# 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 coolest checkerboard magic trick

In the small town of Terni (Italy), there's a couple of young friends named Marco and Leonardo, who like to perform magic tricks to a restricted audience of common friends and relatives. They like to ...
4answers
13k views

### How many chess pieces does it take to “cover” all spaces on a chessboard?

Given an 8x8 chessboard, your goal is to "cover" each space on the board with the fewest possible number of pieces. A space is "covered" if there is a piece on it, or if a piece on the board can be ...
4answers
3k views

### Checkerboard Infection

There is a dangerous bacteria, Checkerichia Coli, (or C. Coli for short) which lives in the squares of checkerboards. Squares with this bacteria living in their digestive systems are said to have "C-...
5answers
3k 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 ...
2answers
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 ...
2answers
4k views

### 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?
2answers
4k views

### How many queens can be on a chessboard without attacking each other?

What is the maximum number of queens that can be placed on a standard 8x8 chessboard such that no one of them is capable of attacking any of the others in a single move?
2answers
348 views

### Combinatorial Agriculture

You have just acquired a $64$ acre farm, in the shape of a square, and divided into an eight by eight array of one acre subplots. You have $21$ crops to plant. Each crop requires its own $3$ acre plot ...
6answers
2k views

### The Bunny's Tour

The Bunny is a new chess piece. It can move in 2 different ways: Diagonally, but only exactly one space (so like a bishop with the limitations of a king). It can also "Bunny-Hop" over another bunny. ...
4answers
1k views

### Arrows on a Chessboard

I've taken an $n$ by $n$ chessboard and drawn an arrow on each square, pointing in one of the eight compass directions. I've done this in such a way that arrows in (orthogonally) adjacent squares ...
3answers
5k views

### Cover 63 squares of a chess board

Can you find 3 similar geometrical figures (common shape but can be different sizes) A, B and C with the following property: If you remove any square from a 8x8 chess board, then the remaining area ...
1answer
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. ...
3answers
2k views

### The knight's game

Alice and Bob play the following game on a standard $8\times8$ chessboard. In the very beginning, Alice picks a square on the chessboard and places a knight on this square. Then Bob and Alice ...
3answers
1k views

### Total no of squares on a Chess Board

Is there any formula than calculates the total number of squares on chessboard? For example in a $8\times8$ chessboard, there are squares of sizes $1\times1$, $2\times2$, $\ldots$, $8\times8$. So I ...
3answers
2k views

### Coloring an n by n grid with four colors

This is a generalization of Place 4x12 detainees on a 7x7 grid of cells. The goal is to color the squares of an $n\times n$ grid with four colors such that at most one square is uncolored no two ...
4answers
1k views

### Discrete Peaceful Encampments: 9 queens on a chessboard

Here's a discrete variation of yesterday's puzzle Peaceful Encampments. You have 8 white queens and 8 black queens. Place all these pieces onto a normal 8x8 chessboard in such a way that no white ...
4answers
362 views

### Discrete Peaceful Encampments: Player 3 has entered the game!

Here's a variation of Discrete Peaceful Encampments: 9 queens on a chessboard (which itself is a variation of Peaceful Encampments). You have 4 white queens, 4 black queens, and 4 red queens. Place ...
3answers
4k views