So far, themed tournaments are not my cup of tea. But I appreciate geometric ideas and have tried to
implement them thematically.
Figure 1.What would you think of a study where a white knight has to choose this route? That would be great, right?
Does something like this already exist?
In Petrov's famous chess problem ("The Retreat of Napoleon I from Moscow") there are two white knights which perform the hunt (see below).
In EG 214 (October 2018) there is a study of Ignace Vandecasteele
(Schakend Nederland 1983) with an interesting knight journey (also shown below).
(Unfortunately, Vandecasteele's study is cooked. Martin Minski informed me that the author added a black pawn on b3, saving the idea. But I have no source for it. Either way, there is a lot of passive material in this study, since in the mainline of the solution only the white knight and the black king move.)
Let's see two more examples.
The one on the left is a study by Gerhard Josten (4th commendation MatPlus 2008) and the one on the right is by Yuri Bazlov (2nd prize draw section, Mikitovics 70 JT 2019). The grey color is used to indicate that most of this knight journey happened in a variation, but not in the mainline.
If you know other examples, I would be happy to get to know them.
The German word Rundlauf consists of the German words for 'round' and 'run'. This term is sometimes used to describe roundtrips. Here are the examples I found in endgame studies from the ARVES page.
The first example is by János Mikitovics (3rd Prize UAPA, 8th Foguelman-95 MT) and shows the rundlauf of a white rook.
The second example is by Richard Becker & Iuri Akobia (1st special honorable mention, 2nd UAPA TT 2015) and unlike all the other examples, it shows the rundlauf of a black piece.
The third example is due to P. Gyarmati & E. Eilazyan (8th commendation, JRI 80 JT) and shows the rundlauf of a white queen.
These examples suggest that the piece has to return to a previously visited square. But also the fourth example (Iuri Akobia, 4th commendation MatPlus 2008) shows, according to the comments, a knight's rundlauf.
Since none of the examples come close to Figure 1, we can perhaps make some compromises for the time being. Here are a few characteristics of the perfect tour that could be lessened.
- It is closed, that is, the starting square is identical to the ending square.
- It is highly symmetrical.
- It is convex.
- It has a significant size.
Mitigating point 4 is the easiest. But small circles of, say, four knight moves are neither rare nor impressive. So this point should remain and it could even be strengthened. The knight in Figure 1 visits two rims and comes close to the two other ones. What about a knight tour visiting three or even all four rims? (But please no tour from a1 to h8 or something like that.)
In the last few months I have been looking for such knight tours from time to
time, but I've always limited the material to NP vs PP.
I have seen many tours and one or two may be submitted as studies and hence they are not yet published
here. But a few other examples can be shown.
The first example shows a tour that could have been the end of my search.
White to move and win.
1. Ng3+ Kf4 2. Nh5+ Kg5 3. Ng7 Kf6 4. Ne8+ Ke5 5. c5! f5 6. Nd6 f4 7. Nxb7 f3 8. Na5 Kd4 9. Nc4 f2 10. Nd2 Kd3 11. Nf1 Ke2 12. Ng3+ and wins.
But there is something irreparably wrong: On the eighth move, the knight can also go back to d6 (and next to c4). Normally, this could probably be assessed as a minor alternative-square-dual, but since the tour is theme, it has to be considered as a
full-grown cook here.
The scheme can be changed at the beginning and the end, as shown in the next two diagrams, but the problem remains.
Here are a few tips.
White to move and win.
Positions with three passed pawns are less promissing, I believe.
(Because of some minor duals, the moves of the example are omitted.)
White to move and win.
A poorly chosen starting point for the knight cannot be repaired.
1. Ne7+ Kg5 2. Nd5 Kg4 3. Ne3+ Kf4 4. Kc1 Ke4 5. Ng4 Kd3 6. Kd1 Kd4 7. Nf2 Kc4 8. Kc1 Kc5 9. Kb2 Kb4 10. Nd3+ Ka4 11. Kc1 Ka5 12. Kd1 Kb5 13. Ke1 Kc4 14. Nb2+ Kb4 15. Kf2 Ka3 16. Nd1 Ka2 17. Kxf3 1-0
White to move and win.
Some starting points can still surprise you.
Unfortunately, this tour is more of a business trip than sightseeing.
(Don't waste time on this: there are duals too.)
White to move and win.
If the white king and knight both take on one pawn, then there's possibly nothing more than a small tour.
(Because of some minor duals, the moves of the example are omitted.)
Addendum 13 September 2023:
I found one more known example.
Peter Krug
18th UAPA, 1st commendation, section B.1
White to move and win.
For more details please see the award.