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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The knight's game
Alice and Bob play the following game on a standard 8 by 8 chessboard.
In the very beginning, Alice picks a square on the chessboard and places a knight on this square.
Then Bob and Alice alternate ...
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Is there a brute-force solution of this puzzle?
There is a puzzle
Suppose a standard $8x8$ chessboard has two (arbitrary) squares removed. The only thing known is that these two squares have different colours. Is it always possible to place 31 ...
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How far can a pawn get 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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How can the knight traverse a chessboard to make a path that sums to 100
THE KNIGHT'S CENTURY.
THEN Dr. Bates drew on a large sheet of paper a reduced chessboard of twenty-five squares, and numbered it in the manner shown in our diagram. He then placed a chess knight on ...
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Attacking chessboard squares with 6 pieces
Place 6 white pieces (a king, a queen, a rook, a bishop, a knight and a pawn) on 6 different squares of a regular 8x8 chessboard so that there is at least one empty square attacked by exactly one ...
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Anna and Boris play the Red Blue game
Anna and Boris play a game on a 9x9 chessboard. Anna goes first and turns alternate thereafter. In each move, Anna puts a red counter on a vacant square while Boris puts a blue counter on a vacant ...
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Yet another pentomino puzzle
Just rearrange the 13 checkered polyominoes shown below to form a chessboard. The solution is unique and unusual.
Clarification: The pieces may be reflected; the coloring on the back is as if the ink ...
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Pawns and a chessboard with no three aligned
This little problem crossed my mind and appeared to be not quite trivial.
How can you place P pawns on a chessboard with the constraint that no pawn is exactly midway between two other pawns?
Sure ...
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Rooks covering Dark Squares on a Chessboard
How many rooks are required such that all dark squares on the chessboard are covered by at least one rook.
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Coloring of a 5 x 5 chessboard
The squares of a 5 x 5 chessboard are painted in one of two colors in an arbitrary way. Prove that there exist 2 rows and 2 columns such that the 4 squares where they intersect are all of the same ...
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Two-Move Chess Game
Consider a standard game of chess. We make the following modification: on a turn,
if a player makes a move which neither captures a piece nor puts their opponent’s
king in check, then they may make a ...
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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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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 ...
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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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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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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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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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Placing 2x1 dominoes on a chessboard with two corners removed
Suppose you have a checkerboard with two opposite corner squares removed, like this:
Is it possible to place 31 dominoes of size 2x1 so as to cover all of these squares?
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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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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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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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Professor Halfbrain and the 9x9 chessboard (Part 1)
Professor Halfbrain has spent has spent the last few days with placing pawns on a $9\times9$ chessboard; each of the $81$ squares on the chessboard had side length $1$.
Halfbrain always started with ...
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