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MatPlus.Net Forum Promenade What's your Loyd number?
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(1) Posted by Andrew Buchanan [Tuesday, Jun 16, 2020 07:02]; edited by Andrew Buchanan [20-07-06]

What's your Loyd number?

The Morphy number is a measure of how closely a chess player is connected to Paul Morphy (1837–1884) by way of playing chess games. It's analogous to the Erdős Number for mathematicians. See for example:

I wondered if an analogous concept of Loyd number works. How many links of joint compositions does it take to chain back to Sam Loyd (1841-1911)? Most compositions do not involve multiple composers, but are there enough co-compositions to connect back to the "Reprobate Prince of Puzzlers"? The joint composition must have both individuals composing in the same period - modern versions/corrections of older problems do not count.

Why Loyd? Well, he was a contemporary of and a compatriot of Morphy - I felt it resonated. I wanted to pick someone wayback, to shine a light perhaps on a few overlooked composers back in the distant past, and so happily it proved. By having someone so far back I hoped there would be no a priori bias for location of composers today. It turned out that Netherlanders are a little favoured but that’s just chance - it’s nothing to do with Loyd being American. As you will see, the trail from Loyd was doubtful at first and difficult to discern, but now we have documented sources, primary in key cases. If we'd picked someone more recent and famous then everyone can probably reach them in 2-3 hops: where’s the fun in that?

So: Loyd. I have checked the vast databases of PDB & WinChloe against one another up to generation 5. Problem IDs are denoted P... & W... WinChloe does not seem to offer the capability to copy/paste output, so I used a character recognition app to textify screenshot .jpg files. Not looked at YACPDB so far: maybe someone else could have a check to see if there's anything relevant there. I also looked online, and found the original for Loyd-Keidanski, and also a second Keidanski-Lasker problem - have updated PDB accordingly. Keidanski (aka Keidanz) was a good player. For generations 0-4, ~ denotes the composer has known no other collaborators in later generations.

Generation 0 (1 composer, of course)
Loyd, Samuel (1841-1911)

Generation 1 (1 or 2 composers?)
Keidanski, Theodore Hermann (1865-1938) via P1318466
~ Potter, Joseph Alonso (1837-1859) via C- W451993. Very strange.

So all lineages must pass through the following:

Keidanski & Loyd 1907 (P1318466)
(= 5+3 )

*Not* McKim, J.B. (?-?) via W484758, C-. Discussion in P1213947 makes clear J.B.McKim was the sole author, anticipating Loyd. Both McKim & Loyd have the same cooked diagram, suggesting "one copied the other's homework". But the cook in one is the declared key in the other! I don't know what's going on. Here's a humble fix: J.B.McKim v A.Buchanan 2020 3bB3/4N3/K2k1p2/p2N1Q2/P7/8/8/8 #2. (The original had wSc7 instead of wSe7.)

Neither Potter nor McKim had any other co-authors as far as we know, so these compositions could not affect later generations in any case.

Generation 2 (1 composer)
Lasker, Emanuel (1868-1941) to Keidanski via P1377072 & P1145029

Two documented problems show the link between these players:

Keidanski & Lasker 1906 (P1377072)
(= 4+2 )

Keidanski & Lasker 1908 (P1145029)
(= 10+6 )

Generation 3 (4 composers)
~ Capablanca y Graupera, Jose Raoul (1888-1942)
~ Gabor, Karl (1886-1938)
Teichmann, Richard (1868-1925) via P1031064 & P1061669
Weenink, Henri G.M. (1892-1931) via P1323350=W519274

A single Lasker-Weenink composition (a modest fairy h#2) has a huge impact on the history of chess, as is broadens the tree enormously (especially for Netherlands composers), largely due (as you will see) to the activity of the prolific and gregarious Jan Hartong at generation 4. Amazingly this historic composition was last edited in PDB just a month ago (05/2020)! At that time, Weenink's name was not given as PDB co-author, but just mentioned in a comment concerning a reprint. However, WinChloe has more detailed. I even solved this very problem a month ago, before the Loyd number business was ever dreamed up! Given there are at least 800,000 chess compositions in existence, what are the chances?

Lasker & Weenink 1925 (P1323350)
(= 3+2 )
h#2 (-:

Beginning to broaden out:

Generation 4 (10 composers)
De Koning, Josef J. M. (from Weenink) (1887-1925)
Feigl, Maximilian (from Teichmann) (1871-1940)
Goethart, Gerardus Hendrik (from Weenink) (1892-1969)
Hartong, Jan (from Weenink) (1902-1987)
Krijtenburg, Jacob (from Weenink) (1915-1960)
Nanning, Frederik Willem (from Weenink) (1892-1958)
~ Nanning, Willem (from Weenink) (1870-1932)
Niemeijer, Meindert (from Weenink) (1902-1987)
~ Prins, Lodewijk (from Weenink) (1913-1999)
Przepiorka, Dawid (from Teichmann) (1880-1942)

Henri Weenink collaborated with Jan Hartong on just 2 problems:

Weenink & Hartong 1919 (P1039210)
(= 12+10 )

Weenink & Hartong 1928 (P1023974)
(= 9+10 )

And now we're off to the races, as Hartong co-composed prolifically with all but a handful of the next generation:

Generation 5 (90 composers)
Albarda, Johannes (from Hartong) (1905-1982)
Amirov, Talip (from Hartong) (1931-1983)
Atanasijevic, Aleksandr (from Hartong) (1922-2007)
Bajtay, Jozsef (from Hartong) (1902-1988)
Bakker, P.A. (from Hartong) (?-?)
Bartel, Erich (from Hartong) (b.1930)
Bartolovic, Vojko (from Hartong) (1932-2005)
Batsleer, J. (from Hartong) (?-?)
Bedoni, Romeo, (from Hartong) (b.1927)
Berg, Evert Jan (from Hartong & Krijtenburg) (1901-1939)
Bettman, Henry Wald (from Hartong) (1868-1935)
Biscan, Dragutin; Biscan, Drago (from Hartong) (1923-2004)
Blom, J.K. (from Hartong) (?-?)
Boumeester, Henk B.F. (from Hartong) (1917-2004)
Brenner, Theo (from Hartong) (?-?)
Buchwald, Julius (from Hartong & Nanning, Frederik Willem) (1909-1970)
Burbach, Johannes Jacob (from Hartong & Nanning, Frederik Willem) (1921-2003)
Cheylan, Yves (from Hartong) (b.1938)
Croes, Govert Aliander (from Niemeijer) (1925-?)
Daniel, Arthur William (from Feigl) (1878-1955)
De Jutter, J. (from Hartong) (?-?)
De Koning, H. (from De Koning, Josef) (?-?)
De Vos, F. (from Hartong) (1893-?)
Dijk, Johannes (from Hartong & Nanning, Frederik Willem) (1866-1955)
Drese, Gerardus Hendrikus (from Hartong & Niemeijer) (1902-1980)
Eerkes, Allard Pieter (from Hartong & Nanning, Frederik Willem) (1911-1993)
Ellerman, Arnoldo (from Hartong) (1893-1969)
Elstner, Rudolf (from Hartong) (1893-1966)
Ernst, Georg (from Przepiorka) (1876-1938)
Feldmann, Tibor (from Goethart) (1919-1990)
Fischer, Jan; Fischer, Jean Charles August (from Hartong) (1909-1939)
Franken, Maurits (from Niemeijer) (?-?)
Gradstein, Stephan (from Nanning, Frederik Willem) (1909-?)
Groenveld, Cornelis (from Hartong) (?-?)
Gussopulo, Demetrio (from Hartong) (1900-1980)
Haring, Jacobus (from Hartong) (1913-1989)
Hegermann, Bernhard (from Hartong) (1897-1970)
Hjelle, David (from Hartong) (1903-1978)
Ivanov, Nikolai A. (from Hartong) (1914-2000) (Ivanov, Nikolai E. in WinChloe)
Jaroszynski, Ignacy (from Przepiorka) (1866-1916)
Jessurun Lobo, Johan R. (from Hartong) (1893-1978)
Kamstra, Hendrik Hermanus (from Hartong) (1899-1971)
Kardos, Tivadar (from Hartong) (1921-1998)
Koetsheid, Petrus Albertus (from Hartong) (1882-1961)
Köhnlein, Friedrich (from Przepiorka) (1879-1916)
Korponai, Jozsef (from Hartong) (1931-1987)
Lamboo, Cornelis Henricus (from Hartong) (1910-?)
Larsen, Karl Adolf Koefoed (from Hartong) (1896-1963)
Le Grand, Henk (from Hartong) (b.1935)
Le Grand, Piet (from Hartong) (b.1935)
Limbach, Saturnin (from Hartong) (1909-1984)
Lindemann, W. (from Hartong) (?-?)
Mai, Guglielmo (from Hartong) (1906-1980)
Mandler, Artur (from Feigl) (1891-1971)
Maruta, Hidajat (from Hartong) (1945-?)
May, Luigi (from Hartong) (1903-1970)
Michel, Francois (from Hartong) (1903-1977)
Monreal, Pierre (from Hartong) (1916-2002)
Moutecidis, Pavlos (from Hartong) (b.1930)
Nowotny, Franz (from Hartong) (1827-1871)
Pauly, Wolfgang (from Niemeijer) (1876-1934)
Pepeljajewa, Jelena N. (from Hartong) (1899-1976)
Rasch Nielsen, Poul Anker (from Nanning, Frederik Willem) (1892-1965)
Rietveld, Johannes Jacob (from Goethart) (1893-1968)
Sackmann, Franz (from Przepiorka) (1888-1927)
Salardini, Erio (from Goethart) (1897-1972)
Sanger, J. (from Hartong) (?-?)
Scheffer, J. (from Hartong) (?-?)
Schor, Laszlo (from Niemeijer) (1897-1984)
Seilberger, Johann J. P. A. (from Hartong & Niemeijer) (1896-1962)
Sorokin, Evgeny P. (from Hartong) (1932-?)
Swane, Jan Arnold Willem (from Hartong) (1901-1971)
Taale, Cornelius J. (from Hartong) (1890-?)
Ten Cate, Pieter (from Hartong) (1902-1996)
Termaat, Nicolaas Ijsbrand Johannes (from Hartong) (1909-?)
Terlings te Vucht, Joh. G. W. M. (from Goethart) (?-?) (WinChloe name "Teulings, J." is wrong)
Van Der Linden, A.F.C (from Hartong) (?-?)
Van Dijk, Johannes (from Hartong) (1866-1955)
Van Engelen, Adrianus Cornelis (from Hartong) (1908-1989)
Van Wageningen, R. (from Hartong) (?-?)
Verdonk, Johannes Bernardus (from Hartong) (1892-1974)
Visbeen, Frank (from Hartong) (1937-1996)
Visserman, Eeltje (from Hartong & Nanning, Frederik Willem) (1922-1978)
Weiss, Ottmar (from Feigl) (aka: Nemo) (1861-1942)
Westbury, Eric E. (from Hartong) (1881-1939)
Wilson, Francis Vaux (from Hartong) (1899-1982)
Wilson, W.H. (from Hartong) (?-?)
Wolfs, J.W. (from Hartong) (?-?)
Wrobel, Marian (from Przepiorka) (1907-1960)
Yamanishi, Jorge T. (from Hartong) (1938-?)

This branches out much more slowly than the Morphy number, where amazingly some generation 3 players are still alive today! (My own Morphy number is 4.) It seemed as if the candle might blow out in the early links, but at Loyd number = 5, there are 90 distinct names. For some generation 5 composers, PDB/WinChloe don't hold birth/death years. Any more details would be gratefully received.

Therefore, the lowest Loyd number that a living composer can hold is 5. To the best of our knowledge, Bartel, Bedoni, Cheylan, both the Le Grand twins, Moutecidis and probably a few others are still with us. Bravo!

Among the generation 6 players, Kostas Prentos connects by Moutecidis; while Joost de Heer connects by the Le Grand twins.

The first living composer to determine his Loyd number was Michael McDowell, but now we have more complete data, his number can be improved to 7 via Erich Bartel and Michel Caillaud. By the same route, I can appear in generation 7 too.

In a more competitive vein, Frank Richter proposed (pardon my edits):
You could extend the idea to a [Petkov] number:
X had a higher placed problem than [Petkov] in tourney 1 => Number 1
Y had a higher placed problem than X in tourney 2 => Number 2
Z had a higher placed problem than Y in tourney 3 => Number 3
You had a higher placed problem than XYZ in tourney 123 => Number 123
But this seems to be real challenge for research ;)

This is slightly analogous with Kasparov number, which is the directed/competitive version of the Morphy number. A modern goal point is perhaps best, given that modern tourney results are relatively accessible, it should be possible for anyone to explore their own directed graph, and see if they can transitively pwn Petko Petkov. I leave this labour to others. What I do know is that Petko himself has a Petkov number of 0: congratulations for this fine achievement! It doesn't get any better than that! :)

Gens Una Sumus!
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(2) Posted by Michael McDowell [Tuesday, Jun 16, 2020 09:50]

Off the top of my head I can get down to Wurzburg via Barnes, Mansfield and White, so that would give me a Loyd number of 10.
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(3) Posted by Michael McDowell [Tuesday, Jun 16, 2020 09:55]

I was too quick there. I composed a joint with Edgar Holladay, who made one with Alain White, so that brings me down to 9.
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(4) Posted by Andrew Buchanan [Tuesday, Jun 16, 2020 10:33]

Werner Keym has 8 via Karl Fabel!
So that puts me at 9: thanks to Werner :)
Is there anyone still alive in the 7s?
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(5) Posted by seetharaman kalyan [Tuesday, Jun 16, 2020 10:44]; edited by seetharaman kalyan [20-06-16]

Should be many. I can readily point out Mlynka Karol, Sygurow, Marandjuk
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(6) Posted by Hauke Reddmann [Tuesday, Jun 16, 2020 11:54]

Andrew, I anticipated you with the Milan number ;-)
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(7) Posted by Juraj Lörinc [Tuesday, Jun 16, 2020 11:58]

Ottmar Nemo has in WinChloe db the following data: = Ottmar WEISS (31-10-1861 , 28-04-1942)

Valery Ivanov with most of the connections listed, has on the other hand the following data: (09-10-1953 , )

So the connection seems dubious in my view.
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(8) Posted by Olaf Jenkner [Tuesday, Jun 16, 2020 12:07]; edited by Olaf Jenkner [20-06-16]

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(9) Posted by Andrew Buchanan [Tuesday, Jun 16, 2020 14:14]; edited by Andrew Buchanan [20-06-16]

seetharaman wrote:
Should be many. I can readily point out Mlynka Karol, Sygurow, Marandjuk

Alas the three you list all connect through Ivanov, which is an invalid link.

Hauke wrote:
Andrew, I anticipated you with the Milan number ;-)

With all due respect to Milan, I am more interested in his Loyd number than I would be in Loyd's Milan number, although they must be the same! :D

Juraj wrote:
Ottmar Nemo has in WinChloe db the following data: = Ottmar WEISS (31-10-1861 , 28-04-1942)

Yes I haven't looked at WinChloe for this at all: but maybe someone else can mine it, there are maybe some other paths & early composers to be identified. "Nemo" means nobody, so sounds fishy (which is another meaning of "Nemo" heh)

Valery Ivanov with most of the connections listed, has on the other hand the following data: (09-10-1953 , )

Thanks well spotted: ouch that's a lot of links are gone. I will edit the base note with this!
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(10) Posted by Zalmen Kornin [Tuesday, Jun 16, 2020 16:14]; edited by Zalmen Kornin [20-06-16]

Arthur Napoleão (aka 'Napoleon') had a Problem "touched up by Loyd", can't recall now exactly which one, not even my source for this information.

*Morphy number: There's also the modality
"Beat x in a Classic Tournament Game'. This gives Yours Truly a certified Alekhine number 3 (I beat Fonrobert in the National semifinals in 82, who beat Engels in an IT in the sixties, who beat Alekhine in Dresden 1936. Alekhine beat (for instance) von Bardeleben in Düsseldorf 1908, who beat Paulsen in Frankfurt 1887. Paulsen beat Morphy in 1857, without clocks, but in a National Congress game...
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(11) Posted by Andrew Buchanan [Tuesday, Jun 16, 2020 16:50]; edited by Andrew Buchanan [20-06-16]

Zalman wrote:
Arthur Napoleão (aka 'Napoleon') had a Problem "touched up by Loyd", can't recall now exactly which one, not even my source for this information.

This gent has about 20 compositions in PDB, but even if we can identify the problem with a Loyd version, he has no other shared compositions known. Congrats on the Alekhine number.
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(12) Posted by Michael McDowell [Tuesday, Jun 16, 2020 17:13]

Sam Loyd
St. Louis Globe Democrat 1906
(= 5+4 )

Mate in 3

This is No.196 in “Sam Loyd and his chess problems”. I presume that the Loyd/Keidanski joint which Andrew refers to is P1318466 in the PDB, which is this position with the superfluous bPg7 removed then reflected. There is no original source given in the PDB, just mention of a reprint in American Chess Bulletin in May 1922 (11 years after Loyd’s death). The Loyd book makes no mention of Keidanski. This doesn’t sound like a joint composition to me.
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(13) Posted by Andrew Buchanan [Tuesday, Jun 16, 2020 17:50]; edited by Andrew Buchanan [20-06-16]

Well that seems quite convincing, Michael, thanks. The thread was very slender. I do have a copy of the Loyd book but 8 time zones away in my London attic. Loyd does not seem to have been someone who composed with others - indeed the concept of collaborative composition, with the exception of Koch & Kockelhorn, was much rarer in those days.

In WinChloe, out of 968 Loyd problems, only two are given as dual authorship. 484758 J.B.McKim & the very odd 451993 Joseph Alonzo Potter. Both are cooked, which wouldn't matter, but neither author had any other joint compositions. Napoleao has no joint compositions in WinChloe.

So, I think the Keidanski improvement is as near as we’re ever going to get to Loyd, so I am inclined to give him the benefit of the doubt. They were active during the same period, and we can't logically exclude that they discussed the problem, years before Loyd died. So if we apply the optimistic retro convention, like castling, we can allow this to be a joint version. And, as of 15 minutes ago, it's my birthday, so I will give myself this one :-)
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(14) Posted by Thomas Brand [Tuesday, Jun 16, 2020 19:56]

Andrew, I'm not sure Werner is the only living composer with Loyd-Number 8: Norman Macleod (Loyd-Number 7) was a "sprayer" co-composing according to PDB for example with Hans Peter Rehm, Kjell Widlert, Chris Feather, Yves Cheylan, Bernd Schwarzkopf, Gerd Rinder, Fadil Abdurahmanovic, Marjan Kovacevic, Mark Ridley -- anyone overlooked?
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(15) Posted by Siegfried Hornecker [Tuesday, Jun 16, 2020 20:29]

Do you know when the last living First American Civil War widow died? In 2008.

Did you know that that the time difference between the Pyramids being built and Cleopatra coming to power is smaller than the difference between Cleopatra's reign and today?

So if you talk about the Motphy number, keep that in mind. It is so low because Morphy's time is not as far away as it looks like, even though technology has advanced at a rate that would make it impossible to recognize the world from back then. Since Morphy's time, we reinvented antibiotics, we invented the car, very much all of modern medicine, telephone, television, modern psychology...
and sliced bread in 1928.
At least we can take comfort knowing that one of the safest occupations these days already existed during Morphy's lifetime. After all, it was one heroic girl, Ada Lovelace, whose idea in the first half of the 1840s was to input something into Babbage's Analytical Engine, making her the world's first... computer programmer.
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(16) Posted by Zalmen Kornin [Wednesday, Jun 17, 2020 04:24]

Norman Macleod collaborated with Hans-Peter Rehm, who collaborated with Jacques Rotenberg. Then we're also in the Loyd's "lineage"...

@Andrew: Oh, yes... after demontrating I could beat anyone, I retired unbeaten (o:
Not least: many happy returns!
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(17) Posted by Kostas Prentos [Wednesday, Jun 17, 2020 08:44]

Michael McDowell's post #12 actually kills the whole premise from the get-go. But if we accept that Keidanski's claim to posterity was valid, then WinChloe is very helpful in complementing Andrew's list: Lasker had a joint fairy helpmate (!) problem with Henri Weenink (WID: 519274).
This would make Weenink's number=3. He had joint works with several Dutch composers, like Niemeijer, Hartong, etc. Hartong(=4) really shared the fun with 72 other authors. Among them, one joint problem with Moutecidis(=5) brings my own number to 6.
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(18) Posted by Kostas Prentos [Wednesday, Jun 17, 2020 09:01]

In OTB chess, I had a pretty good Kasparov number, beating a guy, who had beaten the Bulgarian GM Krum Georgiev, who had beaten Kasparov in the 1980 Chess Olympiad. This was fine, until I bypassed the line and played directly with Krum Georgiev and lost. So, I wonder if the number for OTB chess can be lost, or we only count the results that are convenient.
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(19) Posted by Andrew Buchanan [Wednesday, Jun 17, 2020 10:38]; edited by Andrew Buchanan [20-06-17]

Haha wonderful. The Loyd/Keidanz problem is described in ACB 1922 as a reprint of 1906. In fact that's a typo: the problem is in ACB 1907
Problem 224 By S.Loyd and Dr H.Keidanz, New York (Original), in which year Loyd was certainly alive.
So this silly conceit is indeed well-founded: sweet! It is remarkable that the entire chain hangs by such a slender but definite thread.
Moral: always check primary sources
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(20) Posted by Andrew Buchanan [Wednesday, Jun 17, 2020 18:18]

Kostas Prentos wrote:
Michael McDowell's post #12 actually kills the whole premise from the get-go.

The apparent glee with which you wrote this is what pushed me to prove that Loyd *did* collaborate with Keidanz, so I am grateful to you :)

WinChloe is very helpful in complementing Andrew's list

I do filter for author='Hartong', then Problems -> Statistics -> Authors for the list of 73 authors, but then can anyone here advise how to select these rows so I can copy/paste?

Lasker had a joint fairy helpmate (!) problem with Henri Weenink (WID: 519274)

Amazingly out of all the ~800,000 chess problems which exist, I was looking at *exactly* this one in PDB just a couple of weeks ago (because it's in James Malcom's special interest zone). However, the co-author was only mentioned in a comment about the reprint, so it didn't register. This is quite an impressive coincidence.

This would make Weenink's number=3. He had joint works with several Dutch composers, like Niemeijer, Hartong, etc. Hartong(=4) really shared the fun with 72 other authors. Among them, one joint problem with Moutecidis(=5) brings my own number to 6.

Congratulations, Kostas! I will update the thread with these if I can get the WinChloe selection to work.
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MatPlus.Net Forum Promenade What's your Loyd number?