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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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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