

When a beginner is just starting his journey into chess, it is mostly the visual appeal of the game that seduces him and keeps him going. The understanding of deeper intricacies comes much later, initially it is just the way pieces move on board, the vivid patterns they create is what spark off interest. In the present article, the author Satanick Mukhuty, takes you back to this primal fascination. The topic is Rundlauf , a distinctly geometric theme, and there are five problems - all masterworks by giants of composition. So put your thinking caps on and dive in!   

Problemist Diary Part V - Rundlauf

'Round-trip' would be the most suitable English equivalent of the German word Rundlauf. In the context of chess problems, the term describes the return of a piece to its initial square as in the diagram position by means of a circuitous route. The piece might sometimes traverse a well-defined geometric shape (eg: square, triangle etc), other times it might be a completely weird roundabout path. As a basic example let us consider the following theoretical endgame position:


White to play and win

The Black king has the opposition here and is keeping the white king out. However, if White had the opposition (that is, if it were Black to move in the position) then the black king would have to move away from d7 and allow the white king to make progress

White's winning plan thus consists of carrying out a triangulation with his king and losing a tempo in the process. After 1.Ke5 Kc6 2.Kd4 Kd7 3.Kd5, the same position has been reached with the difference that now it is Black's turn. Note 1.c6+? Kc8 2.Kd6 Kb8 instead would have been only a draw.

Note the white king has carried out a triangular movement to return to its original square and has lost a tempo in the process so that now its Black to move!

In the position above, the black king has to move from d7 after which White wins easily. Triangulation is a known technique in endgames and is the simplest example of a Rundlauf maneuver. But apart from this its occurrence is quite rare in over-the-board play, for moving a single piece multiple times in a loop is seemingly quite a counterproductive act. In chess problems however this effect (owing to its paradoxical nature) is realized with great pomp. Let us begin by looking at a pristinely economic rendition of the theme with a bishop.


Stefan Schneider, Deutsche Schachzeitung 1956, 1st Prize

White to play and mate in 10 moves

The solution begins with 1.Ba4 threatening Bd7#, Black parries with 1...Kf5 and after 2.Bd7+ Ke4 3.Be8 White is again threatening mate in 1 on g6!

White subjects his adversary through a systematic series of mate threats

The play continues 3...Kf5 4.Bg6+ Ke6 5.Bh5 and now Bxg4# is threatened!

The white bishop continues to nag the black king!

Next comes 5...Kf5 6.Bxg4+ Ke4 7.Bd1 threatening Bc2#

The bishop has travelled all around the board to return to its original square c2

With 7...Kf5 8.Bc2+ Ke6 the bishop completes its Rundlauf, but to what end? 

Observe the starting position was the same, only there was a pawn on g4 ... How does this make a difference? 

Well, without the g4 pawn here comes 9.f5+ Kxe5 10.f4# an exquisite pawn mate!

The bishop did all that (rectangulation if you will) to dislodge the g4 pawn and facilitate this stunning mate with a pawn!

The next problem we see is another masterpiece achieved with slender force but this time showing the theme with a knight!


A.Shuriakov & V.Syzonenko, Chervony Girnik 1985

White to play and mate in 12 moves

Here, the starting position is similar to that in Problem 1, the centralized knights on e5 and d6 limit the black king's flight. The key move is 1.Ne8 threatening Nf6#, Black is forced to move 1...Ke4 and the play also continues in the same vein, with white threatening a series of mate-in-1s: 2.Nf6+ Kf5 3.Nh5 (Threat: Ng3#) 3...Ke4 4.Ng3+ Kd5 5.Nxe2 (Threat: Nc3#) 5...Ke4 6.Nc3+ Kf5 7.Nb5 (Threat: Nd6#) 7...Ke4 8.Nd6+ Kd5 and the knight has completed its trip!

After 8...Kd5 the position is same as in the beginning but the pawn on e2 has been snapped off ... How does this make a difference?

Now White can go 9.Nd3! threatening Nb4#, earlier with the black pawn on e2 this could be simply defended by e1=Q, but now Black has to go 9...Kc6 and after 10.d5+ Kc7 (10...Kxd5 11.Nb4+ Ke5 12.f4#) 11.Nb4 there is no way to prevent 12.Na6#

After 11.Nb4 Black finds itself in an unfortunate situation, there is no way to avoid 12.Na6#



Now here is a mind-boggling production by the first German Grandmaster of chess composition Hans Peter Rehm. It shows a pair of rook rundlaufs (yes, a pair!) with amazing perfection!


Hans Peter Rehm, Deutsche Schachblätter 1977, 1st Prize

Mate in 10

The solution begins with 1.Rg6 (threatening Be6#) Black must vacate the c6 square for the king, but how? 1...Rb6 runs into 2.Rg4 after which Rxd4# can't be stopped, so by elimination the best move for Black is 1...Ra6, the play continues 2.Rg4 Be4 3.Rxe4 Ra4 (Note 2...Ra4 right-away leads to quicker mate with 3.c4+ Rxc4 4.Rg6 Rc6 5.Be6#) 4.c4+ Rxc4 5.Re6 Rc6 and both the rooks have completed their round-trips. Now what? 

The position after 5...Rc6 is (almost) same as in the beginning but now there's no bishop on h1 ... Can you see the difference it creates?

The play goes 6.Rg6 Ra6 once again, and then comes 7.Rg4 Ra4 8.c4+ 

Position after 8.c4+ ... What happens if Black takes the pawn en-passant?

8...dxc3 (e.p) runs into 9.Rxa4 and now 10.e4# can't be prevented. So the mainline goes 8...Rxc4 and now comes the final blow 9.Rg6 threatening 10.Rxd6#

With 9.Rg6 it is game over for Black, because now 9...Rc6 takes away the Black king's flight square and allows 10.Be6# 

A brilliant stratagem by a brilliant composer!


The problem we have now is in spirit akin to the king triangulation idea we have seen in the beginning of this article!


René Jean Millour, The Problemist 2004, 1st-2nd Prize

White to play and mate in 20

In the above position a mate is set with Nxc3 if the black bishop ever leaves the b4 square. Therefore the only mobile pieces Black has is the bishop on h3 and the pawn on g7, if White manages to put these two pieces off the board then the bishop on b4 will be forced to move and Nxc3# will then follow! So how does White go about executing this plan? Well, check it out below for yourself!

The white king carried out two picturesque trips along the above lines to bring his plans to fruition. A fascinating work of art by the great French composer René Jean Millour!

So, we saw four renditions of the rundlauf theme with Bishop, Knight, Rook, and King. To bring this to a successful completion we must also have a queen rundlauf. We pose the next problem as an unsolved exercise for you to think about. It's not difficult and that it involves a queen rundlauf should be a big hint!


 Erik Gustav Schultz, Tidskrift för Schack 1904, 1st Prize


White to play and mate in 4

About the author

Satanick Mukhuty is an author and social media manager at ChessBase India. He has a background in Mathematics. He is an avid enthusiast of composition chess and is sincerely committed to promoting it around the world.

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