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 shortest way from A1 to B1
On the square A1 of a regular chessboard is a regular dice, face 1 up and face 2 in front. The only allowed move is to rotate the dice by 90 degrees to an adjacent square.
Find the shortest way from ...
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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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