Wednesday, 4 October 2017

Catching Up

I can't seem to keep up regular posts here.

On 12 July I went into Eastbourne Hospital expecting to have an operation, but after discussion with the surgeon it was decided to postpone it for further tests that are now due on 18th October.

On 15 July I went to a l0cal chirch, St John's Brittany Road, for a concert by Hastings Sinfonia. I tweeted that they should be called sinfffonia since they were far too loud for me. On 16 Juky I went to Eastbourne for a concert at the bandstand. That was more enjoyable. So much so that I went to several other band concerts there on other Sundays. Always preceded by fish and chips. My brothers also came for a meal on the 23rd but didn't stay for the music.

In August 18th to 20th I went to play in the Minor section of the Thanet Chess Congress. However I could only manage three draws against weaker opposition, which decided me not to renew my membership of the Hastings Chess Club in September, having taken a rest from it last year.

During the week beginning 11 September I went to Battle to help with putting the National Chess Library on shelves that had been installed in the English Chess Federation offices there. Good progress was made, though there are still some further bookcases to be set up.

Because I had been thinking of moving back to the midlands, I took it into my head to order a mobile phone. However while chasing after the DRD delivery driver, who was trying to deliver the parcel to the wrong address, I missed the bottom step and slipped, spraining ankle. Later I also returned the phone since I couldn't work out how to use it. So not a happy time. 

More updates to come.

Friday, 7 July 2017

Sources of Magic Knight Tours

List of Sources of Magic Knight Tours in Historical Sequence

Some may of course have been published in an earlier source not yet found

Can any one help to trace the original publication sources of the following 14 tours?

The codes on the left are the names given to the tours in my 1986 catalogue in Chessics #26

Many tours appeared in other French newspapers that I have not located online.


05a Bouvier (Adsum) 1876?

00i Unknown Composer 1880/1881?

00c Francony (Celina) 1881?
05f Francony (Celina) 1881?
27k Francony (Celina) 1881?
05c Francony (Celina) 1882?
05e Francony (Celina) 1882?
23a Francony (Celina) 1882?

27p Reuss (X a Belfort) 1883?
27q Reuss (X a Belfort) 1883?
27r Reuss (X a Belfort) 1883?
27s Reuss (X a Belfort) 1883?

00f Ligondes (Palamede) 1883?
23b Ligondes (Palamede) 1884?


27a Beverley Philosophical Magazine 1848

12a Wenzelides Schachzeitung Feb-Mar 1849 p.94-97
12b Wenzelides Schachzeitung 1850 Fig. 99
27b Wenzelides Schachzeitung 1850 Fig 107

00b Mysore Silk (now in Crumiller Collection) 1852

00m Wenzelides Schachzeitung May 1858 Fig.A
12e Wenzelides Schachzeitung May 1858 Fig.B
12m Wenzelides Schachzeitung May 1858 Fig.C

12o Jaenisch Chess Monthly 1859
12n Jaenisch Chess Monthly 1859

00a Jaenisch Treatise 1862 Fig.49
27c Jaenisch Treatise 1862 Fig 55
27d Jaenisch Treatise 1862 Fig 56
00e Jaenisch Treatise 1862 Fig.62

27i Exner Rösselsprung als Zauberquadrat 1876 (not seen)
34a Exner Rösselsprung als Zauberquadrat 1876 (not seen)
34e Exner Rösselsprung als Zauberquadrat 1876 (not seen)

05b Caldwell English Mechanic 1879

12c Béligne Le Siècle ¶1042 5/12 Mar 1880

00j Reuss (X à Belfort) Le Siècle ¶1252 5/12 Nov 1880
27e Reuss (X à Belfort) Le Siècle ¶1258 12/19 Nov 1880
27f Reuss (X à Belfort) Le Siècle ¶1270 26 Nov/3 Dec 1880 (< Wihnyk 1885)
00d Reuss (X à Belfort) Le Siècle ¶1276 3/10 Dec 1880

05d Bouvier (Adsum) Le Telegraphe ¶1232 or ¶1239) cited in Le Siecle 1882
[Conjecture: second problem may be Francony's discovery of the Mysore tour]

12f Jolivald (de Hijo) Le Siecle ¶1726 12/19 May 1882
12d Jolivald (de Hijo) Le Siecle ¶1732 19/26 May 1882
12g Jolivald (de Hijo) Le Siecle ¶1738 26 May/2 Jun 1882
12h Jolivald (de Hijo) Le Siecle ¶1744 2/9 Jun 1882

27j Beligne Le Siecle ¶1966 16/23 Feb 1883 (Murray 1881)

27l Francony (Celina) Gil Blas ¶1156(1) 23 Feb / 2 Mar 1883 (Murray 1881)
27m Francony (Celina) Gil Blas ¶1156(2) 23 Feb / 2 Mar 1883 (Murray 1882)
Note: 27m is also in Le Siecle ¶1872 at same dates 23 Feb / 2 Mar 1883
where it is attributed to Adsum (Bouvier).

05g Ligondes (Palamede) Le Siecle ¶1996 23/30 Mar 1883

34b Ligondes (Palamede) Le Siecle ¶2086(1) 6/13 Jul 1883
34c Ligondes (Palamede) Le Siecle ¶2086(2) 6/13 Jul 1883
[2086(3) =34a, anticipated by Exner 1876]
[ 2092(1) = 27i, anticipated by Exner 1876]
34d Ligondes (Palamede) Le Siecle ¶2092(2) 13/20 Jul 1883
[2092(3) = 34e, anticipated by Exner 1876]
[These two problems consisted of three tours in one diagram.]

14b Ligondes (Palamede) Le Siecle ¶2098(1) 20/27 Jul 1883
14a Ligondes (Palamede) Le Siecle ¶2098(2) 20/27 Jul 1883
23l Ligondes (Palamede) Le Siecle ¶2098(3) 20/27 Jul 1883
23k Ligondes (Palamede) Le Siecle ¶2098(4) 20/27 Jul 1883
23j Ligondes (Palamede) Le Siecle ¶2098(5) 20/27 Jul 1883
23i Ligondes (Palamede) Le Siecle ¶2098(6) 20/27 Jul 1883
23g Ligondes (Palamede) Le Siecle ¶2098(7) 20/27 Jul 1883
23h Ligondes (Palamede) Le Siecle ¶2098(8) 20/27 Jul 1883
23e Ligondes (Palamede) Le Siecle ¶2098(9) 20/27 Jul 1883
[This problem shows 9 tours in one diagram, 3x3 letters in each cell]

23d Ligondes (Palamede) Le Siecle ¶2110(1) 3/10 Aug 1883
25a Ligondes (Palamede) Le Siecle ¶2110(2) 3/10 Aug 1883
[¶2110(3) = 05d which is anticipated by Bouvier 1882]

23m Ligondes (Palamede) Le Siecle ¶2116(1) 10/17 Aug 1883
23n Ligondes (Palamede) Le Siecle ¶2116(2) 10/17 Aug 1883
23f Ligondes (Palamede) Le Siecle ¶2116(3) 10/17 Aug 1883

03f Ligondes (Palamede) Le Siecle ¶2122(1) 17/24 Aug 1883
01b Ligondes (Palamede) Le Siecle ¶2122(2) 17/24 Aug 1883
00g Ligondes (Palamede) Le Siecle ¶2122(3) 17/24 Aug 1883

14c Ligondes (Palamede) Le Siecle ¶2128(1) 24/31 Aug 1883
01c Ligondes (Palamede) Le Siecle ¶2128(2) 24/31 Aug 1883
23c Ligondes (Palamede) Le Siecle ¶2128(3) 24/31 Aug 1883

34f Ligondes (Palamede) Le Siecle ¶2242(1) 4/11 Jan 1884
14d Feisthanel Le Siecle ¶2242(2) 4/11 Jan 1884

34g Ligondes (Palamede) Le Siecle ¶2248 11/18 Jan 1884 (Murray 1883)

03e Ligondes (Palamede) Le Siecle ¶2254 18/25 Jan 1884

03a Ligondes (Palamede) Le Siecle ¶2260 25 Jan/1 Feb 1884

03d Ligondes (Palamede) Le Siecle ¶2266(1) 1/8 Feb 1884
01a Ligondes (Palamede) Le Siecle ¶2266(2) 1/8 Feb 1884
03c Ligondes (Palamede) Le Siecle ¶2266(3) 1/8 Feb 1884

12i Bouvier (Adsum) Le Siecle ¶2326(1) 11/18 Apr 1884
12j Bouvier (Adsum) Le Siecle ¶2326(2) 11/18 Apr 1884
00l Bouvier (Adsum) Le Siecle ¶2326(3) 11/18 Apr 1884

12k Francony (Celina) Gil Blas ¶1582(1) 10/17 May 1884 (Murray 1882)
00k Francony (Celina) Gil Blas ¶1582(2) 10/17 May 1884
12l Francony (Celina) Gil Blas ¶1582(3) 10/17 May 1884 (Murray 1882)

01e Grossetaite Figaro 1896 (H84) (not seen) = number 84 discovered

00h Ligondes (Palamede) La Mode Du Petit Journal 1906 (not seen)
23o Ligondes (Palamede) La Mode Du Petit Journal 1910 (not seen)
23p Ligondes (Palamede) La Mode Du Petit Journal 1911 (not seen)

16a Lehmann Le Sphinx Aug 1933 (not seen)

27g Murray PFCS ¶2108 #16 Feb 1936 p.166
27h Murray PFCS ¶2239 #17 Apr 1936 p.177
27n Murray Fairy Chess Review vol.3 ¶2350 #1 Aug 1936 p.3
27o Murray Fairy Chess Review vol.3 ¶2351 #1 Aug 1936 p.3
[Other tours in this series proved to be anticipated]

01f Murray Fairy Chess Review vol.4 ¶4132 #3 Dec 1939 p.43
12p Murray Fairy Chess Review vol.4 ¶4133 #3 Dec 1939 p.43
01d Murray Fairy Chess Review vol.4 ¶4134 #3 Dec 1939 p.43
03g Murray Fairy Chess Review vol.4 ¶4132 #6 Jun 1940 p.93
[The Dec 1939 issue was the TRDFCR dated 28 Nov for Dawson's birthday]

23q Marlow The Games and Puzzles Journal #1 Sep-Oct 1987 p.11
01g Marlow The Games and Puzzles Journal #1 Sep-Oct 1987 p.11
25b Marlow The Problemist Vol.12 #19 Jan 1988 p.379
01h Marlow The Problemist Vol.12 #19 Jan 1988 p.379
03b Marlow The Problemist Vol.12 #19 Jan 1988 p.379

01i Roberts The Games and Puzzles Journal #25 (online) Jan-Feb 2003
14e Roberts The Games and Puzzles Journal #25 (online) Jan-Feb 2003

00n Mackay, Meyrignac & Stertenbrink [website] 18/19 Jun 2003
14f Mackay, Meyrignac & Stertenbrink [website] 21 Jun 2003
27t Mackay, Meyrignac & Stertenbrink [website] 24 Jun 2003
00o Mackay, Meyrignac & Stertenbrink [website] 1 Jul 2003
07a Mackay, Meyrignac & Stertenbrink [website] 1 Aug 2003
[The results were reported here:]
[The second numbering of 00n was spotted by me on 19 Jun]

Total = 108

Minor corrections 11 July 2017.

Thursday, 22 June 2017

Research in French Newspapers

I have been looking through the issues of Le Siecle in which H. J. R.Murray reported that A Feisthamel published the magic knight tours as they were discovered. However I find that most of the tours published there are of the two or four knight variety that I prefer to call Emperor tours, since they use rook moves to link the ends of the knight sections. The tours appear mostly in the Friday section of Feisthamel's puzzle column. However they are not presented as tour diagrams, instead they are all cryptotours whose solutions, besides delineating the tours, also serve as a word puzzle in themselves such as an anagram, though these puzzles all seem pretty feeble to me. The issues can be accessed via Gallica here:

In the issue for 3 Feb 1883 Feisthamel also lists a number of other French newspapers or magazines in which toors were published. These include the titles National, Globe, Soir, Telegraphe, Gil Blas, Gaulois, Clairon, Etoile francaise, Paris Journal and two others where single examples appeared. So far I have only located one of these online:Le Gaulois, where the puzzles appear on Mondays and are in two separate series (Jeux D'Esprits and Passe-Temps Hebdomadaire) which alternate fortnightly.

This includes King tours by R. Dubief and by a Monsieur Galtier, the latter being magic tours.
Much scope for further historical research here!

Wednesday, 10 May 2017

Final Dawsonian 6x6 Tours

This set of four Dawsonian tours on the 6x6 board complete my search for solutions.

As with the previous batch of four they differ only in the path taken by the 25-36 linkage.

Since my search has been made "by hand" not by computer programming,
it is quite possible I may have missed one or more solutions,

I also recorded a number of "near-misses" where one of the knight moves
is replaced by some other, such as a wazir, rook or zebra move,
bit these don't seem to be of any particular interest.

Monday, 24 April 2017

More 6x6 Dawsonian Tours

Here is another knight tour on the 6 by 6 board with the square numbers in a closed knight circuit.

These four use the same circuit but in a different position on the board, and numbered from a different point.
They differ only in the route taken from 25 to 36.

Saturday, 15 April 2017

Dawsonian 6x6 Tour

Back in Chessics #22 (1985) I published a solution to the 1881 Carpenter problem of making a tour with the square numbers in sequence along the first rank, and found the solution was unique.

However it has only recently occurred to me to try the similar Dawson problem of a tour with the square numbers in a closed knight circuit. Here is a solution I found late last night, or early this morning, after examining nearly 70 arrangements of the numbered circuits.

It has been known for a long time (apparently in Chess Amateur though I've not located the exact reference) that there are 25 such geometrically distinct circuits. One is too large to fit on the 6-board. The others can be placed on the board in various positions (81 at my last count), and the numbers can be placed on them in up to 12 ways, though many cases are easily eliminated. For instance in the above diagram the node at f5 must be an end-point (1 or 36) since there is only one other move available there.

Addendum: Found another solution mid-day today. This one uses a symmetric circuit.

The occurrence of two-move straight lines in both solutions is surprising.

Saturday, 25 March 2017

Tom Marlow

I regret that I have just learnt that my long-term correspondent Thomas W. Marlow died in September 2011. My first contact with him was around 1980 when he sent me new results on the "Rook around the Rocks" problem that I published in the Problemist November (1979). Our combined results appeared in Chessics #12 (1981). Another of his interests was in Grid Dissection problems (polyominoes) Chessics #23 (1985) p.78-9.

In 1985 as reported in Chessics #24 p.92 he made a computer check on the de Hijo (1882) enumeration of 16-move knight paths in direct and oblique quaternary symmetry, which I recently (Sept 2016) published in diagram form:

He also did significant work on Fiveleaper tours including 52 magic tours, which have a page to themselves in the Knight's Tour Notes:

Possibly his most notable work was his enumeration of all the "regular" magic knight tours on the chessboard (that is those formed of Square, Diamond and Beverley quartes) which was reported in the Problemist January 1988 (p.379) with diagrams of five new magic tours, the first discovered since the work of H. J. R.Murray published in Fairy Chess Review in 1939.

Although we corresponded over several decades we never met in person. I had the impression that he was younger than me, mainly in view of his expertise with computers, but perhaps I was mistaken. I will update this page as further details come to light.

UPDATE 26 April 2017:

I should also have mentioned his discovery in 2003 of the unique 10 by 10 semimagic knight tour with quaternary symmetry that I published in Games and Puzzles Journal (online):

From the new information below it seems that TWM was a good deal older than I thought, and also a rather adventurous individual!

I have heard from Mrs Dorothy E. Marlow as follows:


"Tom  ... was a very quiet, reserved, private person, and would not relish any publicity, but I will provide you with a few details.

He was Thomas William Marlow, born 24 January 1927. Apart from his National Service, which he spent mainly in Burma, his working life was with the LCC/GLC, taking early retirement when the GLC was abolished. He then became an advisor for the Citizens Advice Bureau, which for more than 20 years he found stimulating and rewarding.

His personal hobbies/interests were anything and everything concerning Mathematics. I always said that he was a human computer! He also liked travelling - as independently as possible as he disliked organised groups, although sometimes they were necessary. Most of our holidays were of the walking / trekking / backpacking type in such places as the Himalayas, the Andes, New Zealand, etc. In the UK it was anywhere among the mountains - Snowdonia, the Lake District and the Munros in Scotland. As the years started to take their toll, it became long-distance footpaths & coastal paths. I have some wonderful memories.

Another hobby, which I nearly forgot to mention, was gliding. He had been a glider pilot for about 60 years and kept his own glider at the London Gliding Club at Dunstable."


Tuesday, 7 February 2017

Knight's Tour Notes Update

I've been asked to give an update on the progress of my work on knight's tours that I have been trying to put into book form. Back in October last year I reported having the material in the form of eight monographs each of about 100 pages.  These soon combined to form four volumes, each of about 200 pages. The latest development is that these have spontaneously rearranged themselves to form three volumes each of around 260 pages.

Volume 1 covers History, consisting mainly of an update of the Chronological Bibliography that I produced in 1990, in 25-year stages, including diagrams of magic tours, separated by essays on methods of construction and ending with a catalogue of quaternary pseudotours.

Volume 2 is on Symmetry and Shape in Knight's Tours and consists of enumerations of tours on small boards, square, oblong or shaped, plus examples on larger boards. It includes a catalogue of all the tours on the 6x6 board, and an account of Mixed Quaternary Symmetry on 8x8 and 12x12 boards.

Volume 3 whose title is undecided is on Theory of Moves and of Magic Tours in general, together with catalogues of tours by Leapers from Wazir to Antelope, and Multi-Movers from King to Wizard. The later sections include Magic Squares using up to seven move types. An appendix lists all the 280 magic knight tours in arithmetical form.

This seems to have reached a stable configuration, so I am hopeful of completing it soon.

Thursday, 19 January 2017

Magic Wizard Problem Continued

Magic Wizard Tour Problem Continued

The original double latin square by E. T. Parker in the 1960 paper, differs from the version shown as the frontispiece in the Coxeter/Ball Mathematical Recreations, in being more geometrically regular:

This has only 15 'Witch' moves that pass over the centres of cells: 06-07 (N), 09-10 (R), 25-26 (N), 32-33 (N), 36-37 (B), 40-41 (N), 48-49 (C), 54-55 (B), 57-58 (C), 62-63 (Z), 69-70 (R), 86-87 (A), 89-90 (N), 96-97 (N), 98-99 (B). Where the letters indicate tthe directions of the moves: A = antelope, B = bishop, C = camel, N = knight, Z = zebra.

Working from this by permuting the ranks and files several times I have arrived at the following square:

This has only 4 Witch moves: 44-45 (N), 51-52 (Z), 94-95 (B), 99-00 (N), shown by the straight lines. One of these is the closure move 99-00. So regarded as an open tour it uses only three Witch moves. Can this be further improved?

What is in effect the same double latin square can be presented in other forms by permutation of the left or right digits (since a latin square is just a pattern independent of the actual symbols used). But whether a better permutation can be chosen to make a Wizard tour more likely is not clear to me.

It seems that every version will have one vertical and one horizontal move lke 09-10 and 69-70 in these examples, or 49-50 and 79-80 in the previous examples.