There was more snow overnight and in the morning on the 18-19th, but it thawed again quite quickly.
Delamere Street is closed to traffic at the end, where it meets Flag Lane, though cars were still driving through ignoring the signs last night and today. It looks as though work will be going ahead on the section of road through to Harrison Drive and Dunwoody Way, that has been planned for some months.
We had our first snow of the year last night, but by this afternoon it had all thawed, before I could take a photo to prove it. So I had no trouble getting out to Crewe Chess Club this evening, to play third board in an F-team match against Alsager, which I managed to win against a young opponent.
I'm thinking of entering the Blackpool Chess event next month, but I'm not sure I fancy traipsing about the seafront in the icy wind, and the Hotel costs are getting higher, and there are still threats of rail strikes, which put me off entering the Hastings tournament earlier this month.
Professor Knuth sent me an email that included a knight's tour sent to him for his birthday on January 10. This is a 10x10 tour of the type showing a queen on cell 85 (his age) and guarding all the cells with prime numbers, and various other features. I will put it in the Figured Tours page shortly.
I've been spending an inordinate amount of time checking up on the 6x7 symmetric knight tours. There was an error in the 266 diagrams of the Sulian (axial symmetric) tours, and it took me quite a while to find the duplicate among them, since the total should be 265 according to Knuth. I did this by classifying them by geometrical properties like number of straight line moves. It turned out that tour 166 in the list was the same as 165.
Similarly when I drew out diagrams for the Eulerian tours I found 262, which was one short. I had to try check most of the enumeration again before I found the missing one. Now I have to arrange them to appear on the corrected website pages, but I'm somewhat undecided on the best arrangement method. Probably I will group together those that have the same angles in the centre cells.
Here is a puzzle to solve based on the search. Complete the tour, given the four pairs of moves in the top corner-adjacent cells. I published this also in Mathstodon but it attracted no interest there. There are twelve such choices for the near-corner angles that have a unique solution.
Some cases have no solution. Others have up to 30 solutions, so this method of enumerating the tours does not provide a good way of classifying them.
The new bus station began operation this weekend. There is obviously still a lot of work to be done on it. The old bus station has been closed off ready for demolition. The new arrangement is much more compact. There is one entry and one exit for buses. This means the buses coming from the south need to go round the houses to get to the entrance, but this may only be temporary. The buses have to reverse out of the bays which looks as if it could be awkward if there are other buses coming in from behind. Here are some photos I took.
The first and fourth photos are from the Delamere street exit. The second and third are from the Victoria street entrance.
I took a number 31 bus up to Leighton Hospital, to see if I could get a box of catheters to keep me supplied over the next weekend as my order had not yet arrived. This was successful. The A&E building seems to have expanded considerably, into what used to be a large car park, since I was there last. Then I took a number 12 bus back to Crewe.
New results sent to me on enumeration of the smallest board tours by Andrew Usher in the USA and of queen tours by Walter Trump in Germany have led me to upgrade the relevant Knight's Tour Notes pages on my website. The trouble is that each of these updates has led to the realisation that all the other related pages also need updating. First I did the Shaped Boards section. Then the Walker Tours section (on pieces with lateral and diagonal moves.
A result about the impossibility of magic queen tours with rotary symmetry on the 6x6 board has led me to put new results into the Magic Theory page, and that led me to reinstate the page on 4x4 Magic Squares, which had become mixed up with the page on Multimover tours. Now I am recasting the whole section on Other Pieces. A lot of the pages are out of date compared with the PDF versions I issued in 2019.
The whole of the History pages also need to be updated, due to newer information, some of which was put into the 2019 PDF versions. So it's proving a big task. After that I will have to try to put everything into book form again. Or maybe I need to start a dedicated website for Knight's Tour Notes alone. All this leaves little time for other original work.
I've now completed my account of the Onitiu Problem, which has featured in these diary pages over the past two years. It forms a third page in the Figured Tours section on my Knight's Tour Notes pages.
https://www.mayhematics.com/t/f3_Onitiu%20Problem.htm
Quite a lot of work there that I'm pleased with, though still a number of gaps, and constructing solutions on larger boards is beyond the limits of my drawing program.
This is a differently coloured and enlarged version of the Giraffe Move Pattern that I published here in 2021. It shows the successive cells reached from the centre cell in successive numbers of Giraffe {1,4} moves. The colouring is still based on the rainbow sequence, but achieves more contrast between areas, with the orange and yellow areas coming between the darker areas. Is it too fanciful to imagine it as an architectural plan of some ancient temple?
I seem to have missed a month. I've been busy updating my website pages dealing with Knight's Tours on Shaped and Holey Boards. This was stimulated by new enumerations of 11-cell and 14-cell tours sent to me by Andrew Usher from the US. I've found it rather laborious, partly because I'm experiencing eye strain, and have to ration the time I spend online, to avoid getting a headache.
There have also been developments concerning magic queen tours on odd-sided boards. This is in work by Walter Trump in Germany. I suppose I will have to update the magic tour pages next.
Meanwhile in Crewe town centre work on clearing the site for the Bus Station is under way very slowly.
Here is another photo
Latest photo of the demolition work, taken 14 July, below:
Beautiful blue sky today and cool in the shade,
but I'm not looking forward to the heat wave forecast for next week.
Demolition work now complete (4 September 2022). Fortunately three trees along Delamere Street have survived the devastation so far.
