Questions tagged [checkerboard]

A puzzle involving checkerboards: grids of squares alternating black and white in color, most commonly an 8x8 board.

Filter by
Sorted by
Tagged with
37
votes
3answers
5k views

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 ...
29
votes
4answers
12k 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 ...
19
votes
4answers
2k 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-...
29
votes
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 ...
20
votes
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 ...
13
votes
2answers
2k 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?
10
votes
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. ...
31
votes
2answers
3k 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?
11
votes
2answers
347 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 ...
25
votes
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 ...
41
votes
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. ...
12
votes
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 ...
4
votes
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 ...
16
votes
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 ...
6
votes
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 ...
28
votes
3answers
4k views

A lonely pawn on the chessboard

Alice and Bob and the referee Conny play the following game with a pawn on a standard $8\times8$ chessboard: In the beginning, Conny places the pawn into the center of a randomly chosen square. All $...
27
votes
7answers
8k views

Two Knights, two Bishops, two Rooks and two Kings on a 4x4 chessboard

Place two Knights, two Rooks, two Bishops and two Kings on a 4x4 chessboard, so that: 1) The Kings are not attacked at all. 2) All other pieces are attacked exactly once. Ignore color, so every ...
10
votes
1answer
461 views

How many total checkmates can you possibly make against the enemy king?

Just an interesting idea for a puzzle that I had So, I decided to see how many possible checkmate I could theoretically make, in a legal position that can be legally reached. Always assume that the ...
19
votes
1answer
1k 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 ...
16
votes
2answers
1k 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, ...
13
votes
4answers
1k views

Professor Halfbrain's chessboard theorems

Professor Halfbrain has spent his last weekend with analyzing $n\times n$ chessboards. Halfbrain says that a subset $S$ of squares on such a chessboard is queen-connected, if a chess queen can move ...
12
votes
3answers
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 ...
7
votes
2answers
261 views

Keep the chessboard differences below eight

Can one place the numbers $1-64$ in the squares of a chessboard so that every two squares that share an edge have a difference of at most seven?
5
votes
1answer
989 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). ...
10
votes
3answers
916 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 ...
9
votes
1answer
456 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 ...
8
votes
3answers
5k views

Tiling a Chessboard with tetrominos

Is it possible to tile a $10\times10$ chessboard with (non-overlapping) T-tetrominos? If so, how? If not, prove it's impossible. Bonus: Which Tetris pieces can used to tile a 10$\times$10 ...
7
votes
4answers
251 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 ...
6
votes
1answer
408 views

The Knight Checker or Football Chess

Both Players uses 8 Knights on this chessboard game : The Knight Checker. All pieces starts in Rank 1 relative to players. White to move first. The Knight pieces makes regular moves as in a chess game ...
6
votes
2answers
153 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?
5
votes
1answer
267 views

A Battle of Dysfunctional Kings (Chess)

So recently I've learned about fairy chess and I've decided to write a puzzle based around the topic. Today's variation features a chess board which is missing eight squares (A1, A8, C3, C6, F3, F6, ...
3
votes
1answer
474 views

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 ...
3
votes
1answer
120 views

Keep the grid differences below $x$

Inspired by Keep the chessboard differences below eight Given an $n\times m$ grid of squares, what is the smallest possible integer bound $x$ for which it is possible to fill the squares with the ...
0
votes
1answer
197 views

Fastest Way To 6 Pawns On the B To H Files

MASSIVE UPDATE: I decided to play around with this again today, and I found MAJOR improvmemts for the B to G file games. See if you can beat me! If not, give proof as to why my game is optimal (To ...