Questions tagged [checkerboard]
A puzzle involving checkerboards: grids of squares alternating black and white in color, most commonly an 8x8 board.
225 questions
3
votes
1
answer
280
views
Partial knight's tour with crosslinks
We have many puzzles to find complete knight's tours – including on 4D boards, irregular boards and nonplanar boards – but few puzzles to find partial tours where only some cells are visited. I ...
- 10.5k
7
votes
1
answer
606
views
The Drunken Bishopawn’s Staggering Tour
Here’s an original version of the puzzle: this question.
Once upon a time, there was a Bishopawn: a hybrid chess piece that moves like a bishop (freely on diagonals) and, like a pawn, could step one ...
- 33.9k
9
votes
2
answers
1k
views
Shortest tour from a Bishopawn
A Bishopawn is here defined as a Bishop that can also advance one square, just like a Pawn. That means the Bishopawn can change its square color and visit all the squares!
What is the minimum number ...
- 7,968
9
votes
2
answers
916
views
Minimum Crossed Knight Chess Tour
The Knight's Tour is a famous sequence of moves in a Chessboard.
We now search for a Knight Tour such that the number of intersections drawn by the tour is minimal.
Here is a valid Knight tour given ...
- 7,968
-1
votes
2
answers
321
views
Chess - Amazons - Magnus Carlen vs Gukesh 2025 Norway
Parts of this puzzle are taken from this nice puzzle of @Will.Octagon.Gibson.
An Amazon is a fairy chess piece that can move like a queen or a knight.
In this famous game at Norway in 2025, ...
- 7,968
19
votes
7
answers
3k
views
What is the maximum number of Amazons that can be placed on a 5x5 chessboard so that no piece attacks another?
An Amazon is a fairy chess piece that can move like a queen or a knight.
What is the maximum number of Amazons that can be placed on a 5x5 chessboard so that no piece attacks another?
Attribution:
...
- 32.1k
9
votes
2
answers
517
views
Can 3 Nightriders checkmate a lone King (with help of friendly King) on an infinite chess board?
Nightrider, or NN, is a fairy chess piece similar to the knight, but it can continue leaping in the same direction in one move while the touched fields are empty (like the bishop). It is stronger than ...
15
votes
1
answer
822
views
Sam Loyd's broken chessboard
Puzzle from Sam Loyd: Rearrange the eight pieces in order to form a perfect 8x8 chessboard.
Comment: This is not a "trial and error" puzzle. There is a hidden strategy* behind it and your ...
- 965
19
votes
9
answers
3k
views
Prove that it's always possible to remove one rook so that the remaining rooks still satisfy the same property of no empty ranks or files.
Redundant rook puzzle:
Fifteen rooks (and no other pieces) are placed on a standard 8x8 chessboard such that there is at least one rook in each rank and file (that is, horizontal and vertical rows).
...
- 32.1k
5
votes
1
answer
756
views
Fastest checkmate by castling
Given that the two chess players cooperate, what is the fastest checkmate with the castle (either White's or Black's) as a final move?
- 7,968
8
votes
2
answers
740
views
Can you swap the positions of the 8 Chess bishops?
Goal:
Swap the bishops so that at the end the white bishops completely fill the top row and the black bishops completely fill the bottom row.
Details:
Move bishops one at a time according to standard ...
- 32.1k
6
votes
2
answers
681
views
Odd neighbors. Can you place coins on a 6x6 chessboard so that every square has an odd number of adjacent squares that contain a coin?
Can you place coins on a 6x6 chessboard, at most one coin per square, so that for each square, whether occupied or not, the number of coins on adjacent squares (sharing a common edge) is odd?
...
- 32.1k
17
votes
2
answers
2k
views
Unneighbourly circuit. Is there a closed rook tour on a 4x4 chessboard where the rook never moves to an adjacent square?
Place a Chess rook on an arbitrary square of a 4x4 chessboard. The rook is allowed to move horizontally or vertically but not to an adjacent square (that is, it must move at least two squares).
Is ...
- 32.1k
12
votes
2
answers
534
views
How many Ducks are needed to trap a Queen?
Duck chess is a popular variant on chess.com, but this question is not about it. Just borrow the cute ducks and its movement rule:
A duck piece can move to any vacant square on its move. It must move
...
5
votes
2
answers
835
views
Nonattacking pegasi on the 12×12 board
There were two questions asked in quick succession about nonattacking nightriders and then camelriders on an 8×8 board. In both cases a "striping" argument provides a decent upper bound.
It ...
- 10.5k