| No.351 Lev Grolman (Russia) & Georgy Evseev (Russia) |
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No.351 by Lev Grolman & Georgy Evseev – Cyclical Zilahi in a play of 6 Nightriders (3 white and 3 black)! (JV)
Definitions:
Grasshopper(G): Moves along Q-lines over another unit of either color to the square immediately beyond that unit. A capture may be made on arrival, but the hurdle is not affected.
Nightrider(N): A Rider along a straight line on squares lying a Knight`s move away from each other.
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No.351 Lev Grolman & Georgy Evseev
Russia
original-22.07.2013
 h#2 3 solutions (10+13)
Grasshoppers: a1,d1,g1,e3,f3,g3,е8 Nightriders: b1,c2,d3,e5,e6,e7 Solutions: (click to show/hide)
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Very clever, reminds of this one: http://www.yacpdb.org/?id=43512
I wonder if fourth-battery with fourfold cycle can be arranged if the rear piece is from hopper family already? Like:
white PAa3 Gb3c3d3e3 Pg3, black Kg4
One grasshopper is eliminated, one departs to guard/interfere, one checkmates and one stands still to guard h3 and serve as a hurdle for pao.
🙂 The authors have given the same problem as a prior realisation of the idea in orthodox H#
That’s hilarious 🙂 I didn’t click the ‘Solution’ link until now, in the morning i simply set up the position on computer to move the pieces around.
Yes, the cycle is very clever and these Nightriders look nice on the diagram. Still, wNe5 could be wS and in 2 solutions wSe7 would be enough. For the solutions, bNd3 coud be bS but it is a cookstopper.
Also wGe3 is only a hurdle when wNd5 guards c3. It is a helpmate and white economy matters the most. Adding bGa3 and bPa7 (-wPb7) would give a true function to wNe7 and wGe3 after 1.Nxe5 Na5!
No, your idea is faulty, as Na5 guards c1 and then Ga1 has no function at all. So, hurdle function is still better. Unfortunately, we were not able to find correct position with wPe3.
Yes, for that reason I started with bGa3, wPb3 and wSe5 but after putting wNe5 back I forgot about it, it was so easy to eliminate new cooks by removing wPb3 :), I apologize.
Anyway, after seeing how many potential cooks there are, the realization looks as a miracle. You two must have been very patient, determined, skilful and imaginative to achieve the delicate balance of correctness with all these pieces. I bow to that.
I am still a bit ‘too optimistic’, perhaps some change in the scheme might naturally eliminate some cooks which come with this scheme. After all, wNe5 could indeed be replaced by wS. I know that it’s hard for the author to abandon the original concept (3+3 N’s), but the true content of this problem is a play of 3 bN’s, 2 wN’s and 1 wS (in disguise). So, in the very essence, there is no true cycle of 3+3 N’s.
I can’ see why wS would be less worthy or interesting, except for a superficial visual effect.
About the theme of cyclical Zilahi – play of 6 Nightriders (3 white and 3 black) I`ve some old problems, one of them is the following:
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I.1.Nxe4 Ne3 2.Nf6 Nxf7#
II.1.Nxd3 Nec5 2.Nf4 Nxd4#
III. 1.Nxc2 Ndc5 2.Nf8 Nxg8#
Cyclical Zilahi here without Switchbacks but with reciprocal cyclical captures between black and white Nightriders, plus Bivalve. In my opinion in analogical conceptions the Switchback is theoretically also possible but in practical aspect it follow to unaesthetic constructions because of many cooks. From the other hand, I am not confident that the switchbacks are the best additional motives here.