Questions tagged [checkerboard]
A puzzle involving checkerboards: grids of squares alternating black and white in color, most commonly an 8x8 board.
8
votes
2answers
702 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 ...
7
votes
1answer
818 views
Knight's Tour on a 7x7 Board starting from D5
Average Knight's Tour puzzle but this time on a 7x7 and starting from D5
9
votes
3answers
340 views
What’s the most possible checkmates in one, but with no promoted pieces, in a position?
What is the most possible checkmates in one without promoted units in a position? It must all be legal, of course.
Consider this a part two of this question: How many total checkmates can you ...
6
votes
2answers
751 views
Chess with symmetric move-square
Every move in chess involves moving a piece to a square. Let us call this square the "move-square" for that turn.
In the following, the move-square of the black player must be symmetrical (over the ...
0
votes
1answer
188 views
Fastest Way To 6 Pawns On the B To H Files
MASSIVE UPDATE: I decided to play around with this again today, and I found MAJOR improvmemts for the B to G file games. See if you can beat me! If not, give proof as to why my game is optimal (To ...
9
votes
1answer
415 views
How many total checkmates can you possibly make against the enemy king?
Just an interesting idea for a puzzle that I had
So, I decided to see how many possible checkmate I could theoretically make, in a legal position that can be legally reached.
Always assume that the ...
4
votes
1answer
305 views
Chess Massacre Variants-Play Find The Fastest Way?
I have thought up several variations of massacre chess.
Massacre chess is a game where almost every single move is a capture.
The idea here is that only the chosen type of piece can capture. It ...
15
votes
3answers
2k views
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:
...
6
votes
3answers
152 views
Discrete Peaceful Encampments: Player 4 has entered the game!
Here's a variation of Discrete Peaceful Encampments: Player 3 has entered the game! (which itself is a variation of Peaceful Encampments).
You have 3 white queens, 3 black queens, 3 red queens, and ...
5
votes
3answers
190 views
Discrete Peaceful Encampments: Player 3 has entered the game!
Here's a variation of Discrete Peaceful Encampments: 9 queens on a chessboard (which itself is a variation of Peaceful Encampments).
You have 4 white queens, 4 black queens, and 4 red queens. Place ...
15
votes
4answers
1k views
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 ...
8
votes
1answer
322 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 ...
5
votes
1answer
242 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
158 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
183 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
377 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
145 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
258 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
votes
4answers
293 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
votes
2answers
331 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
vote
2answers
256 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
207 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
votes
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
939 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
156 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
377 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
votes
1answer
159 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
312 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
votes
1answer
220 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
2k 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
269 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 ...
27
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
545 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
263 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
380 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
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 ...
3
votes
1answer
229 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
votes
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
788 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
275 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
645 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
149 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
157 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 ...
3
votes
1answer
442 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
719 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
136 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 ...
