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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Black and white queens on an 8x8 chessboard

What is the largest number of queens that can be placed on a regular $8\times8$ chessboard, if the following rules are met: A queen can be either black or white, and there can be unequal numbers ...
3k views

A chess board and a coin! [closed]

You have a standard chessboard, consisting of $64$ squares ($32$ white and $32$ black) each of dimensions $4\times4$ cm, and you have a standard coin of $2$ cm diameter with tail and head. You flip ...
740 views

Placing seven point-sized pawns

Can you place seven (point-sized) pawns on a $7\times7$ checkerboard, so that every pawn is placed precisely in the middle of one of the little checkerboard squares, and all distances between pairs ...
199 views

Swapping knights

On a $3\times3$ grid we have: with $8$ moves needed to swap the red and blue knights. What is the minimum numbers of moves to swap the knights on a $4\times4$ grid?
1k views

Professor Halfbrain and the 99x99 chessboard (Part 2)

This puzzle is the continuation of "Professor Halfbrain and the 99x99 chessboard (Part 1)". The difference is that "four corners of a rectangle" has now become "$2\times2$ subsquare". Professor ...
2k views

Professor Halfbrain and the 99x99 chessboard (Part 1)

Professor Halfbrain has spent the last weekend with filling the squares of a $99\times99$ chessboard with real numbers from the interval $[-1,+1]$. Whenever four squares form the corners of a ...
3k views

Crippled King Crossing a Canyon

A chess king has been injured in battle against an evil wizard, and can no longer move northeast or southwest. This king is on the North rim of a canyon, and must flee to safety on the South rim. ...
507 views

Crosses on a 10x11 chessboard

A cross consists of six unit squares and looks as follows: O OOOO O (this may also be rotated by several right turns, or horizontally ...
1k views

Professor Halfbrain and the 9x9 chessboard (Part 2)

This puzzle is the continuation of Professor Halfbrain and the 9x9 chessboard (Part 1). The difference is that "distance at least $2$" has now become "distance more than $2$". ...
1k views

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 ...
2k views

Rooks on a 15x15 chessboard

On a 15x15 chessboard there are 15 rooks that do not attack each other (via ordinary rook moves). Then each of the rooks makes one move like that of a knight. Is it possible that after all this is ...
2k views

Dominos on a checkerboard

What's the maximal number of dominos (2x1 tiles) that can be placed on a checkerboard (8x8 square) so that every domino covers exactly 2 squares of the checkerboard and no two dominos form a 2x2 ...
750 views

Concentrating tokens on an infinite board

One token is placed on each square of an infinite checkerboard. One square is marked with an X. You want to get as many tokens on the marked square as possible. To do this, you may make any finite ...
339 views

Tiling an Odd Polygon with Dominoes

There is a polygon whose edge lengths are all odd integers. Prove that this polygon's interior cannot be tiled by dominoes whose dimensions are $1\times 2$. An example of such a polygon is a "...
1k views

Desegregate the Knights

You are given a 3 by 3 chessboard with a knight on each corner, where the knights in the top row are black and in the bottom row are white. On each turn, you may move a knight of either color (the ...
4k views

Switch The Knights

On a small $4 \times 3$ chessboard, the top row is filled with black knights and the bottom row with white knights. On each move, you may move one knight (as it moves in chess) to an unoccupied ...
602 views

Trapping pieces on an infinite chessboard

Alice and Bob are playing an unusual game of chess. We begin with a piece on a square of an infinite chessboard. On each of her turns, Alice moves the piece. On each of his turns, Bob destroys a ...
823 views

Let's revisit this later (a two player knight's game)

Alice and Bob play a game on the following irregular chessboard. (Note the blacked out squares are not legal moves.) Alice starts the game by placing a knight on any square she chooses. They then ...