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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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 ...
41
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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. ...
41
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3answers
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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 ...
40
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4answers
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Could you solve a chessboard math puzzle at gunpoint?

Professor Veryevil pointed the gun at Shirley Knowsalot. "And why shouldn't I just kill you now?" asked the professor. "What about your shtick where you always give the hero a math puzzle that ...
35
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4answers
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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 ...
30
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5answers
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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 ...
30
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2answers
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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?
28
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3answers
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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
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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 ...
26
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4answers
2k views

Black wants to go first!

Billy and Matthew decide to play a game of Chess. They live far away, so they decide to do it online. Matthew wants to play first, but the game randomly gave him the color black (who goes second.) ...
26
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2answers
3k 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 ...
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 ...
26
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4answers
2k views

Lions and Zebras on a Chess Board

The black knight is our lion chasing 8 white bishop zebras which can't capture. Can the zebras evade the lion forever, if team zebra positions all the pieces and has the first turn? Rules: The game ...
26
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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 ...
25
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2answers
2k views

Rooks on a 15x15 chessboard

On a 15x15 chessboard there are 15 rooks that do not attack each other (via ordinary rook moves). Then each of the rooks makes one move like that of a knight. Is it possible that after all this is ...
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 ...
23
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1answer
585 views

The life of a Knight: Conway style

So I was thinking about Conway's game of life and the ridiculous kinds of patterns that can be made (Things that move across infinite space etc) and then I thought, hey could a chess knight do this as ...
22
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2answers
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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 ...
21
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4answers
1k views

Checkerboard Infection: The Aftermath

As in this previous puzzle, we are again playing with our favorite bacteria, C. Coli, whose natural habitat is an 8x8 checkers board. These are very nasty bacteria - once they are in a cell of a ...
20
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4answers
4k views

Mutilated chessboard

Remove the square in the top-left corner of a $2015 \times2015$ chessboard. Can the remaining mutilated chessboard be tiled with $1\times4$ and $4\times1$ rectangles?
20
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3answers
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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 ...
20
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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 ...
20
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3answers
692 views

Concentrating tokens on an infinite board

One token is placed on each square of an infinite checkerboard. One square is marked with an X. You want to get as many tokens on the marked square as possible. To do this, you may make any finite ...
19
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4answers
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Chessboard Rook Problem

Let's say that you have a chessboard (they are 8x8 spaces) with a rook on it (only moves horizontally & vertically). You can put walls horizontally or vertically between the spaces. If the rook ...
19
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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-...
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 ...
17
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4answers
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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 ...
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....
16
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3answers
728 views

Placing seven point-sized pawns

Can you place seven (point-sized) pawns on a $7\times7$ checkerboard, so that every pawn is placed precisely in the middle of one of the little checkerboard squares, and all distances between pairs ...
16
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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, ...
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 ...
15
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3answers
857 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. ...
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: ...
15
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1answer
664 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 ...
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 ...
14
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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 ...
14
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3answers
445 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!
13
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5answers
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 ...
13
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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?
12
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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 ...
12
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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 ...
12
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1answer
1k views

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 ...
12
votes
4answers
555 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 ...
12
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2answers
620 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 ...
12
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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 ...
12
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2answers
2k views

Checkers with the devil

After however much inordinate time passed for the tree-pruning game to finish, you ended up winning, and Satan was infuriated. He was sure he'd come up with a game keep you in hell. But once again, ...
11
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2answers
1k views

Professor Halfbrain and the 99x99 chessboard (Part 2)

This puzzle is the continuation of "Professor Halfbrain and the 99x99 chessboard (Part 1)". The difference is that "four corners of a rectangle" has now become "$2\times2$ subsquare". Professor ...
11
votes
4answers
403 views

Checkerboard Infection Variant

There is an insidious virus (less contagious than C. Coli, but still dangerous) which plagues the squares of checkerboards. This virus spreads through social interaction: whenever the majority of a ...
11
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5answers
725 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 ...
11
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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 ...