Enter Your Reply

.         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.]