# 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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### Two rooks for Bobby Fischer

Bobby Fischer liked to play the following game on a standard $8\times8$ chessboard: In his first step, Bobby placed a white rook and a black rook somewhere on the chessboard (on two different ...
673 views

### Polyominoes on a checkerboard

Professor Halfbrain has spent his entire weekend by cutting lots of wooden $50\times50$ checkerboards into lots of polyominoes. He looked at various pattern polyominoes with area $49$, and always ...
534 views

### Placing dominoes on a 3x100 checkerboard

Alice and Bob play a game by alternately placing dominoes on a $3\times100$ checkerboard (3 rows, 100 columns). Alice has the first move. A move of Alice consists in placing a $1\times2$ (horizontal) ...
2k views

### The Erasmus rook tour

Professor Erasmus has found a special way of moving a rook across a standard $8\times8$ chessboard that he modestly calls the "Professor-Erasmus-rook-tour". The professor claims that in this tour, ...
462 views

### 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 ...
355 views

### Capture The Runaway Mouse

Say you have a grid of 16x16 squares. Label them A through P and 1 through 16. Now say that at H8 there's a mouse that moves at 1 slot every turn. Also, you get to block a tile every turn. Say the ...
225 views

### 8 queens equivalent on checkers [closed]

I'm a computer programmer trainer and sometimes I do some puzzle exercises with my students. Right now we did a checkers game and I would like to make them program to solve something with their ...
1k views

### Solutions for generic polyomino puzzles

Inspired by Mosaic with tetris blocks I was wondering if there were any generic algorithms to solve or show there was a solution to these types of problems (i.e. placing polyominos on a 2D board). ...
303 views

### How many Kings can you Achieve?

In a standard American game of checkers what's the maximum amount of kings a player can get, and what is the move sequence? Keeping in mind the force capture rule
416 views

### Dominoes on a Chess Board [duplicate]

Imagine an 8x8 chessboard has two opposite corners taken out, with 62 squares left over. Is it possible to lay 31 dominoes with the size 2x1 so they cover all of the empty, left over, squares?
11k views

### How many paths are there through a chess board? [closed]

A pawn is placed on the lower left corner square of a standard 8 by 8 chessboard. A 'move' involves moving the pawn, where possible, either: one square to the right, one square up, or diagonally one ...
765 views

### How do I count Hamiltonian paths of grid?

Let's say there is a 5x5 grid with a starting position in the upper left corner, and an ending position is lower left corner. How do I count how many Hamiltonian paths there are through the grid? I ...
753 views

### Can more than 24 knights of each color be placed on a chessboard without any pieces attacking opposite color?

The maximal number of knights of a single color that can be placed on a chessboard without any knight being one knights-move away from any other is 32; such a position may easily be achieved by ...
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. ...
590 views

### Partitioning a chessboard

You should see a standard chessboard - it is printed on paper. How many ways can you cut it up (around the squares) such that each piece has twice as many squares of one colour than of the other ...
1k views

### 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 ...
2k views

### How many Queens and Knights does it take to cover a chessboard?

Given an 8x8 chessboard, your goal is to "cover" each space on the board. A space is "covered" if there is a piece on it, or if a piece on the board can be moved to that space in one move. If you ...
4k views

### How many squares can 4 queens control?

Though there is no strict mathematical proof, it has been shown via brute-force that no arrangement of 4 or fewer queens can control every square on a standard 8x8 chessboard. So, out of the 64 ...
7k 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?
552 views

### Moving a pawn around on a chessboard

Suppose you have a checkerboard with two opposite corner squares removed, like this: Can you move a pawn on the board only horizontally and vertically, one square at a time, and have it touch every ...