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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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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. ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
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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?
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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 $...
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3answers
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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 ...
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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 ...
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2answers
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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 ...
25
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4answers
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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.) ...
25
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2answers
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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 ...
25
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4answers
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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 ...
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4answers
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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 ...
23
votes
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
543 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 ...
21
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3answers
662 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 ...
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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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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 ...
19
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4answers
4k views

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
votes
4answers
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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?
19
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1answer
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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 ...
19
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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-...
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3answers
717 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 ...
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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 ...
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2answers
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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, ...
14
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3answers
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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: ...
13
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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 ...
13
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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?
12
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5answers
9k 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 ...
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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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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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 ...
11
votes
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
267 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
votes
2answers
341 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 ...
11
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2answers
535 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 ...
11
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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 ...
10
votes
1answer
373 views

Lights out game on a chessboard

Alice and Bob play a game with an 8×8 grid of lights, all initially on. They take turns choosing a light which is on and turning it off, with Alice going first. However, the grid is rigged such that ...
10
votes
2answers
181 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: ...
10
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2answers
475 views

Maze Solving Robot, More Difficult Variant

You are trying to design a maze solving robot, capable of solving "valid" mazes. A valid maze is an 8 by 8 checkerboard, surrounded by walls, where Between each pair of orthogonally adjacent squares, ...
10
votes
1answer
153 views

Combinatorial Agriculture, part 2

Your 64 acre square farm has been doing well and you decide to expand with an orchard. The orchard is also in the form of an 8-by-8 square of subplots, each of which can hold one tree. You have 3 each ...
10
votes
1answer
568 views

Let's revisit this later (a two player knight's game)

Alice and Bob play a game on the following irregular chessboard. (Note the blacked out squares are not legal moves.) Alice starts the game by placing a knight on any square she chooses. They then ...
9
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. ...
9
votes
1answer
432 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 ...
9
votes
3answers
860 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
3answers
266 views

The Flea Circuit

Starting on a square of the checkerboard, "The Flea" is trained to jump to the center of another square. Then it keeps jumping (center to center) from square to square all around the board. It is ...
9
votes
2answers
474 views

Trapping pieces on an infinite chessboard

Alice and Bob are playing an unusual game of chess. We begin with a piece on a square of an infinite chessboard. On each of her turns, Alice moves the piece. On each of his turns, Bob destroys a ...
9
votes
1answer
393 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 ...
8
votes
5answers
986 views

Professor Halfbrain and the 9x9 chessboard (Part 2)

This puzzle is the continuation of "Professor Halfbrain and the 9x9 chessboard (Part 1)". The difference is that "distance at least $2$" has now become "distance more than $2$". Professor Halfbrain ...