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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.

8
votes
1answer
303 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 ...
3
votes
1answer
204 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, ...
2
votes
1answer
139 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
votes
2answers
179 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: ...
6
votes
1answer
347 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 ...
7
votes
1answer
140 views

Permuting rows and columns to switch white rooks with black rooks

An adversary places eight white rooks and eight black rooks on sixteen squares of a chessboard, subject to these rules: In any row, there must be exactly two rooks, one of each color. In any column, ...
5
votes
3answers
249 views

Crazy queen in checkers

Checkers Checkers, also called draughts, is an interesting game. all pieces are placed on black tile and are all pawns at the start. When a pawn reach the final line, a powerful piece is created: the ...
11
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4answers
252 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 ...
8
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2answers
298 views

Covering a chessboard with L-tetrominoes

We all know the classic puzzle of trying to tile a mutilated chessboard with $2\times1$ dominoes. Let's imagine that, instead of dominoes, we have $n^2$ L-shaped tetrominoes and we want to tile a $2n\...
1
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2answers
216 views

The Monster and the Chessboard [duplicate]

You have a standard checkerboard with 64 squares and a coin in each square, randomly facing heads or tails up. There is an evil monster in the room with you and he arbitrarily selects some square and ...
26
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 ...
3
votes
2answers
200 views

Is it possible to pack the tetrominoes exactly on the checkboard?

I have this as an exercise but I'm not sure what's the best way to approach it. I've tried the pack them but wasn't able to do so. I see that having them combined will yield in 10 whites and 10 blacks ...
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 ...
4
votes
3answers
781 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 ...
1
vote
1answer
154 views

King of Captures

The player's black King (above) is about to capture the remaining opponent pieces as continuation of his move and 10 white pieces have already been captured on the same turn/move. What is the position ...
10
votes
1answer
368 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 ...
-3
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1answer
152 views

How many positions can the queen control? [closed]

Given the size of board (n) and the position of the queen (r,c) how can we calculate the total number of squares which can be controlled by the queen?
7
votes
4answers
309 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). ...
-1
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1answer
215 views

Colouring an n times n grid using n colours

Inspired by the four colours puzzle. The goal is to color the squares of an $n\times n$ grid with $n$ colors such that All squares are coloured. no two squares of the same color touch at an edge or ...
6
votes
3answers
1k 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 ...
9
votes
3answers
262 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 ...
26
votes
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 ...
23
votes
1answer
541 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 ...
7
votes
1answer
258 views

Least amount of moves is required

You have 8x8 board and 9 identical pieces placed in a 3x3 square at the bottom left corner of the board. You are going to play a very simple game. Your task is to move these 9 pieces to the 3x3 square ...
5
votes
3answers
355 views

Place 16 queens in a $16\times 16$ board peacefully, also in subboards!

What is the smallest number, $n$ in which $n$ queens can live in a $n\times n$ board peacefully? Of course not more than 8. ☺ (read about the eight queen puzzle) But this was not the question. ...
10
votes
1answer
152 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 ...
3
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1answer
218 views

Filling a chessboard with -1, 0 and 1

You have a standard chessboard $(8\times8)$. And you have a lot of numbers from the set $[-1, 0, 1]$. You have to place one number in each square so that the sums on each row, column, and the two ...
41
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4answers
4k views

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 ...
8
votes
2answers
752 views

Eight queens on the chessboard with mirrors

A 8-by-8 chessboard has two mirrors added on its left and right margin. The mirrors reflect the queen moves so that a queen threatens additional squares on the board. A queen threatens all squares in ...
2
votes
1answer
271 views

Crippled King Crossing a Canyon - Up and Down

Please don't flag me. I am not a duplicate of Crippled King Crossing a Canyon. What are the chances now, if the crippled king only can't walk up and down? The rest of the rules are the same as ...
8
votes
1answer
642 views

Jepetto's punctured chessboard [duplicate]

Jepetto the toymaker was thinking about a new toy to add to his tiling product line. His new design involved a punctured chessboard: an ordinary $8 \times 8$ chessboard, except with a single square ...
19
votes
4answers
3k 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?
2
votes
2answers
145 views

Two sums on a chessboard

There is an $n\times n$ chessboard with an even positive integer $n$. We put all the numbers $1,2,...,n^2$ into the squares of the chessboard, where each number appears once and only once and each ...
6
votes
1answer
152 views

Knight on a rectangular chessboard

On a rectangular $ 4 \times 2016 $ chessboard, a knight begins in the lower left corner, makes several knight moves, visits all squares of the chessboard at least once and in the end returns to the ...
2
votes
1answer
356 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 ...
6
votes
5answers
2k 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 ...
16
votes
3answers
715 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 ...
6
votes
2answers
127 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?
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 ...
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 ...
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. ...
6
votes
3answers
477 views

Crosses on a 10x11 chessboard

A cross consists of six unit squares and looks as follows: O OOOO O (this may also be rotated by several right turns, or horizontally ...
8
votes
5answers
939 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 ...
9
votes
3answers
815 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 ...
25
votes
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 ...
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 ...
21
votes
3answers
656 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 ...
7
votes
4answers
279 views

Tiling an Odd Polygon with Dominoes

There is a polygon whose edge lengths are all odd integers. Prove that this polygon's interior cannot be tiled by dominoes whose dimensions are $1\times 2$. An example of such a polygon is a "...
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 ...
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 ...