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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7
votes
2answers
395 views

Another Rook's Tour of the Chessboard

Place numbers 1 to 64 in the cells of this 8 x 8 board in such a way that consecutive numbers occupy neighboring cells (either vertically or horizontally). Shaded cells must be occupied by prime ...
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2answers
1k views

A King's Short Walk

Place the numbers 1 to 25 on the cells of this board so that any two consecutive numbers occupy cells that are horizontally, vertically or diagonally adjacent. Prime numbers should occupy shaded cells....
3
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1answer
125 views

Exchanging stones on a 8x8 board with sum of two adjacent numbers not being prime

You are given 64 stones labelled with number 1 to 64 each. All those stones are randomly placed on the squares of a 8x8 chess board such that each square is occupied with exactly one stone. A move is ...
12
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1answer
749 views

Transform each square of a chessboard to zero

Each square of an 8x8 chessboard is marked with a positive integer. The integers can be changed according to the following two rules: (1) all integers in a row are doubled (2) all integers in a column ...
20
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2answers
1k views

Beans under the chessboard

Under every grid cell of a chessboard, I put either one bean or nothing. Now if you choose a (grid) rectangular area on the chessboard, then I will tell you the parity of the number of beans under ...
25
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2answers
1k views

The Knight's Romp

Recently I was messing around with a singular knight on a chess board, and I came up with an interesting dilemma. Can you move a knight, from starting on any square, such that its path covers every ...
6
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1answer
500 views

Chess - Knight Mate

What is the fastest, in terms of moves, for a legal game to come to a checkmate, either black or white with a Knight and such that both all other cases of the checkmated King are attacked by an ...
5
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0answers
198 views

Choosing squares on a square board [closed]

I have an $8 \times 8$ board. On the board, I want to choose 2 unit squares in each column and row such that none of the chosen squares are touching. This means they cannot share a side or a corner. ...
4
votes
1answer
170 views

Chess - I will eat!

Suppose that you are playing White, and your aim is to eat a black piece (pawns qualitfy) in the fewest moves as possible and Black are not cooperating at all, and, even more, Black's aim is to ...
4
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1answer
109 views

How many queens are needed to attack all white squares?

This question: How can 3 queens control the white squares? got me thinking... What is the fewest number of queens needed to attack every white square? Rules: Only queens allowed Every white square is ...
30
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5answers
5k views

How can 3 queens control the white squares?

It is well known that there is no way of arranging 4 queens on a checker board in such a way that every square is occupied or threatened. Now consider a slight variation where we only need to cover ...
10
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1answer
441 views

Grid infection with diagonal adjacencies

A community consists of 81 houses laid out in a 9 x 9 square grid. Every household is friends with their eight orthogonal and diagonal neighbors (except for the houses on the perimeter which have only ...
4
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2answers
192 views

Maximum number of kings that can exit

N kings are placed on a chessboard, with at most one king on any square. Following standard rules of movement (one square in any direction), every king must be able to reach some edge of the board ...
5
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4answers
450 views

Most Captures Chess

In Most Captures Chess puzzle, you will need to provide a legal game where it is Blacks to play and where they have the most different ways to capture a White piece. For instance, the next game allows ...
0
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1answer
129 views

How many roads in a Tak square?

The board game Tak is played on a chess-like board of variable size (most commonly, 5x5 and 6x6). Players place and move pieces on the board with the goal of creating a "road", which is a ...
5
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3answers
275 views

A tribute to "Most ways to uncheck the king"

Today, we had the great privilege to see @Paul Panzer's answer being ticked at @thesilican's absorbing puzzle. I here propose a variant of his puzzle where it's not mandatory to use a legal chess game....
5
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2answers
180 views

Switching Black and White

In this Chess puzzle, your aim is to switch black and white, with a legal game, and arrive at the final position: This aim is likely unreachable. So you must try to get the maximum number of pieces ...
25
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6answers
3k views

Chess solitaire: The King's longest walk

Challenge: maximize the number of moves white needs for its king to reach a square of your choosing, adhering to the following rules: Black does not move Like normal: The king may not be in a ...
6
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2answers
350 views

Fastest draw from opening position in chess

When playing a normal game of chess, assuming the opponents are cooperating: In how many moves can a draw be unavoidable, excluding voluntary draws or draws by repetition of moves? 1 While not ...
7
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2answers
1k views

The Popular Letter Chessboard

You are given a Chess board with black and white squares. You must fill your Chess board with Merriam Webster English words, or other equivalent dictionnaries if you prefer such that each square ...
4
votes
1answer
207 views

Kings' Chess Harem

Pursueing these two related puzzles, Chess Bloodshed and Devouring Nobility I create for you Kings' Chess Harem where you have to find, with the minimum number of moves, a legal game where all pawns ...
10
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2answers
1k views

Chess Bloodshed

This puzzle is the idea of Dmitry Kamenetsky in a comment of my puzzle Devouring Nobility. Find, with the minimum number of moves, a legal game where all pieces are captured except the two kings.
3
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2answers
216 views

Magic rotated checkerboard function made in python!

Here's a puzzle for all you python programmers out there: I defined a function that goes like this: ...
3
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1answer
203 views

Create the freest arrangement of white chess pieces on board by consequently moving your pieces

You start with this board. You're the White. Freedom Index of initial arrangment of your chess pieces is equal to 20 (each pawn has two moves, each knight has two moves) Your goal is to have as much ...
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3answers
2k views

Painting a chessboard

On the following chessboard every white square meets at least two red squares. Let's paint a new chessboard so that every white square meets exactly two red square. Every square should be painted ...
10
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1answer
677 views

Playing with a chess cipher

Alice and Bob both love encryption, and Alice loves to play chess. Unfortunately, Bob isn't very good at chess, so he doesn't think it's very fair to have to play the game for real. So instead of ...
10
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1answer
324 views

A chessboard tiling with corners removed in 3D

A famous problem asks whether an 8x8 chessboard with two opposite corners deleted can be tiled with dominoes, where a domino is a rectangle congruent to two adjacent squares of the board. Now, let C ...
4
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1answer
137 views

A interesting and a bold chess puzzle

Here is a chess puzzle I have made . It needed a lot of thinking . If you are white , how would you play in this position ? State your best moves !! Please don't use Stockfish or Alphazero or any ...
15
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1answer
695 views

Arrange ten pawns into ten lines of three

This is not a chess problem! In the following position you can see six pawns that have been arranged into lines of three. Each pawn stands at the intersection of exactly two lines and each line ...
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3answers
327 views

Class Chess Tournament

A class of 36 students are expecting to play in the chess tournament held by Math Department. When the schoolmaster arrived he said "Lets start the games but first we must setup all the chess ...
15
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2answers
2k views

A Rook's Territory in the Chessboard

Shade 32 cells, four on each row and column, of an 8 x 8 blank chessboard (all its cells originally white) so that a rook sitting on any shaded cell can reach any other shaded cell, moving just along ...
3
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2answers
194 views

Black War Heroes or Whites Save the Queens?

After Black Cavalry successfully captured White princesses, White empire learns their Black opponent is hungry for more and wants White Twin Queens dead! White will never let such a disaster happen ...
6
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1answer
344 views

Whites capture whites and Blacks capture blacks

This is my first Chess Puzzle! Let suppose you start a Chess game. Whites' aim will be to place all their alive pieces on white squares in a minimum of moves and black will do the same, but with ...
15
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3answers
898 views

Four fanatics and one checkerboard

Four checkers-playing fanatics eagerly pair up for two simultaneous games of checkers but somehow find themselves with just one board. They do have enough checkers for two games, so it is time to act. ...
7
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2answers
797 views

Knights and Queen puzzle

This is not original. I just want to share this problem. If you have heard of it, please give opportunities for those who haven't to answer. Horst and Queenie are playing a game on a $200\times200$ ...
1
vote
1answer
79 views

k-threats Chinese Cannons Chess: Part 2

Inspired from the N-Queens problem, I here propose you a puzzle from Xiangqi wich is Chinese Chess equivalent, mostly played in Asia. The most different piece from Xiangqi is the cannon. You can ...
4
votes
1answer
103 views

k-threats Chinese Cannons Chess: Part 1

Inspired from the N-Queens problem, I here propose you a puzzle from Xiangqi wich is Chinese Chess equivalent, mostly played in Asia. The most different piece from Xiangqi is the cannon. You can ...
6
votes
1answer
144 views

Most moves by Most number of Pieces

Using one color, White or Black, place as many chess pieces (kings, queens, bishops, knights, rooks, and pawns, or combinations thereof) as you can on a checkerboard so that when the number of pieces ...
18
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2answers
2k views

Playing with one Queen on a chessboard

Alice and Bob play a special chess game with alternate moves. Alics starts with an empty chessboard and puts a Queen at a field in the first row (A8-H8) or the right column (H1-H8). Now Bob is moving ...
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3answers
1k views

How many chess pieces do we have to put at least?

In a $8\times8$ chessboard, a cell is qualified if an adjacent cell (a cell which is on top, left, below, or right of the cell) excluding itself has a chess piece on it. How many chess pieces do we ...
20
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3answers
3k views

A chess board with numbers

A 8x8 chess board is marked with the numbers from 1 to 64 sequentially from left to right, row by row and top to bottom. Now a minus sign is added to 32 of those numbers such that in each row and in ...
17
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4answers
2k views

Paint 21 Squares of a 7×7 Board Without Forming a Rectangle

Got a nice puzzle from my friend, when he was competing in IWYMIC/IMC 2011. Paint $21$ of the $49$ squares of a $7 \times 7$ board so that no four painted squares form the four corners of a rectangle....
6
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3answers
899 views

Cover 63 squares of a chess board, differently

In this other puzzle, ThomasL asks for three similar pieces which can be arranged to exactly cover all of an 8x8 chessboard, except for a single square — for any of the 64 possible single squares. I ...
46
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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 ...
14
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3answers
465 views

A missing part of a checkerboard

Fill out the missing part (the grey area) and explain the pattern behind the colors of this $9 \times 9$ checkerboard tiles!
7
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3answers
1k views

A Plethora of Puzzled Pawns

Inspired by this question According to FIDE rules, the pawn may move to a square occupied by an opponent’s piece diagonally in front of it on an adjacent file, capturing that piece. So, what's in ...
4
votes
1answer
529 views

How to connect a chessboard and a cipher into puzzle?

Let's say you have (a) a chessboard with figures and (b) a text from a book. The figures configuration is the Cardan grille, https://en.m.wikipedia.org/wiki/Cardan_grille When you put the chessboard ...
9
votes
2answers
464 views

Minimum number of turns to capture all pieces in Checkers

On an 8x8 checkerboard, there are 12 red kings and 1 black king. The kings behave as they would in any normal game of checkers, being able to move in any diagonal direction one space and jump any ...
15
votes
1answer
1k views

Chess problem: Make a crossword in 3 moves

A crossword position is a legal chess position with the following property: The board can be thought of as a crossword grid where the pieces on board work as clues. Each type of piece is a clue for ...
8
votes
2answers
750 views

Walk a Crooked Path

Here is a $7\times7$ board with three squares removed. You walk a path from square to square (adjacent horizontally or vertically), without visiting any square more than once. What is the most ...