George Duke wrote on Wed, Mar 10, 2010 10:58 PM UTC:
. 6^6^6 is enough to look at Rook's movements in
# 1-> ._. I triangles. Starting at 26, -27-18-11-6-3 is five-
# 234-> ._._. II stepper, ever fully being blockable. Returning is
56789-> ._._._. III is 3-2-5-10-17-26 in different back-path to same
10-16-> ._._._._. IV cell. There are two Bishop bindings. Bishop has
17-25-> ._._._._._. V pathway 26-17-10-5-2-1. This Bishop cannot reach
26-36-> ._._._._._._.VI triangles with an odd sum of (Level + Cell). She
is the corner Bishop, and the other Bishop is the odd Bishop, as with the above six-sided and all equilaterals. Rook reaches eventually every triangle, and Bishop half of them. As n increases, the corner Bishop gains one each level. For example on 11^11^11, which is 121 triangles, the corner Bishop reaches 66 and the odd Bishop 55 for strategic planning. More primitive triangles are more normal than squares. [66 and 55 are now correct without other's comment.]
