Tuesday, 19 April 2022

Numbers and a Tour

 I have a new publication! Directory of Numbers. It is a 24-page listing of the numbers up to 9999 with prime factorisations, except that four-digit numbers divisible by 2 or 5 are omitted. These are easily divided by 2, 5 or 10 and the factors of the resulting smaller number can then be looked up.


I have also found a solution to the 18x18 Onitiu Problem of a knight tour with 180 degree rotational symmetry. This just fills a gap in my work, since I have not been able to find a solution to the 90 degree rotation on this board.  Here is the new result:

The square numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324 are shown on the red line. The blue line is a rotation of the red. There are no intersections between the red and blue lines, but single links 63-64 and 225-226, shown as heavy black moves.