recently I've been investigating many things in higher dimensions (chess being one)
This is how moves a king would have (one space in any direction) in different parts of the board:
1D:
2 moves away from the sides
1 moves at the corner
2D:
8 moves away from the sides
5 moves at an edge
3 moves at a corner
3D:
26 moves away from the sides
17 moves at a face
11 moves at an edge
7 moves at a corner
4D:
80 moves away from the sides
53 moves at a cell
35 moves at a face
23 moves at an edge
15 moves at a corner
5D:
242 moves away from the sides
161 moves at a teron
107 moves at a cell
71 moves at a face
47 moves at an edge
31 moves at a corner
6D:
728 moves away from the sides
486 moves at a peton
323 moves at a teron
215 moves at a cell
143 moves at a face
95 moves at an edge
63 moves at a corner
(Hope I've caculated all that right and got the right terminolgy!) btw I could go beyond that!
I've set rules for pieces so that:
An extra piece for each dimension (for each new type of diagonal)
a knight moves (1,2,3,...etc) one square more each direction (or one square orthogonally and diagonly which means the same thing)
Both of these mean that the number of "spaces" each way increases by two:
8X8, 10X10X10, 12X12X12X12 etc.
I having trouble with one aspect right now:
How many of each piece shold each person get! Any ideas?