Thursday, 25 February 2021

Dawsonian 10 by 10 Tours

 These tours that I have been posting initially on Twitter are part of some work I am doing to put an updated page on Figured Tours on my Knight's Tour Notes pages. I found I had no examples of Dawsonian tours on larger boards. That is tours showing the square numbers in knight paths, preferably symmetric circuits. T. R. Dawson constructed a complete set of such tours on the 8x8 board.

Rectangle 1x4

Hexagon

Octagon

Constructing these tours makes a good puzzle for solving. Probably the larger board makes it a little easier to complete the paths than on the 8x8 board. My procedure is to start with the shorter sections 1-4, 4-9, 9-16 and so on, trying not to leave inaccessible unused cells. Fitting the last two segments 64-81, 81-100 are of course the tricky part of the problem. Sometimes one ends up with two loose ends that do not connect by a knight move.

Addendum: A fourth example to complete the set of symmetric convex polygons.

Rectangle 2x3


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