All Questions
Tagged with checkerboard optimization
47 questions
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
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
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
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
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
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
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
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 ...
- 8,725
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
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
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
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
4
votes
2
answers
266
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 ...
- 5,782
5
votes
4
answers
467
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 ...
- 6,518
0
votes
1
answer
165
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 ...
- 1
5
votes
3
answers
366
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....
- 6,518
5
votes
2
answers
256
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 ...
- 6,518
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 ...
- 10.1k
6
votes
2
answers
430
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 ...
- 10.1k
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 ...
- 6,518
4
votes
1
answer
319
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 ...
- 6,518
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.
- 6,518
4
votes
1
answer
296
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 ...
- 468
3
votes
2
answers
273
views
Black War Heroes or Whites Save the Queens?
After Black Cavalry successfully captured White princesses,
White empire learns their Black opponent is hungry for more and wants White Twin Queens dead!
White will never let such a disaster happen ...
- 6,518
1
vote
1
answer
104
views
k-threats Chinese Cannons Chess: Part 2
Inspired from the N-Queens problem, I here propose you a puzzle from Xiangqi wich is Chinese Chess equivalent, mostly played in Asia.
The most different piece from Xiangqi is the cannon. You can ...
- 6,518
4
votes
1
answer
140
views
k-threats Chinese Cannons Chess: Part 1
Inspired from the N-Queens problem, I here propose you a puzzle from Xiangqi wich is Chinese Chess equivalent, mostly played in Asia.
The most different piece from Xiangqi is the cannon. You can ...
- 6,518
6
votes
1
answer
179
views
Most moves by Most number of Pieces
Using one color, White or Black, place as many chess pieces (kings, queens, bishops, knights, rooks, and pawns, or combinations thereof) as you can on a checkerboard so that when the number of pieces ...
- 6,728
13
votes
3
answers
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 ...
- 6,334
9
votes
2
answers
818
views
Walk a Crooked Path
Here is a $7\times7$ board with three squares removed.
You walk a path from square to square (adjacent horizontally or vertically), without visiting any square more than once. What is the most ...
- 55.7k
6
votes
4
answers
593
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 ...
- 2,709
2
votes
1
answer
209
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 ...
- 6,728
10
votes
5
answers
559
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).
...
- 6,728
9
votes
3
answers
321
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 ...
- 6,728
7
votes
1
answer
396
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 ...
- 1,647
23
votes
3
answers
809
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 ...
- 33.8k
32
votes
3
answers
5k
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 ...
- 471