From the Fairy Board identify:
[1] The 2 ways to arrange 4 non-attacking kings on a 4 X 4
board with 1 in each row and column.
See Hertzsprung's problem: ways to arrange n non-attacking kings on an n X n
board,
with 1 in each row and column (A002464)
[2] The 4 ways to place a non-attacking white and black rook
on 2 X 2 chessboard.
See Number of ways to place a non-attacking white and black rook on n X n
chessboard (A035287)
[3] One of the 4 ways to place 10 nonattacking superqueens
on a 10 X 10 board.
See Number of ways of placing n nonattacking superqueens on an n X n board (A051223)
Blue23
Sunny day in the Ocean Depths of Ultraworld
Sheen of blues
Directional Contiguous Polyknights with 5, 6 and 7 moves, where a 1-move is a stationary knight
F3Layer2 is the pattern arising from applying 3 factorial
to 3 colours and then again to the 3 blocks of dimensions 2 by 3
Free, one-sided, and fixed polyknights
There are three common ways of distinguishing polyominoes and polyknights
free polyknights are distinct when none is a rigid transformation ( translation, rotation, reflection or glide reflection ) of another ( pieces that can be picked up and flipped over ). one-sided polyknights are distinct when none is a translation or rotation of another ( pieces that cannot be flipped over ).
fixed polyknights are distinct when none is a translation of another ( pieces that can be neither flipped nor rotated ). Yellow submarine shows polyknights of various types with 2 cells.
Chessboard Polyominoes with n squares. ( A001933 )
2,
1, 4, 7, ...
meditate & study
study & meditate
or contemplate ?
