All Questions
Tagged with chessboard or checkerboard
204 questions
16
votes
3
answers
2k
views
Threatening queens
Two queens placed on a chessboard are said to threaten each other if the two lie in the same row, column or diagonal, and there are no other queens on the line segment between them.
For which ...
- 387
48
votes
4
answers
4k
views
Can you checkmate a king you can't see?
Motivation
If you play bullet chess with time management skills as poor as mine, you often end up in endgame situations that require delivering checkmate by playing several premoves in a row. For ...
- 19.1k
4
votes
1
answer
128
views
How quickly can the knight be trapped? [duplicate]
A Chess knight is placed on an infinite chessboard. If it cannot move to a square previously visited, how can you make it unable to move in as few moves as possible?
Clarifications:
The chessboard is ...
- 21.4k
7
votes
1
answer
436
views
Given that the sum on one of the squares is 3 cents, and on another one 17 cents, find the total amount of money on both diagonals of the checkerboard
A number of coins are placed on each square of a standard 8x8 checkerboard such that the sums of every two squares having a common side differ by one cent. Given that the sum on one of the squares is ...
- 21.4k
9
votes
1
answer
1k
views
Who wins in this knight-placement game?
Two players take turns placing knights on the squares of a standard 8x8 chessboard, so that no knight can take another. The player who is unable to do this loses. Which player has a winning strategy ...
- 21.4k
26
votes
3
answers
1k
views
White (king and 2 bishops) vs Black (king and 1 knight). White to play and mate in 2
White to play and mate in 2.
Attribution: Glen Ferri
- 21.4k
18
votes
1
answer
2k
views
Place some or all of the White Chess pieces on a chessboard in such a way that none of them can legally move
Place some or all of the White Chess pieces on a standard chessboard in such a way that no piece can legally move.
If you use two bishops they must be on different colored squares.
No pawn can be on ...
- 21.4k
1
vote
1
answer
169
views
Place the given chess pieces on the given chessboards so that no piece attacks another
Beginner puzzles
These puzzles are intended to be suitable for people who are new to puzzle solving.
Clarification: Both experienced solvers and new solvers are welcome to post solutions to these ...
- 21.4k
5
votes
1
answer
584
views
Where should the chess pieces be placed in 4x4, 6x6 and 9x9 chessboards?
Here are 3 related chess problems. The color of the pieces is not important. Unlike a legal chess game there are no limits to the number of pieces of each type in these puzzles.
Puzzle 1: On a 4x4 ...
- 21.4k
3
votes
1
answer
175
views
A variant of the 2-Chess Games overlapped
This is a variant of this previous puzzle.
Create two valid Chess games (A and B) with the minimum number of moves such that overlapping the two games creates a valid chess position.
The following ...
- 6,518
6
votes
3
answers
757
views
Overlap two Chess Games
Create two valid Chess games (A and B) with the minimum number of moves (you will sum the number of moves of A and B) such that overlapping the two games creates a valid chess position.
The following ...
- 6,518
7
votes
3
answers
3k
views
How can 4 chess queens attack all empty squares on a 6x6 chessboard without attacking each other?
How can 4 chess queens be placed on a 6x6 chessboard so that every empty square is attacked by at least one queen AND no queen attacks another queen.
Clarification: Although I did not mention it in ...
- 21.4k
15
votes
1
answer
2k
views
The shortest way from A1 to B1
On the square A1 of a regular chessboard is a regular dice, face 1 up and face 2 in front. The only allowed move is to rotate the dice by 90 degrees to an adjacent square.
Find the shortest way from ...
- 671
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 ...
- 21.4k
12
votes
1
answer
543
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 ...
- 21.4k
5
votes
1
answer
986
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 ...
- 21.4k
14
votes
1
answer
459
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 ...
- 143
0
votes
1
answer
399
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.
- 3,223
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 ...
- 21.4k
6
votes
2
answers
449
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 ...
- 31.4k
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 ...
- 589
4
votes
0
answers
216
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 ...
- 140
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 ...
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 ...
- 681
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 ...
- 2,408
4
votes
2
answers
654
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 ...
- 317
5
votes
2
answers
709
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. ...
- 6,518
8
votes
3
answers
965
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 ...
- 6,518
3
votes
3
answers
322
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 ...
- 5,180
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, ...
- 5,180
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 ...
- 6,976
9
votes
3
answers
592
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 ...
- 6,976
3
votes
1
answer
227
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 &...
- 1,007
8
votes
2
answers
458
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, ...
- 343
2
votes
2
answers
241
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?
- 6,518
3
votes
1
answer
438
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 ...
- 8,695
2
votes
2
answers
451
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 ...
- 8,695
6
votes
1
answer
219
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 ...
- 12.3k
4
votes
0
answers
207
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 ...
- 1,256
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 ...
- 19.2k
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....
- 19.2k
3
votes
1
answer
173
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 ...
- 12.3k
12
votes
1
answer
818
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 ...
- 12.3k
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 ...
- 7,455
27
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 ...
- 4,877
7
votes
1
answer
548
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 ...
- 6,518
4
votes
1
answer
265
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. ...
- 57
4
votes
1
answer
211
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 ...
- 6,518
5
votes
1
answer
156
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 ...
- 7,855
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 ...
- 10.4k