Tuesday, 4 December 2018


November seems to have passed without a diary entry.

I've been attending some MathsJam events, a regular one in Bexhill and a one-off in Brighton where I gave a short presentation on the disphenocingulum.

My book on Knight's Tours is near enough completed in 800 pages. There is just the Index to do, and then arranging the publication, probably via the Lulu organisation.

However I am also making efforts to find a new place to move to in the Midlands. Every ten years or so I feel the need of a change of scene. A reduction in my monthly rent is also needed.

The National Chess Library on which I did a lot of work is now advertised at the bottom of the English Chess Federation website. It needs to be better publicised to attract visitors.

Sunday, 21 October 2018

Chess in Crewe

Over the week end 11 to 15 October I travelled to Crewe to take part in the chess congress organised there by Crewe Chess Club. Playing in the Minor section I managed to score 2.5 out of 5, by two wins and a draw against weaker players. In the other two games I played quite well but made mistakes. The first was against the eventual winner who won all his games.

The tournament was played at the Ibis hotel which is somewhat isolated on an industrial estate a longish walk from the station. Breakfast was included in the price, but on the final morning the fried potato pieces were apparently reheated from the previous day and inedible, but otherwise the food was OK. The coffee or tea provided in the room was very meagre, and no biscuits, but a complimentary bottle of water. The lighting in the room was also poor. There was a pleasant Nature walk around the hotel through woods beside a stream.

I also used the time to look around the Crewe town centre which is a mixture of boarded up shops, like the former BHS store, and new developments like the Lifestyle Centre, though the former Library building seems to have been abandoned. The Asda supermarket is enormous but very dreary from the exterior. A busker playing "Somewhere over the Rainbow" was helpful in adding cheer to the place. Neither W H Smith's nor Waterstone's stocked a Crewe A to Z. Presumably people now rely on accessing maps on the internet via their smart phones.

On the Friday I also took time to take the number 3 bus down to Tunstall in Stoke on Trent to take a further look at possible properties to rent if I move that way. Travelling on the trains to Crewe and back worked OK as regards the times. This was the first time for several years I had been on the London Underground. I had forgotten how deep the Northern line goes, with so many escalators, The main problems were on the final leg home from London Bridge when they kept announcing platform changes. I also had to stand from there to High Brooms. Probably I should have travelled earlier to avoid the rush hour.

Monday, 8 October 2018

A London Walk

On Thursday I bought a day return to London, for use on the Friday, with the aim of attending the British Chess Problem Society meeting. I didn't get round to travelling until the afternoon, but still arrived with plenty of time to spare. Looked around London Bridge Station to check the way to the Underground for future reference - it's quite a maze.

Eventually found my way out to Tooley Street which was jam-packed all down its length with buses bumper to bumper. Walked through Hays Galleria and along the Embankment.

The red-brick building that was my old school, St Olaves Grammar, is now subsumed into a monstrous concrete hotel, that still looks as if it requires a few more floors to be added. The whole area behind the school, where the London Mayor's offices now are used to be an industrial area full of tall cranes, long since gone. It is now a tourist hot spot for viewing Tower Bridge.

I took a walk over Tower Bridge, through the crowds of tourists, and along the cobbled walk on the north side of the river below the Tower of London. This comes out at the Monument built by Hooke and Wren to commemorate the 1666 Fire of London.

Walking up Pudding Lane I took a wrong turning along Eastcheap and Great Tower Street, heading back towards the Tower instead of up Gracechurch Street. Realising I'd gone wrong I took a left turn somewhere and headed towards the "Gherkin" building that I could glimpse between the other high-rise buildings. Found it quite easily and was back to Bishopsgate.

There was stilll time to spare before the meeting at 6pm so I walked up past Bishopsgate Institute and took a stroll round Spitalsfield, which is now a covered market with numerous restaurants.

Finally to the meeting in the small Hall at the back of St Bottolph's Church. It was pleasant to see some old faces of Problemists not seen for some time. I'm hoping to be able to get back into some composing ad solving, bit need to get up to date on the latest stipulations.

More later perhaps.


Sunday, 23 September 2018

Need for a Change

I seem to be unsettled lately. Can't concentrate on anything.
Maybe I need to get on with my proposed move to the Midlands.
Being in the same place for ten years is a long time for me.
Time for a change, a new scene, or a new stimulus.
It might also have something to do with the Brexit impasse.
The whole country needs a good shake-up.

Sunday, 16 September 2018

A Visit to the Midlands

I took the train and coach up to Leicester last Saturday (8 September) though regretted choosing to  walk from Waterloo to Victoria Coach Station, forgetting that the South Bank and Westminster Bridge would be crowded with sight-seers on a Saturday. I preferred to do this rather than risk the change of trains at East Croydon, between different train operators, since in my experience the transfer tends to takes longer than allowed for, especially when the train is late arriving.

On the Sunday I went to Leicester Secular Hall for their Open Day and for the lecture on Chapman Cohen in the evening. In between I visited old haunts in Leicester, where I lived for ten years, and found quite a bit of rebuilding had been done, as compared with last time I was there two years ago, when everything was being knocked down. The Abbey Park fortunately is much the same.

On the Monday I took to the trains again to visit Stoke on Trent, mainly because I had noticed some small terraced houses to rent, similar to the one I had in Leicester, at a reasonable rent. Also because I had only been to that area once before and wanted to see if I would like to live there. Generally I got a good impression, particularly the bus system centred on Hanley. I took a number 3 bus to Tunstall and had a walk in the park there.

Returned home on the Tuesday, but have felt somewhat tired since, so probably overdid the walking and travelling. For some reason I'm getting pains in my hands. Just getting old I suppose. If I do get round to moving to Stoke it will be my last move, but I do feel the need for a change of scene, as well as to make a saving on my rent, and have the freedom of my own front door.

Friday, 24 August 2018

Light Music and an Old Film

Listening to "Light Music" is one of my interests, to which end I am a member of the Light Music Society and have the set of four CDs of British Light |music Classics produced by Ronald Corp, And his others on American and European Classics.

Instead of Beethoven's Ninth that was on the Classic FM evening concert I decided to put on the fourth CD in the collection. This includes a piece called "Cavalcade of Youth" by Jack Beaver, whose name I was unfamiliar with. It includes a stately tune (used for a radio programme called "The Barlows of Beddington" that I've never heard of).

The notes in the leaflet that comes with the CD give Jack Beaver's dates as 1900 - 1963 and says he often contributed music to British films anonymously. It mentions The Thirty-Nine Steps (1933) which is well known and The Case of the Frightened Lady (1940) for which he provided what was considered the first "tabloid piano concerto".

Since I like Richard Addinsell's Warsaw Concerto, and Charles Williams' Dream of Olwen, I thought I would search for this Jack Beaver piece on You Tube. Sure enough they have a whole selection of his film music. Much of it sounds surprisingly familoar. The piano piece is called Portrait of Isla.

I also found that You Tube has the whole film of The Case of the Frightened Lady, and found it sufficiently intriguing to watch through for an hour last night. It is based on an Edgar Wallace play, and this theatricality shows. It is set in a creepy old house owned by an aristocratic family led by Lady Lebanon and her son, a composer. Her Secretary is Isla the Frightened Lady of the title.

As one might expect from an Edgar Wallace story it is a whodunnit, solved by Inspector Tanner of the Yard and his comical sidekick. Quite a few familiar actors of that period in the cast. Definitely a pleasant taste of nostalgia for me.

Thursday, 9 August 2018

Walking in the Rain

A nice quiet cool walk along the prom in the rain with my umbrella this afternoon.
Cool being the most operative word. Hardly anyone about.

Monday, 30 July 2018

Knight's Tour Notes Update

My efforts to put the information from the website into book form have taken a backward step, to leap forward again I hope. The material has broken apart again to take the form of a series of smaller books of around 80 or 96 pages.

This has quickly resolved into ten parts:
0 - Bibliography with Glossary
1 - Theory of Moves (including leapers)
2 - Odd and Oddly Square Boards (6x6 10x10, etc)
3- Symmetry (including mixed quaternary)
4- Simple Linking of Pseudotours
5 - Oblong Boards
6 - Shaped and Holey Boards
7 - Magic Square Knight Tours
8 - Multimover Magic (King, Queen, etc)
9 - Miscellanea (Figured, Lettered, HexBoards etc)

Updated 4 August.

Saturday, 23 June 2018

disphenocingulum again

It seems my alternative disphenocingulum (J90) has been discovered before.
It is number 25 on this page of "near miss" Johnson solids.


This claims that there is some distortion in the cingulum triangle.
Though in my models I could not detect any distortion. It must be very small.

The author appears to be Jim McNeill as named here:


Wednesday, 13 June 2018

The Disphenocingulum

As a result of contacts on twitter I have become interested in polyhedra, in particular the "Johnson Solids" which are formed of regular polygons but are not the usual suspects.

In particular a drawing was posted of the "disphenocingulum".  As a result I decided to make a model in card and ended up with two different versions. The 12 orange triangles form the "cingulum". The "spheno" parts form the roof and keel:

Corresponding flat diagrams of the pieces and their connections are:

The version on the right appears to conform to the patterns shown in the Wikipedia and MathWorld entries for Johnson Solid 90, but the version on the left does not.

So is my new version an alternative ("isotope") of the disphenocingulum? Or is one of them not an authentic Johnson Solid because it has a pair of triangles that are coplanar? It is difficult to tell from the models if some pairs of triangles are at an angle to each other or are flat together. The angle may be very small. In fact the one on the right seems flatter to me than that on the left.

Wednesday, 9 May 2018

Magic Four-Camel Tour of 1887

Following on from the four Giraffe tour reported previously I have now come across this four Camel tour in my researches in the column "Un Probleme Par Jour" conducted by A. Feisthamel in the French newspaper "Le Siecle". This tour is by "Adsum a Saint-P" (According to H.J.R. Murray this was a pen name of Charles Bouvier). It is mentioned on 13 May 1887 then presented as a problem for solution on 14 May, with the solution appearing on 21 May 1887. The diagonal sums are complementary (i.e. adding to 520). Each rank consists of pairs of complements (adding to 65). 

01 62 13 58 07 52 03 64
49 21 53 02 63 12 44 16
09 39 11 50 15 54 26 56
61 14 59 08 57 06 51 04
20 35 22 41 24 43 30 45
40 10 38 31 34 27 55 25
32 60 28 47 18 37 05 33
48 19 36 23 42 29 46 17

This is the earliest mention of a tour by a {1,3} mover that I am aware of. It seems surprising that later French writers on Mathematical Recreations, such as Lucas and Kraitchik, don't seem to have been aware of these results. Feisthamel indicates that they are only single examples from much more extensive work. Was the work of these composers all lost after their deaths, or is it still hidden away in some obscure French archives?

Sunday, 6 May 2018

Sources of Magic Knight Tours, Further Update

I have located another of the tours with missing sources:
(23b) Ligondes (Palamede) Le Siècle ¶2836 4/11 December 1885.
Murray gives the date as 1884, so it may also be in an earlier source,
such as Count Ligondes' own private publication which I have not seen.

This seems to be the last one-chain magic tour published in Le Siècle. 
Two and four-chain solutions continue to appear up to 30 April 1894,
which is the last date it is signed by A. Feisthamel. From 1 May 1894
the column "Un Probleme Par Jour" has a new editor, Emile Franck.

Sunday, 22 April 2018

Magic Four-Giraffe Tour From 1887

On 9 October 2013 I reported here my construction of a Magic Two-Giraffe Tour, i.e. consisting of two sections of {1,4} Giraffe moves joined by two rook moves. In that tour the diagonals add to 272 and 248 which together sum to 520 which is twice the magic constant of the ranks and files.

While studying the cryptotours published in Le Siecle in the column "Un Probleme Du Jour" edited by A. Feisthamel, from 1876 to 1894, I have found this much earlier work on the same subject. This uses four Giraffe paths connected by four rook moves. In this tour the diagonals add to the magic constant 260 as well as the ranks and files.

Diagonally Magic Four-Giraffe Tour by A. E. Reuss of Strasbourg
Problem 3221, Le Siecle 5 March 1887, solution 12 March 1887.

01 25 09 23 42 56 40 64 
43 49 39 63 02 26 16 22 
03 27 15 21 44 50 38 62 
45 51 37 61 04 28 14 20 
32 08 24 10 55 41 57 33 
54 48 58 34 31 07 17 11 
30 06 18 12 53 47 59 35 
52 46 60 36 29 05 19 13 

The rook moves are 16-17, 32-33, 48-49 and the closure move 64-1. The tour is symmetric about the vertical axis, the ranks consisting of complementary numbers adding to 65, but is not quite symmetric about the horizontal axis.

Naturally I wonder whether Reuss constructed others of this type, or is this just a one-off? Knight tours that he published in the same column were under the pen-name of "X a Belfort".

Wednesday, 11 April 2018

Sources of Magic Knight Tours: Update

Two minor updates to the list of sources of magic knight tours of the standard chessboard have come to light from my researches in Le Siecle.

Tour 00i by an Unknown composer appears as problem 772 on 25 April 1979 with solution on 2 May 1879. The word puzzle used with it is given as by M. Jacquemin-Molez but the composer of the design is not identified. The column is signed as by A. Feisthamel as usual, but if by him the designer would probably be cited as M. A. F. so I think we have to classify it as still Unknown and from an earlier source. The 1879 date is one or two years earlier than the 1880/81 date given by Murray.

Tour 00f by Palamede (the pseudonym of Count Ligondes) appears as problem 2134 on 31 August 1883 with solution on 7 September 1883. There does not seem to be any mention of its cyclic properties.

Wednesday, 28 March 2018

National Chess Library

Here is a new image of the layout of the bookcases in the ECF Offices at Battle,
with the bookcases numbered 1 to 49.

And a key to the present subject arrangement.

1-2 History, 3-6 Game Collections, 7-10 Openings
11-14 English Periodicals 15 Office Use
16-17 Middle Game 18 Endgame 19 Problems
20 Variants 21-22 Archive

23-25 Introductory Books 26 Office Use
27 Russian 28-30 East European 31 Multilingual
32-34 German 35 Braille 36 Library Catalogues
37-38 West European 39 French
40 Chess Handbooks 41-42 Reference
43 World Championship 44 UK Regional
45 Year Books 46-49 Tournaments.

Monday, 26 February 2018

Magic Square in Figured Tour

In my booklet on Figured Tours published in 1997, there is a knight's tour, A5 on the 8x8 board in which the first nine even numbers form a magic square. The tour is by T. R. Dawson and originally published in Vie Rennaise 19 November 1932. It led me to wonder if the same task could be done on a smaller board of minimum size.

The 3x5 board with a cell added at the middle of each side is of 19 cells, that can be chequered to show 9 dark cells in the form of a diagonal square and 10 light cells. Unfortunately this board has no knight tour, for the same reason as the 3x5 board, formation of a closed path firmed by the knight moves available at b3 and f3.

However if the extra cells are added on the long sides to form a rotary symmetric board as shown below the board becomes tourable. In fact there are 62 symmetric tours. Among these there are just six in which the square formed by the even numbers is magic. As shown here:

I wonder if this result can be new?

Monday, 12 February 2018

National Chess Library

Since September last year I have been travelling weekly by bus to Battle to help with the arrangement of the National Chess Library books on the shelves. The Library is now in the Offices of the English Chess Federation at the Watch Oak. Here is a plan I made of the current arrangement of the subjects on the shelves.

The Library is made up of a number of separate collections, the largest of which are the ECF's own collection and that from Harry Golombek. The books are labelled to show which donor collection they are from, and are now mostly arranged on the shelves by subject rather than collection. Because of the way the Library has accumulated there are many duplicates. Duplicate periodicals are being stored in the loft and duplicate books are on the bottom shelves. The Library is open for visitors, but the offices are closed at week ends.

Sunday, 28 January 2018

Knight's Tour Book Contents

I must try to post something each month at least. New Year's Resolution.
So here is the list of contents of my Knight's Tour Notes book as it now stands.
It is now back to a single book of around 800 pages.

z Theory of Moves 5 Nets, Boards, Moves, Pieces, Freedom, Mobility,
z Theory of Journeys 12 Shortest Path, Angles, 3-, 4-, 6-, 8-Moves, Touring Tests.
z Theory of Magic 24 Magic Arrays, Magic Rectangles, Magic Squares, Step Sidestep.
z Wazir Tours 36 Labyrinths, 6×6, Non-Intersecting, Around the Rocks, Snakes, Figured.
z Knight Move Geometry 53Nets, Triangles, Quadrangles, Polygons, Intersections.
z Symmetry 58 Symmetry, Coding, Generic, Central Angles, Straits and Slants.
z Shaped Boards 68 Octonary 72 Biaxial 80 Birotary 98 Rotary 120 Axial 132 Unary.
z Rectangular Boards 156 Borders, Schwenk Theorem, Symmetries, Oblongs
z Oblong Boards 159 3-rank 180 4-rank, Mediaeval 4×8 202 5-rank  6-, 7-, 8-, up to 24×37.
z Odd Square Boards 217 3×3, The 5×5 Board, 7×7,9×9, 11×11, 13×13, 15×15.
z The 6×6 Board 225 quaternary, binary, angle method, slants, open 3-slant, semimagic
z 6×6 Asymmetric 232 Closed Tours: 4-slant, 6-slant, 8-slant, 10-slant, 12-slant.
z Earliest Knight's Tours 272  Adli. Suli, Mediaeval mss, Aladdin, Nikolai, Nilakantha
z Rediscovery (1725-1825) 275 Euler, Vandermonde, Collini, Warnsdorf, Generation Rules.
z Squares and Diamonds 291 FPH, von Schinnern, Ciccolini, Franz, Wenzelides, Jaenisch
z Roget's Nets 300 Straits & Slants, 3-slant, Reentrant, S&D, Given slants, Max slants
z Pseudotours 309  Simple Linking 311 Octonary 317 Crosspatch 319 Collinian
z Double Halfboard Tours 323 Symmetric Rhombic Halfboard.
z More Squares and Diamonds, 330 Symmetric Rhombic Non-halfboard
z Compartmental 342 Tours from Crosspatches, 346 Enumeration of 8×8 Tours
z Graphic Tours: 348 Directions, Intersections, Circulation 351 Angles Max and Min
z Shapes 359 Triangles, Quadrangles 362 Stars 364 Pictorial 365 Monograms.
z 8×8 Asymmetric Tours 368 Legendre, Rothe, Bilduer, Maximum Asymmetry.
z Near Symmetry 370 Bergholtian, Octonary, Quaternary, Axial, Rotary, Diagonal
z 8×8 Symmetric Tours 382 History 391 Symmetrisation, Given Centre 396 All Centres
z Mixed Quaternary Symmetry 406 h:j:k types: h=1, k=3, h>1 k>3, h=3, j=4, k = 5
z Quaternary Pseudotours, 434 8-fold, 4-fold, 2-fold, 1-fold, Table.
z Tours from QP 489 Aladdin, Vandermond, Non-Crossing, Jaenischian, 493 Other QP.
z Lettered Tours 497 Cryptotours, Alphabetical Tours, Chess Art Here??
z Figured Tours 507 Historical development.
z Magic 8×8 Knight Tours 524 Beverley, Wenzelides, Mysore, Jaenisch, Le Siecle,
z Ligondes 1911, Lehmann 1933, Murray 1936, Marlow 1987, Roberts 2002, Completion 2003.
z Catalogue of the 8×8 Magic Knight Tours 552 Historical, Geometrical, Arithmetical.
z Theory of Magic Knight Tours 578 Existence, Braids, Quartes, Testing Procedure.
z Large Even Square Boards 588 10×10 597 12×12 612 14x14 614 16×16 622 Even Larger
z Leapers 629 Camel. Shaped, Zebra, Zebra-rider,.Giraffe, Antelope, {1,5}, {2,5}, {1,6}, {1,7}.
z King Tours 641 Knots, 2×n  3×n  4×n  5,6×n  7×n, 8×8  Alternating, Figured
z Magic King Tours 655 Magic  Biaxial Diamagic  Axial Diamagic  Larger
z Double-movers 661 2-move R, 2-Move Q, 664 Emperor, Templar, Empress
z 673 Nightrider, Lancelot, Prince, Hospitaller, Night-Commuter
z 675 Caliph?, Gnu, Bison, Fiveleaper, Root-50, Root-65, Root-85.
z Triple-movers 683 3-move R, Hyperwazir 3-Move Q, Pterodactyl,
z Triple Knights WDN, WTN, Centaur, WAN, DFN, TFN,
z Quadruple-movers 692 4-move Magic R Tours, 4-MoveQ, WDTN,
z Multi-movers 704 5-6-MRT, 5+MQT, Raven, Amazon, Wizard.
z Alternative Worlds 722 Non-Crossing Paths 730 Rider Crossovers 731 Hoppers
z New Boards 733 Bent Boards 736 Space Chess, Higher Dimensions, 745 Honeycombs,
z End Notes 751 Bibliography 787 Solutions 790 Glossary 796 Index

The z is a wingding knot symbol that hasn't come out.