Tuesday, May 2, 2017

Travel Battle Campaign Map

Looking at Bob Cordery's Travel battle Napoleonic campaign maps, I was quickly struck by the rotational symmetries of the 4-piece quadrants in both maps.  I wondered if there was an easy way of eliminating, or at least reducing those symmetries.

To save a bit of time, I copied one of Bob's printed campaign maps onto a picture file, and, using Microsoft Paint (it might be primitive by industry standards, but it has the features I want and use often) made certain modifications.

1.  Selected the leftmost column of four, and transplanted it on the right hand  side.
2.  Observing that the top and bottom centre blocks of four were rotationally symmetrical, rotated one only piece in each, left 90 degrees..

Here is the map thus produced:

I agree, many would like symmetry as offering a fair and even playing field, as in chess.  But others will prefer asymmetry as posing problems of its own.

The above map offers useful  4 entry points on three sides; 3 on the north side if you discount the farm driveway at the top left.

North-south there are two distinct through-routes, but east-west there is but one.

Note that the above 4x4 array contains 24 gameboard pairs. The gameboard pairs offer 16 permutations.  So of the pairs above, at least 8 must be identical, however oriented (e.g. top left vertical and top right vertical; bottom left and right vertical, and I can see one other pair that appears four times.  

Interesting, this sort of thing...


  1. Archduke Piccolo,

    I hope to look at ways of making the process of 'placing' the boards a little more random, and with luck I should be able to write a blog entry about it in the very near future.

    All the best,


    1. It certainly is an interesting exercise from a mathematical point of view!