Questions tagged [checkerboard]
A puzzle involving checkerboards: grids of squares alternating black and white in color, most commonly an 8x8 board.
172
questions
7
votes
2answers
349 views
How many squares can a limp queen move to?
Consider a large chessboard. A limp rook is a chess piece that moves one step orthogonally, but it turns $90$ degrees after every move. The limp rook makes some moves, not crossing over its own path, ...
2
votes
2answers
186 views
Quickest chess stalemate with Queens exchange
Continuing my previous puzzle.
If both players cooperate, what is the quickest stalemate in chess that includes a Queens exchange, in a legal game?
3
votes
1answer
384 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 ...
2
votes
2answers
348 views
Two genies and their kind of chess
While playing chess Parcly and Tori Taxel, best friends and genies, got bored and transformed all the pieces into pawns to make pretty patterns. They found this 22-pawn arrangement where every 3×3 ...
6
votes
1answer
178 views
42 lines on a chessboard with associated numbers
The 64 squares of a chessboard can be associated with 42 lines as follows:
the 8 rows
the 8 columns
13 diagonals from north-west to south-east
13 diagonals from north-east to south-west
Those ...
4
votes
0answers
143 views
Police and Thieves
I played this game when I was young, but cannot find it online. It is played on a checkers board (e.g. the black squares of a chess board) between two players P and T. The game goes as follows:
P ...
7
votes
2answers
408 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 ...
5
votes
2answers
1k views
A King's Short Walk
Place the numbers 1 to 25 on the cells of this board so that any two consecutive numbers occupy cells that are horizontally, vertically or diagonally adjacent. Prime numbers should occupy shaded cells....
3
votes
1answer
132 views
Exchanging stones on a 8x8 board with sum of two adjacent numbers not being prime
You are given 64 stones labelled with number 1 to 64 each. All those stones are randomly placed on the squares of a 8x8 chess board such that each square is occupied with exactly one stone.
A move is ...
12
votes
1answer
755 views
Transform each square of a chessboard to zero
Each square of an 8x8 chessboard is marked with a positive integer.
The integers can be changed according to the following two rules:
(1) all integers in a row are doubled
(2) all integers in a column ...
20
votes
2answers
1k views
Beans under the chessboard
Under every grid cell of a chessboard, I put either one bean or nothing.
Now if you choose a (grid) rectangular area on the chessboard, then I will tell you the parity of the number of beans under ...
25
votes
2answers
1k views
The Knight's Romp
Recently I was messing around with a singular knight on a chess board, and I came up with an interesting dilemma.
Can you move a knight, from starting on any square, such that its path covers every ...
6
votes
1answer
508 views
Chess - Knight Mate
What is the fastest, in terms of moves, for a legal game to come to a checkmate, either black or white with a Knight and such that both all other cases of the checkmated King are attacked by an ...
4
votes
1answer
251 views
Choosing squares on a square board
I have an $8 \times 8$ board. On the board, I want to choose 2 unit squares in each column and row such that none of the chosen squares are touching. This means they cannot share a side or a corner. ...
4
votes
1answer
175 views
Chess - I will eat!
Suppose that you are playing White, and your aim is to eat a black piece (pawns qualitfy) in the fewest moves as possible and Black are not cooperating at all, and, even more, Black's aim is to ...
4
votes
1answer
116 views
How many queens are needed to attack all white squares?
This question: How can 3 queens control the white squares? got me thinking...
What is the fewest number of queens needed to attack every white square?
Rules:
Only queens allowed
Every white square is ...
30
votes
5answers
5k views
How can 3 queens control the white squares?
It is well known that there is no way of arranging 4 queens on a checker board in such a way that every square is occupied or threatened.
Now consider a slight variation where we only need to cover ...
11
votes
1answer
451 views
Grid infection with diagonal adjacencies
A community consists of 81 houses laid out in a 9 x 9 square grid. Every household is friends with their eight orthogonal and diagonal neighbors (except for the houses on the perimeter which have only ...
4
votes
2answers
201 views
Maximum number of kings that can exit
N kings are placed on a chessboard, with at most one king on any square. Following standard rules of movement (one square in any direction), every king must be able to reach some edge of the board ...
5
votes
4answers
455 views
Most Captures Chess
In Most Captures Chess puzzle, you will need to provide a legal game where it is Blacks to play and where they have the most different ways to capture a White piece.
For instance, the next game allows ...
0
votes
1answer
132 views
How many roads in a Tak square?
The board game Tak is played on a chess-like board of variable size (most commonly, 5x5 and 6x6). Players place and move pieces on the board with the goal of creating a "road", which is a ...
5
votes
3answers
283 views
A tribute to "Most ways to uncheck the king"
Today, we had the great privilege to see @Paul Panzer's answer being ticked at @thesilican's absorbing puzzle.
I here propose a variant of his puzzle where it's not mandatory to use a legal chess game....
5
votes
2answers
186 views
Switching Black and White
In this Chess puzzle, your aim is to switch black and white, with a legal game, and arrive at the final position:
This aim is likely unreachable. So you must try to get the maximum number of pieces ...
25
votes
6answers
3k views
Chess solitaire: The King's longest walk
Challenge: maximize the number of moves white needs for its king to reach a square of your choosing, adhering to the following rules:
Black does not move
Like normal: The king may not be in a ...
6
votes
2answers
358 views
Fastest draw from opening position in chess
When playing a normal game of chess, assuming the opponents are cooperating:
In how many moves can a draw be unavoidable, excluding voluntary draws or draws by repetition of moves?
1 While not ...
7
votes
2answers
1k views
The Popular Letter Chessboard
You are given a Chess board with black and white squares.
You must fill your Chess board with Merriam Webster English words, or other equivalent dictionnaries if you prefer such that each square ...
4
votes
1answer
221 views
Kings' Chess Harem
Pursueing these two related puzzles, Chess Bloodshed and Devouring Nobility I create for you Kings' Chess Harem where you have to find, with the minimum number of moves, a legal game where all pawns ...
10
votes
2answers
1k views
Chess Bloodshed
This puzzle is the idea of Dmitry Kamenetsky in a comment of my puzzle Devouring Nobility.
Find, with the minimum number of moves, a legal game where all pieces are captured except the two kings.
3
votes
2answers
220 views
Magic rotated checkerboard function made in python!
Here's a puzzle for all you python programmers out there:
I defined a function that goes like this:
...
3
votes
1answer
205 views
Create the freest arrangement of white chess pieces on board by consequently moving your pieces
You start with this board. You're the White. Freedom Index of initial arrangment of your chess pieces is equal to 20 (each pawn has two moves, each knight has two moves)
Your goal is to have as much ...
19
votes
3answers
2k views
Painting a chessboard
On the following chessboard every white square meets at least two red squares.
Let's paint a new chessboard so that every white square meets exactly two red square. Every square should be painted ...
10
votes
1answer
806 views
Playing with a chess cipher
Alice and Bob both love encryption, and Alice loves to play chess. Unfortunately, Bob isn't very good at chess, so he doesn't think it's very fair to have to play the game for real. So instead of ...
10
votes
1answer
329 views
A chessboard tiling with corners removed in 3D
A famous problem asks whether an 8x8 chessboard with two opposite corners deleted can be tiled with dominoes, where a domino is a rectangle congruent to two adjacent squares of the board.
Now, let C ...
4
votes
1answer
142 views
A interesting and a bold chess puzzle
Here is a chess puzzle I have made . It needed a lot of thinking .
If you are white , how would you play in this position ? State your best moves !!
Please don't use Stockfish or Alphazero or any ...
15
votes
1answer
697 views
Arrange ten pawns into ten lines of three
This is not a chess problem!
In the following position you can see six pawns that have been arranged into lines of three. Each pawn stands at the intersection of exactly two lines and each line ...
1
vote
3answers
330 views
Class Chess Tournament
A class of 36 students are expecting to play in the chess tournament held by Math Department. When the schoolmaster arrived he said "Lets start the games but first we must setup all the chess ...
16
votes
2answers
2k views
A Rook's Territory in the Chessboard
Shade 32 cells, four on each row and column, of an 8 x 8 blank chessboard (all its cells originally white) so that a rook sitting on any shaded cell can reach any other shaded cell, moving just along ...
3
votes
2answers
204 views
Black War Heroes or Whites Save the Queens?
After Black Cavalry successfully captured White princesses,
White empire learns their Black opponent is hungry for more and wants White Twin Queens dead!
White will never let such a disaster happen ...
6
votes
1answer
346 views
Whites capture whites and Blacks capture blacks
This is my first Chess Puzzle!
Let suppose you start a Chess game.
Whites' aim will be to place all their alive pieces on white squares in a minimum of moves and black will do the same, but with ...
14
votes
3answers
908 views
Four fanatics and one checkerboard
Four checkers-playing fanatics eagerly
pair up for two simultaneous games of checkers
but somehow find themselves with just one board.
They do have enough checkers for two games, so it is time to act.
...
8
votes
2answers
817 views
Knights and Queen puzzle
This is not original. I just want to share this problem. If you have heard of it, please give opportunities for those who haven't to answer.
Horst and Queenie are playing a game on a $200\times200$ ...
1
vote
1answer
85 views
k-threats Chinese Cannons Chess: Part 2
Inspired from the N-Queens problem, I here propose you a puzzle from Xiangqi wich is Chinese Chess equivalent, mostly played in Asia.
The most different piece from Xiangqi is the cannon. You can ...
4
votes
1answer
107 views
k-threats Chinese Cannons Chess: Part 1
Inspired from the N-Queens problem, I here propose you a puzzle from Xiangqi wich is Chinese Chess equivalent, mostly played in Asia.
The most different piece from Xiangqi is the cannon. You can ...
6
votes
1answer
149 views
Most moves by Most number of Pieces
Using one color, White or Black, place as many chess pieces (kings, queens, bishops, knights, rooks, and pawns, or combinations thereof) as you can on a checkerboard so that when the number of pieces ...
18
votes
2answers
2k views
Playing with one Queen on a chessboard
Alice and Bob play a special chess game with alternate moves. Alics starts with an empty chessboard and puts a Queen at a field in the first row (A8-H8) or the right column (H1-H8). Now Bob is moving ...
12
votes
3answers
1k views
How many chess pieces do we have to put at least?
In a $8\times8$ chessboard, a cell is qualified if an adjacent cell (a cell which is on top, left, below, or right of the cell) excluding itself has a chess piece on it. How many chess pieces do we ...
20
votes
3answers
3k views
A chess board with numbers
A 8x8 chess board is marked with the numbers from 1 to 64 sequentially from left to right, row by row and top to bottom.
Now a minus sign is added to 32 of those numbers such that in each row and in ...
17
votes
4answers
2k views
Paint 21 Squares of a 7×7 Board Without Forming a Rectangle
Got a nice puzzle from my friend, when he was competing in IWYMIC/IMC 2011.
Paint $21$ of the $49$ squares of a $7 \times 7$ board so that no four painted squares form the four corners of a rectangle....
6
votes
3answers
905 views
Cover 63 squares of a chess board, differently
In this other puzzle, ThomasL asks for three similar pieces which can be arranged to exactly cover all of an 8x8 chessboard, except for a single square — for any of the 64 possible single squares.
I ...
46
votes
3answers
5k views
Cover 63 squares of a chess board
Can you find 3 similar geometrical figures (common shape but can be different sizes) A, B and C with the following property:
If you remove any square from a 8x8 chess board, then the remaining area ...