All Questions
Tagged with checkerboard graph-theory
7 questions
29
votes
4
answers
3k
views
Rolling cube on an infinite chessboard
Imagine a six-sided die, D6, the right size to exactly occupy a square on a chessboard.
The die can move to any adjacent square, but does so by rolling rather than sliding, so the topmost side of the ...
- 2,408
3
votes
1
answer
438
views
Genies' chess on a 10×10 board
The work of Hearth Taxel revealed some other results related to genies' chess. For example, there is an arrangement $A$ of pawns on a 10×10 board such that no 3×3 submatrix is empty and
$A$ is ...
- 8,725
7
votes
2
answers
1k
views
Another Rook's Tour of the Chessboard
Place numbers 1 to 64 in the cells of this 8 x 8 board in such a way that consecutive numbers occupy neighboring cells (either vertically or horizontally). Shaded cells must be occupied by prime ...
- 19.2k
8
votes
2
answers
917
views
Eight queens on the chessboard with mirrors
A 8-by-8 chessboard has two mirrors added on its left and right margin. The mirrors reflect the queen moves so that a queen threatens additional squares on the board. A queen threatens
all squares in ...
- 11.7k
42
votes
1
answer
3k
views
Crippled King Crossing a Canyon
A chess king has been injured in battle against an evil wizard, and can no longer move northeast or southwest.
This king is on the North rim of a canyon, and must flee to safety on the South rim. ...
- 32.8k
11
votes
1
answer
628
views
Generalisation of tours on chessboards
It's well-known that a knight placed on one square of a chessboard can get to any other square, but a bishop can only reach half the squares from a fixed starting point. Another question on this site ...
- 118k
10
votes
6
answers
3k
views
The Bunny's Tour
The Bunny is a new chess piece. It can move in 2 different ways: Diagonally, but only exactly one space (so like a bishop with the limitations of a king). It can also "Bunny-Hop" over another bunny. ...
- 14.5k