Questions tagged [checkerboard]
A puzzle involving checkerboards: grids of squares alternating black and white in color, most commonly an 8x8 board.
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King 2 men, but don't kill a man
I found mention of this challenge in a Science paper called "Checkers is solved" from 1996, but no example was given.
Beginning at starting position, play moves according to rules of ...
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Chess with jumping
Puzzle Statement:
Consider the game of chess, but with a slight modification of the rules as follows: all heavy pieces (i.e., the queens and rooks) are allowed to jump as far across the board as they ...
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Painting a Checkerboard
I love checkers - but I've played it so much that the color of my board is faded and dull. Today, I resolved to paint it. Unfortunately, I slipped and fell :(
Now there's paint all over my ...
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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 ...
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The game of life on an infinite chessboard
There is an infinite chessboard. The chessboard is divided in two by a horizontal line that extends indefinitely. Above the dividing line, the cells of the chessboard must remain empty. Below you can ...
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Bow or lazy checkmate?
Suppose that both players cooperate, find the shortest, in terms of number of moves, black checkmate such that the game is valid and white pieces never go on rows 4 to 8.
e.g. ...
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Chess lead change
Given the following Chess piece relative values and such that both players cooperate, what is the fastest way such that White first has an advantage of at least +10 piece value then secondly, Blacks ...
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Checkmate N Kings with M Knights Perfectly
We have this Existing Puzzle which has got the valid and invalid cases listed ; the Accepted Answer is along the lines of what is invalid and what is valid.
But there was a flaw or fault in the Puzzle ...
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Checkmate N Kings with M Knights
There are N White Kings on the Chess Board.
There are M Black Knights.
There is no Black King and no other Piece. Only M+N Squares are occupied.
Each White King is attacked by atleast 1 Black Knight, ...
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The Game of Golden Squares
On a magic chessboard of infinite size, the squares are either wooden or golden. If 4 or more of its 8 neighbors (a king's move away) are golden, a wooden square becomes golden the next day. Golden ...
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Coloring the squares
You can choose from 4 colors to color every square of the following $10\times 10$ grid.
After you finish, I'm going to take a connected block with at most three colors away. Your goal is to minimize ...
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Geometric game on a n*n chessboard
You can get famous (OK, Warhol-15 minutes-famous :-)!
First a few definitions. Of course, two rooks of the same colors don't attack, but since two colors are needed, "attacking" here means &...
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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, ...
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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?
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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....
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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....
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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.
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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:
...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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