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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10
votes
1answer
347 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 ...
9
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1answer
279 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
90 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 ...
41
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3answers
8k 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 ...
15
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1answer
671 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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5answers
726 views

Professor Halfbrain's infinite chessboard theorems

After his first set of theorems involving queen-accessibility, Professor Halfbrain started wondering about infinite chessboards rather than just ones with arbitrary large dimensions. He came up with ...
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3answers
314 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 ...
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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
158 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
312 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
863 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. ...
12
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4answers
561 views

What’s the most possible checkmates in one, but with no promoted pieces, in a position?

What is the most possible checkmates in one without promoted units in a position? It must all be legal, of course. Promotions are allowed in the game, but the position is not allowed to start with ...
7
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4answers
362 views

No Square Allowed

On a Chessboard, place as many chess pieces as you can. Position the center of each piece on the center of a square. Avoid placing any 4 pieces at the corners of a square (even a tilted square). ...
7
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2answers
544 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
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1answer
69 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
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1answer
82 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
135 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 ...
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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
870 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 ...
43
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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 ...
35
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4answers
14k 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 ...
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3answers
446 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!
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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
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1answer
232 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
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2answers
438 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 ...
7
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4answers
373 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 ...
30
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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?
4
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1answer
395 views

Chess Massacre Variants-Play Find The Fastest Way?

I have thought up several variations of massacre chess. Massacre chess is a game where almost every single move is a capture. The idea here is that only the chosen type of piece can capture. It ...
15
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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
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2answers
740 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 ...
7
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1answer
859 views

Knight's Tour on a 7x7 Board starting from D5

Average Knight's Tour puzzle but this time on a 7x7 and starting from D5
15
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3answers
2k views

A Wacky, Wacky Chessboard (That Makes No Sense)

So yesterday I found this in the mail. A chessboard. But on the squares, things were written. Plaintext version: ...
10
votes
1answer
519 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 ...
0
votes
1answer
217 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 ...
6
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2answers
791 views

Chess with symmetric move-square

Every move in chess involves moving a piece to a square. Let us call this square the "move-square" for that turn. In the following, the move-square of the black player must be symmetrical (over the ...
7
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3answers
184 views

Discrete Peaceful Encampments: Player 4 has entered the game!

Here's a variation of Discrete Peaceful Encampments: Player 3 has entered the game! (which itself is a variation of Peaceful Encampments). You have 3 white queens, 3 black queens, 3 red queens, and 3 ...
17
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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 ...
9
votes
1answer
382 views

A chess game with odd moves?

A friend and I like to play chess regularly. Like me, he is a lover of a good puzzle, which is what drew us to the game. The thrill of finding a checkmate in a board riddled with pieces cannot be ...
23
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7answers
5k views

Explore the square with 100 hops

This is a puzzle that was a fad when I was back in school. (It's not sooo long ago, but way before Smartphones with AngryBirds or DoodleJump came up...). For quite a while, everybody was scribbling ...
10
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3answers
6k 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 board, ...
6
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1answer
459 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
1answer
328 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, ...
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5answers
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 ...
2
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1answer
394 views

Row of alternating coin

I stumbled upon a mathematical puzzle that goes like this: You have 2n coins that alternate between head and tail. For example, if n=3, then it looks like H T H T H T, where H = head and T = tail. To ...
10
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2answers
194 views

make it to the top of the triangle

Suppose you have a triangle that extends infinitely downwards, with circles inside, arranged in this arrangement: ...
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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 ...
26
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3answers
4k views

16 pawns on a chess board with no three collinear: how do I go about solving this?

Here's a problem that was posed to me but I haven't seen anything about it anywhere online! I'm beginning to wonder if I'm just getting played! You have a chessboard and sixteen pawns. The puzzle is ...