Questions tagged [checkerboard]

A puzzle involving checkerboards: grids of squares alternating black and white in color, most commonly an 8x8 board.

Filter by
Sorted by
Tagged with
5
votes
2answers
223 views

Patriotic Solitaire

You are given a $3\times n$ checkerboard, covered with $n$ red, $n$ white, and $n$ blue checkers. Call a board patriotic if every column has a red, white and blue checker. You want to make the given ...
12
votes
2answers
2k views

Checkers with the devil

After however much inordinate time passed for the tree-pruning game to finish, you ended up winning, and Satan was infuriated. He was sure he'd come up with a game keep you in hell. But once again, ...
6
votes
1answer
395 views

Checkers Against The King

The king has invented a new game called King's Checkers. The rules are simple, it's exactly like regular Checkers, the only difference? The king plays first and all his pieces are automatically "king",...
6
votes
1answer
705 views

2 bishops versus a lone king

There are 4 pieces on the board, the white and black kings, as well as 2 white bishops (on differently colored squares). The only way a stalemate occurs is if the black king is not in check, but ...
25
votes
4answers
1k views

Arrows on a Chessboard

I've taken an $n$ by $n$ chessboard and drawn an arrow on each square, pointing in one of the eight compass directions. I've done this in such a way that arrows in (orthogonally) adjacent squares ...
-2
votes
1answer
505 views

Partitioning a chessboard

You should see a standard chessboard - it is printed on paper. How many ways can you cut it up (around the squares) such that each piece has twice as many squares of one colour than of the other ...
5
votes
2answers
558 views

Pedro's pawn game

Yesterday, my good friend Pedro told me about Pedro's pawn game which is played with $7$ white and $7$ black pawns on a $7\times7$ checkerboard. In the starting situation, there is a white pawn on ...
8
votes
2answers
665 views

Dominoes on a chessboard

Mary has a box with special $2\times1$ dominoes. Each dominoe has two red corners and two blue corners, and these dominoes come in two different types: The first type has the lower left and the upper ...
12
votes
5answers
10k views

How many paths are there through a chess board? [closed]

A pawn is placed on the lower left corner square of a standard 8 by 8 chessboard. A 'move' involves moving the pawn, where possible, either: one square to the right, one square up, or diagonally one ...
6
votes
2answers
458 views

Placing dominoes on a 3x100 checkerboard

Alice and Bob play a game by alternately placing dominoes on a $3\times100$ checkerboard (3 rows, 100 columns). Alice has the first move. A move of Alice consists in placing a $1\times2$ (horizontal) ...
9
votes
1answer
413 views

Generalisation of tours on chessboards

It's well-known that a knight placed on one square of a chessboard can get to any other square, but a bishop can only reach half the squares from a fixed starting point. Another question on this site ...
16
votes
2answers
1k views

The Erasmus rook tour

Professor Erasmus has found a special way of moving a rook across a standard $8\times8$ chessboard that he modestly calls the "Professor-Erasmus-rook-tour". The professor claims that in this tour, ...
26
votes
2answers
3k 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 ...
-1
votes
3answers
216 views

8 queens equivalent on checkers [closed]

I'm a computer programmer trainer and sometimes I do some puzzle exercises with my students. Right now we did a checkers game and I would like to make them program to solve something with their ...
5
votes
1answer
966 views

Solutions for generic polyomino puzzles

Inspired by Mosaic with tetris blocks I was wondering if there were any generic algorithms to solve or show there was a solution to these types of problems (i.e. placing polyominos on a 2D board). ...
2
votes
1answer
292 views

How many Kings can you Achieve?

In a standard American game of checkers what's the maximum amount of kings a player can get, and what is the move sequence? Keeping in mind the force capture rule
1
vote
1answer
561 views

How do I count Hamiltonian paths of grid?

Let's say there is a 5x5 grid with a starting position in the upper left corner, and an ending position is lower left corner. How do I count how many Hamiltonian paths there are through the grid? I ...
9
votes
1answer
450 views

Moving a pawn around on a chessboard

Suppose you have a checkerboard with two opposite corner squares removed, like this: Can you move a pawn on the board only horizontally and vertically, one square at a time, and have it touch every ...