30x30 Ribbon Tour

 This is about the largest board I can draw a tour on, and I've had to reduce the scale as compared with the previous tours. I'm not sure if I've reduced the links, shown in black, to a minimum. This board like the 6x6 and 18x18 allows 90 degree rotational symmetry.

12x12 Ribbon Tour

This 12x12 knight tour with 180 degree rotational symmetry completes the set of ribbon tours constructed over the last few days, the others being on boards 18x18 and 24x24. I've also been showing them on Twitter. 

Also shown here is the well known 6x6 tour of similar design. This like the 18x18 tour has 90 degree rotational symmetry.

A 24x24 Ribbon Tour

This tour solves the same task as on the 18x18 case published previously, but proved much more difficult to achieve. Given the diagonal braids shown in blue, and putting in the natural connections in each 6x6 area, similar to the 6x6 tour with the same diagonal pattern, results in a pseudotour of twelve separate circuits (4 of 14 cells, 4 of 20, 4 of 60 and 2 of 100, giving the total 576 = 24x24). 

The task is then to put in the minimum number of links to join the circuits up into a single tour and to ensure that it is a symmetric tour, which on this size of board means 180 degree rotational symmetry (which I call rotary symmetry). This is tricky since some of the circuits are themselves symmetric. 

 

More on diagonal braids

 It is possible, as shown here, to put an extra set of obtuse diagonal braids between those used in my 18x18 tour, to cover any size area, but they cannot be incorporated in a tour since they leave isolated cells uncovered at intervals of {0,3} moves, as if the whole board is composed of centreless 3x3 boards. All other cells are used. 

Knight's Tour 18x18

This is a tour I constructed yesterday, partly inspired by some work by Robert Bosch on twitter, showing patterns on 24x24 boards. This is a closed tour on the 18x18 board which has 90 degree rotational symmetry (birotary symmetry as I call it). It features complete diagonal braids of oblique angle type. It is based on the familiar 6x6 tour of this type.

Simplified Spelling

I have revised the page on "Simplified Spelling" on my website, and also the "Anthology of Well-Known Verse" which shows well known pieces in the new spelling scheme.

Here is a summary of the spelling scheme as it now is. Largely unchanged: a, b, d, e, f, g, h, i, k, l, m, n, o, p, r, s, t, u, v, w, y, z. Redefined: c = 'sh' sound in 'ship', 'match'; j = 'zh' sound in 'ridge' 'leisure'; q = 'th' in 'then'; x = 'th' in 'thin'. Ambiguities: u as in 'cut' or 'put'; Indefinite vowel sound shown as a or r. Longer vowel sounds consist of a, e, i, o, u followed by a, i, u or by r, y, w if vowel follows. These may be reduced to a single letter at the end of a word.

Some new spellings: 'church' becomes tyurtc, 'judge' becomes dyudj. The indefinite article 'a' stays as a or becomes ei according to pronunciation. Similarly the definite article 'the' becomes qa or qi. I have given up trying to distinguish between the u sounds in 'cut' and 'put', or using a special letter for the indefinite vowel sound. This means more current spellings are unchanged.

Blog Update

 I just managed to get round to updating my profile on this Blogger account, so that it now shows my current location, Crewe instead of St Leonards on Sea. It took a lot of trial and error before I could locate the page to make the updates. It also had my old email address, long out of date. I've left the same photo of myself as I was back in 2009 when I started this Diary.

An Autumnal Walk

 I decided to take a longish walk this morning, 

since I haven't been getting much exercise. 

These are some of the photos I took along the way

//

For unknown reasons these have not appeared in the sequence in which they were taken. 

Joining Symmetric Tours

 These are images that I put on twitter, partly stimulated by work by Robert Bosch. 

They show ways of combining repetitions of a symmetric tour in an array 2x2, 3x3, 4x4 to form a single larger symmetric tour. The odd case simply uses a series of Vandermonde style links (two deletions and two insertions). The even cases use a linkage octagon (four deletions and four insertions) around the centre point, and the centre of each quarter in the 4x4 case.  

The tours used are from Wenzelides 1849 and Haldeman 1864.

Catching Up Again

 Some photos from 30 August and 3 September. 

Butterfly on the buddleia outside my back window

Three images from a walk in Queen's Park.

Crewe Town Centre Dereliction

I took a walk for exercise this morning, going as far as the Manchester Bridge and back. On the course I took these photos of the derelict area around Crewe Bus Station which were due for demolition and redevelopment this summer. No sign of any further action so far. This will serve as a "before and after" record if there ever is an "after".

The first three photos were taken along Delamere Street on the way out and the other three along Victoria Street on the way back.

A Surprise in the Post

Last week I was surprised to receive a copy of this new book from the BCPS:

It consists of a selection of the best problems published in The Problemist over the years, together with history of the Society and biographical notes on prominent members. This will be well worth close study over the coming weeks or months of shutdown.

I was very pleased to find two of my own problems presented. One is my Grasshopper Retro, which is certainly by far my best composition. The other is a Serieshelpmate in 17 with Neutralising King that I composed for the New Ideas Tourney while on the train to the Bournemouth meeting in 1989. To be honest, I had entirely forgotten about this, and never followed it up with other examples.

Being currently in lockdown because of the virus I have started to update some of the neglected pages on my website. These include the History Timeline where many of the links had vanished into the ether. So far I have eliminated the dead links and rearranged the material into 400-year Ages (instead of 500) but there are still many obvious omissions. I'm also putting up more of the 7-man compositions in my Grasshopper Chess Problem Collection.

Magic Knight Tours 8x10 and 8x14

On my 80th Birthday, and shortly after, I was sent a series of 80-cell magic knight tours on the 8x10 rectangle by Guenter Stertenbrink and later some by Awani Kumar. 

Some of the tours in the Stertenbrink list are closed tours with a complete braid along the bottom border. This can be extended, in four different ways, to cover a further four rows forming a magic 8x14 tour. Here is one example that I sent to these correspondents on 18 February.

These tours answer the final missing cases of Magic Knight Tours on rectangular boards.

07 62 07 52 09 56 01 58

06 51 06 61 04 59 10 55

49 08 63 08 53 12 57 02

64 05 50 05 60 03 54 11

09 48 65 04 27 30 83 86

02 67 46 11 82 85 28 31

47 10 03 66 29 26 87 84

68 01 12 45 88 81 32 25

13 44 99 70 23 34 89 80

00 69 14 43 90 79 24 33

41 16 71 98 35 22 77 92

72 97 42 15 78 91 36 21

17 40 95 74 19 38 93 76

96 73 18 39 94 75 20 37

Underlined: add 100.

The formations on the fifth to eighth ranks down are familiar: a double Beverley quad, and a Snake-head formation as in the 12x12 magic tour by the Rajah of Mysore.

I am not able to do geometrical diagrams as yet on my new computer, but have made some progress with installing HTML-Kit and Cute-FTP which will enable me to update some of the pages on my website. I have already begun to update the History section, where a lot of the links no longer work, but have not yet uploaded this work to the website. .

Next Weekend 13 -15 March I am due to play in the Blackpool Chess Congress, though I've been having doubts whether to go in view of the Coronavirus outbreak.

Frodsham Chess Congress

Last weekend I took the trains to Frodsham, near Chester, to take part in the Minor section of the Chess Congress held there. I stayed at the Old Hall Hotel in the town, a twenty minute walk to the venue, which was the Community Centre in Fluin Lane. I won my first game on the Friday evening, lost the next two on the Saturday, then drew one and won one on the Sunday, scoring 2.5/5.

There were quite a few other players from the Crewe Chess Club there as well, though I think some of them were traveling there by car each day. The Arbiter Francis Bowers was staying at the same hotel and we travelled together as far as Crewe on the return journey on Sunday evening. I think that was the first time I'd met him since the World Circular Chess in Lincoln some years ago.

Here are the results of the congress:
https://chess-results.com/tnr511730.aspx?lan=7&art=0&flag=30
Clicking on a player's name shows the games they played and the results.

I treated the weekend as a sort of holiday and spent some time walking around to see the local sights. Such as the Castle Park (though without a Castle) which was full of dog-walkers. Then on Sunday morning along to the river where there is an impressive Victorian railway viaduct, dated MDCCCL in prominent Roman numerals, high up. Unfortunately I forgot to take a camera.

New Computer

This is just a test post using a new computer.
My old Samsung laptop seized up, apparently due to a faulty disc.
The new one is a Lenovo laptop with Windows 10 and WiFi connection.
It is taking me a while to get used to and to transfer files from the old machine.
This seems to have worked so far!