Wednesday 22 October 2014

Crane working on Hastings Pier

I meant to post this photo of the crane working on Hastings Pier a while ago.
It was taken 28 September. The crane has since gone.



How it was brought there and taken away I didn't see.
I don't think they were drilling for oil!
Impressive engineering work.

Monday 13 October 2014

Magic Rectangle Tours

I have been doing a search for magic rectangle tours
on 3 by 7 board (and others) by pieces with limited moves,
and have found only these three so far.

They all contain the rank 8, 9, 10, 11, 12, 13, 14 (in some order)
adding to magic constant 77. The files add to 33.

Each tour is presented in forward and reverse numbering,
and oriented with the 1 (or 2) in the top left.

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Amazon (Queen + Knight) magic tours:

15 01 19 02 21 03 16 == 06 19 01 20 03 21 07
12 14 09 11 08 13 10 == 12 09 14 11 13 08 10
06 18 05 20 04 17 07 == 15 05 18 02 17 04 16

This uses seven types of move
Rook 02, 03, 04, 05, 06, Bishop 11, Knight 12

01 19 18 04 03 15 17 == 02 17 20 01 06 15 16
12 09 13 08 14 11 10 == 10 13 09 14 08 11 12
20 05 02 21 16 07 06 == 21 03 04 18 19 07 05

This uses nine types of move
Rook 01, 02, 03, 04, 05, Bishop 11, 22, Knight 12

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Raven (Rook + Nightrider) magic tour:

01 17 15 05 21 02 16 == 06 20 01 17 07 05 21
14 13 12 09 08 11 10 == 12 11 14 13 10 09 08
18 03 06 19 04 20 07 == 15 02 18 03 16 19 04

This uses seven types of move:
Rook 01, 02, 03, 04, 05, Nightrider 12, 24

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Does anyone know of previous work on this subject?
I published some results on the 3 by 5 board
in Chessics #26 (1986) including a symmetric tour
using only four types of move.

I can only find an article by Marian Trenkler of Slovakia
http://math.ku.sk/~trenkler/
published in Mathematical Gazette 1999.


Sunday 12 October 2014

A Figured King Tour

The wazir tour with squares in a row on boards 2x2, 6x6, 10x10 and so on was published in Chessics #21 (1985). It occurred to me yesterday to look at the same problem on the 8x8 board but using the king as the touring piece. It appears that a solution with the square numbers in order of magnitude is just beyond the realm of possibility (with a knight move in place of one of the king moves it can probably be done). However I did find a solution with the numbers slightly out of order:



I set this as a puzzle on twitter, but haven't had any claims of anyone solving it yet. Of course the tour is not completely determinate. Some of the parallel pairs of moves can be replaced by crossing diagonal moves. But with the condition "minimum crossovers" it is probably unique. It includes a 6x6 solution with the numbers in correct sequence in the central area.