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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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11 votes
2 answers
2k views

How can the knight traverse a chessboard to make a path that sums to 100

THE KNIGHT'S CENTURY. THEN Dr. Bates drew on a large sheet of paper a reduced chessboard of twenty-five squares, and numbered it in the manner shown in our diagram. He then placed a chess knight on ...
Will Octagon Gibson's user avatar
12 votes
1 answer
513 views

Attacking chessboard squares with 6 pieces

Place 6 white pieces (a king, a queen, a rook, a bishop, a knight and a pawn) on 6 different squares of a regular 8x8 chessboard so that there is at least one empty square attacked by exactly one ...
Will Octagon Gibson's user avatar
5 votes
1 answer
959 views

Anna and Boris play the Red Blue game

Anna and Boris play a game on a 9x9 chessboard. Anna goes first and turns alternate thereafter. In each move, Anna puts a red counter on a vacant square while Boris puts a blue counter on a vacant ...
Will Octagon Gibson's user avatar
14 votes
1 answer
382 views

Yet another pentomino puzzle

Just rearrange the 13 checkered polyominoes shown below to form a chessboard. The solution is unique and unusual. Clarification: The pieces may be reflected; the coloring on the back is as if the ink ...
username4231's user avatar
0 votes
1 answer
386 views

Rooks covering Dark Squares on a Chessboard

How many rooks are required such that all dark squares on the chessboard are covered by at least one rook.
Sny's user avatar
  • 3,157
18 votes
4 answers
3k views

Coloring of a 5 x 5 chessboard

The squares of a 5 x 5 chessboard are painted in one of two colors in an arbitrary way. Prove that there exist 2 rows and 2 columns such that the 4 squares where they intersect are all of the same ...
Will Octagon Gibson's user avatar
6 votes
2 answers
436 views

Pawns and a chessboard with no three aligned

This little problem crossed my mind and appeared to be not quite trivial. How can you place P pawns on a chessboard with the constraint that no pawn is exactly midway between two other pawns? Sure ...
Florian F's user avatar
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9 votes
1 answer
3k views

Two-Move Chess Game

Consider a standard game of chess. We make the following modification: on a turn, if a player makes a move which neither captures a piece nor puts their opponent’s king in check, then they may make a ...
godlification's user avatar
4 votes
0 answers
208 views

King 2 men, but don't kill a man

I found mention of this challenge in a Science paper called "Checkers is solved" from 1996, but no example was given. Beginning at starting position, play moves according to rules of ...
Noone AtAll's user avatar
25 votes
1 answer
3k views

Chess with jumping

Puzzle Statement: Consider the game of chess, but with a slight modification of the rules as follows: all heavy pieces (i.e., the queens and rooks) are allowed to jump as far across the board as they ...
acegikmoqsuwy2000's user avatar
10 votes
4 answers
1k views

Painting a Checkerboard

I love checkers - but I've played it so much that the color of my board is faded and dull. Today, I resolved to paint it. Unfortunately, I slipped and fell :( Now there's paint all over my ...
BaileyA's user avatar
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29 votes
4 answers
3k views

Rolling cube on an infinite chessboard

Imagine a six-sided die, D6, the right size to exactly occupy a square on a chessboard. The die can move to any adjacent square, but does so by rolling rather than sliding, so the topmost side of the ...
Laska's user avatar
  • 1,919
4 votes
2 answers
604 views

How far can a pawn get on an infinite chessboard?

There is an infinite chessboard. The chessboard is divided in two by a horizontal line that extends indefinitely. Above the dividing line, the cells of the chessboard must remain empty. Below you can ...
3m0o's user avatar
  • 317
5 votes
2 answers
700 views

Bow or lazy checkmate?

Suppose that both players cooperate, find the shortest, in terms of number of moves, black checkmate such that the game is valid and white pieces never go on rows 4 to 8. e.g. ...
JKHA's user avatar
  • 6,033
8 votes
3 answers
963 views

Chess lead change

Given the following Chess piece relative values and such that both players cooperate, what is the fastest way such that White first has an advantage of at least +10 piece value then secondly, Blacks ...
JKHA's user avatar
  • 6,033
3 votes
3 answers
319 views

Checkmate N Kings with M Knights Perfectly

We have this Existing Puzzle which has got the valid and invalid cases listed ; the Accepted Answer is along the lines of what is invalid and what is valid. But there was a flaw or fault in the Puzzle ...
Prem's user avatar
  • 5,152
14 votes
3 answers
2k views

Checkmate N Kings with M Knights

There are N White Kings on the Chess Board. There are M Black Knights. There is no Black King and no other Piece. Only M+N Squares are occupied. Each White King is attacked by atleast 1 Black Knight, ...
Prem's user avatar
  • 5,152
14 votes
4 answers
2k views

The Game of Golden Squares

On a magic chessboard of infinite size, the squares are either wooden or golden. If 4 or more of its 8 neighbors (a king's move away) are golden, a wooden square becomes golden the next day. Golden ...
Eric's user avatar
  • 6,536
9 votes
3 answers
583 views

Coloring the squares

You can choose from 4 colors to color every square of the following $10\times 10$ grid. After you finish, I'm going to take a connected block with at most three colors away. Your goal is to minimize ...
Eric's user avatar
  • 6,536
3 votes
1 answer
218 views

Geometric game on a n*n chessboard

You can get famous (OK, Warhol-15 minutes-famous :-)! First a few definitions. Of course, two rooks of the same colors don't attack, but since two colors are needed, "attacking" here means &...
Hauke Reddmann's user avatar
8 votes
2 answers
450 views

How many squares can a limp queen move to?

Consider a large chessboard. A limp rook is a chess piece that moves one step orthogonally, but it turns $90$ degrees after every move. The limp rook makes some moves, not crossing over its own path, ...
littlecat's user avatar
  • 343
2 votes
2 answers
237 views

Quickest chess stalemate with Queens exchange

Continuing my previous puzzle. If both players cooperate, what is the quickest stalemate in chess that includes a Queens exchange, in a legal game?
JKHA's user avatar
  • 6,033
3 votes
1 answer
432 views

Genies' chess on a 10×10 board

The work of Hearth Taxel revealed some other results related to genies' chess. For example, there is an arrangement $A$ of pawns on a 10×10 board such that no 3×3 submatrix is empty and $A$ is ...
Parcly Taxel's user avatar
  • 7,720
2 votes
2 answers
442 views

Two genies and their kind of chess

While playing chess Parcly and Tori Taxel, best friends and genies, got bored and transformed all the pieces into pawns to make pretty patterns. They found this 22-pawn arrangement where every 3×3 ...
Parcly Taxel's user avatar
  • 7,720
6 votes
1 answer
215 views

42 lines on a chessboard with associated numbers

The 64 squares of a chessboard can be associated with 42 lines as follows: the 8 rows the 8 columns 13 diagonals from north-west to south-east 13 diagonals from north-east to south-west Those ...
ThomasL's user avatar
  • 12.2k
4 votes
0 answers
201 views

Police and Thieves

I played this game when I was young, but cannot find it online. It is played on a checkers board (e.g. the black squares of a chess board) between two players P and T. The game goes as follows: P ...
user21820's user avatar
  • 1,137
7 votes
2 answers
1k 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 ...
Bernardo Recamán Santos's user avatar
5 votes
2 answers
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....
Bernardo Recamán Santos's user avatar
3 votes
1 answer
160 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 ...
ThomasL's user avatar
  • 12.2k
12 votes
1 answer
797 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 ...
ThomasL's user avatar
  • 12.2k
21 votes
2 answers
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 ...
WhatsUp's user avatar
  • 7,397
26 votes
2 answers
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 ...
TakingNotes's user avatar
  • 3,449
7 votes
1 answer
542 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 ...
JKHA's user avatar
  • 6,033
4 votes
1 answer
262 views

Choosing squares on a square board

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. ...
mahal's user avatar
  • 57
4 votes
1 answer
204 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 ...
JKHA's user avatar
  • 6,033
5 votes
1 answer
147 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 ...
Joel Rondeau's user avatar
  • 7,610
32 votes
5 answers
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 ...
Paul Panzer's user avatar
  • 10.3k
14 votes
1 answer
712 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 ...
Mike Earnest's user avatar
  • 32.4k
4 votes
2 answers
252 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 ...
FlanMan's user avatar
  • 5,742
5 votes
4 answers
465 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 ...
JKHA's user avatar
  • 6,033
0 votes
1 answer
155 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 ...
Mateo Gg's user avatar
5 votes
3 answers
343 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....
JKHA's user avatar
  • 6,033
5 votes
2 answers
242 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 ...
JKHA's user avatar
  • 6,033
24 votes
6 answers
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 ...
Retudin's user avatar
  • 9,218
6 votes
2 answers
420 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 ...
Retudin's user avatar
  • 9,218
7 votes
2 answers
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 ...
JKHA's user avatar
  • 6,033
4 votes
1 answer
301 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 ...
JKHA's user avatar
  • 6,033
10 votes
2 answers
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.
JKHA's user avatar
  • 6,033
3 votes
2 answers
250 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: ...
risky mysteries's user avatar
4 votes
1 answer
275 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 ...
KarmaPeasant's user avatar