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MatPlus.Net Forum General Longest unique king walk in a seriesmover?
 
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(1) Posted by James Malcom [Monday, Jan 18, 2021 19:46]

Longest unique king walk in a seriesmover?


Most long seriesmovers involve the king treading back and forth on the same footpath. They are always long, but never unique, in that each square is visited only once. So, what is the longest "unique" king walk in a seriesmover?

I did some cobbling, and produced this. I found nothing as long in PDB from my searches.

ser-Za1 34, aka White moves to a1
(= 7+10 )

1 Ka6 24. Kxc8 26. Kxa8 30 Kxe4 32. Kxc3 33. Kxb2 34. Ka1

At 33 squares for the king route, this is just more than half the board.
 
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(2) Posted by Hauke Reddmann [Monday, Jan 18, 2021 21:22]

I can only say I *did* see such, and I estimate
the record on about at least double as much...
Unfortunately I can't deliver.
(Used the same technique of guard chains and
bishop swing doors...)
 
 
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(3) Posted by Joost de Heer [Monday, Jan 18, 2021 22:41]

@Hauke: There are king marches of 100+ moves, but what Rewan wants to show is that during the king walk, each square is reached exactly once. Doube of 33 would be 66, and there are only 64 squares on the board..
 
   
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(4) Posted by Hauke Reddmann [Tuesday, Jan 19, 2021 10:47]

Oh, sorry, I did understand it wrong. Obviously, the other
king marches went for longevity records.
 
   
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(5) Posted by James Malcom [Wednesday, Jan 20, 2021 04:12]

I've bumped it up to 35 now.

ser-Ze1 35
(= 4+14 )

1. Kf1 6. Kxa1 16. Kxe8 21. Kxh5 23. Kxh3 24. Kxh4 25 Kxg3 27. Kxh1 31. Kxd5 33. Kxc3 34. Kxd2 35. Ke1

EDIT: And 36 with a promoted bishop.

ser-Ze1 36
(= 4+15 )

 
   
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(6) Posted by Ján Golha [Wednesday, Jan 20, 2021 09:30]

40 moves

White Kg1
Black Sd8 Re8 Pc6 Kf6 Sd5 Pe5 Pc4 Ph4 Pc3 Pg3 Rh3 Pd2 Ba1 Bh1
 
   
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(7) Posted by Joost de Heer [Wednesday, Jan 20, 2021 10:35]

Ján's position as diagram:
(= 1+14 )

ser-ze140
But d7 is visited multiple times.
 
 
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(8) Posted by Joost de Heer [Wednesday, Jan 20, 2021 19:51]

@Rewan: pawn on h5 seems to be unnecessary. Furthermore, the three white pawns can be replaced with one single black pawn on c4.
 
   
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(9) Posted by Ján Golha [Thursday, Jan 21, 2021 12:00]

(= 1+15 )


ser-ze136

1.Kg1-f1 2.Kf1-e2 3.Ke2-d1 4.Kd1-c2 5.Kc2-b1 6.Kb1*a1 7.Ka1-a2 8.Ka2-a3 9.Ka3-a4 10.Ka4*a5 11.Ka5-a6 12.Ka6-b7 13.Kb7-c8 14.Kc8-d8 15.Kd8-e8 16.Ke8-f8 17.Kf8-g8 18.Kg8*h7 19.Kh7-h6 20.Kh6-h5 21.Kh5-g4 22.Kg4*h3 23.Kh3*h4 24.Kh4*g3 25.Kg3-h2 26.Kh2*h1 27.Kh1-g2 28.Kg2-f3 29.Kf3-e4 30.Ke4*d5 31.Kd5*c4 32.Kc4*c3 33.Kc3-d3 34.Kd3*e3 35.Ke3*d2 36.Kd2-e1 z
 
   
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(10) Posted by Joost de Heer [Thursday, Jan 21, 2021 12:10]

Then this should be possible too:

(= 1+16 )

ser-ze138
(f1 is visited only once during the solution)
 
   
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(11) Posted by James Malcom [Thursday, Jan 21, 2021 20:18]

Well done, Ján and Joost; 38 is exceptional.
 
   
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(12) Posted by Nikola Predrag [Friday, Jan 22, 2021 01:57]

(= 2+14 )
ser-zh840
 
   
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(13) Posted by James Malcom [Friday, Jan 22, 2021 02:28]

Bravo! By the way, for math's sake, 55 squares is the max possible, since the BK take out 9 squares.

EDIT: Oh, and using the same trick...

ser-Zh8 41
(= 2+15 )

 
   
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(14) Posted by Nikola Predrag [Friday, Jan 22, 2021 04:52]

This is not the same trick on f8, only on e8.
 
   
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(15) Posted by James Malcom [Friday, Jan 22, 2021 05:11]

Yes it is the same trick. The squares are just different, so your point is?
 
   
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(16) Posted by Nikola Predrag [Friday, Jan 22, 2021 06:46]

Your point of the task.
 
 
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(17) Posted by Joost de Heer [Friday, Jan 22, 2021 13:03]

BK takes out 3 squares when in the corner.
 
 
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(18) Posted by Joost de Heer [Friday, Jan 22, 2021 13:05]

f8 is visited twice in the version with the king capturing the queen.
 
   
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(19) Posted by James Malcom [Saturday, Jan 23, 2021 19:19]

You're correct, so 40 is the current known length.
 
   
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(20) Posted by Nikola Predrag [Saturday, Jan 23, 2021 20:15]

There's 41 looking promising for more but so far, I've got only 42 with legal 3 bSs and illegal 43 (8 bPs & 3 bSs, no bQ).
 
   
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MatPlus.Net Forum General Longest unique king walk in a seriesmover?