# chessboard Published articles for chessboard. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## A Rook Game DevFeed: [A Rook Game]() Original publisher: [Read original article]() Published: 2014-08-31T17:51:37Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Algorithm](), [Mathematics]() Tags: [algorithm](), [board-games](), [chessboard](), [game](), [games](), [mathematics](), [strategy](), [symmetry]() ### AI overview This article presents a rook game on an 8x8 chessboard in which players move only south or west. It shows that symmetry provides the optimal strategy: move the rook to the diagonal whenever possible and return it there after the opponent moves it away. The first player wins from an off-diagonal starting square; otherwise, the second player wins. ### Source excerpt Problem: Two players take turns moving a rook on an 8x8 chessboard. The rook is only allowed to move south or west (but not both in a single turn), and may move any number of squares in the chosen direction on a turn. The loser is the player who first cannot move the rook. What is the optimal play for any starting position? rook-board Solution: Take advantage of the symmetry of the board. ## Busy Beavers, and the Quest for Big Numbers DevFeed: [Busy Beavers, and the Quest for Big Numbers]() Original publisher: [Read original article]() Published: 2012-02-08T19:42:22Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [Mathematics](), [Math and Logic](), [Computing]() Tags: [ackermann-function](), [busy-beaver](), [chessboard](), [computing](), [infinite](), [mathematics](), [numbers](), [primer](), [theory](), [turing-machine]() ### AI overview This article examines how the ability to describe very large numbers reflects progress in mathematical and scientific thought. It introduces historical examples, including Archimedes' estimate for the number of grains of sand in the universe, and connects them to computational topics such as Busy Beavers. ### Source excerpt Finding Bigger Numbers, a Measure of Human Intellectual Progress Before we get into the nitty gritty mathematics, I'd like to mirror the philosophical and historical insights that one can draw from the study of large numbers. That may seem odd at first. What does one even mean by "studying" a large number? Of course, I don't mean we stare at the number 1,000,000,000,000, which is quite large, and wonder how mankind can benefit from its elusive properties. ## Tiling a Chessboard with Dominoes (Opposite Colors Removed) DevFeed: [Tiling a Chessboard with Dominoes (Opposite Colors Removed)]() Original publisher: [Read original article]() Published: 2011-11-18T10:32:54Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Algorithm]() Tags: [algorithm](), [analysis](), [chessboard](), [color](), [dominoes](), [proofs-without-words](), [tiling]() ### AI overview A constructive solution shows that a chessboard with two opposite-colored squares removed can be tiled with 2-by-1 dominoes. The article explains the placement pattern and notes that the corresponding algorithm runs in linear time. ### Source excerpt This is a natural follow-up to our first gallery entry on the impossibility of tiling certain chessboards with dominoes. Problem: Suppose we remove two squares from a chessboard which have opposite color. Is it possible to tile the remaining squares with 2-by-1 dominoes? Solution: Notice that if we remove two squares of opposite color, then there is only one way to place dominoes on the remaining squares according to this scheme (one cannot tile a domino across the "walls"). ## Tiling a Chessboard DevFeed: [Tiling a Chessboard]() Original publisher: [Read original article]() Published: 2011-06-26T20:24:09Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [color](), [standard]() Tags: [chessboard](), [color](), [dominoes](), [mathematics](), [standard](), [tiling]() ### AI overview The article uses coloring arguments to show that certain chessboard and grid regions cannot be tiled with dominoes. It first analyzes 2-by-1 dominoes on a chessboard with two opposite corners removed, then applies a specially chosen coloring to a 3-by-1 domino problem and generalizes the proof method. ### Source excerpt Problem: Take a chessboard and cut off two opposite corners. Is it possible to completely tile the remaining board with 2-by-1 dominoes? Solution: Notice that every domino covers exactly one white tile and one black tile. Counting up the colors, we have 32 white and 30 black. Hence, any tiling by 2-by-1 dominoes will leave two extra white squares unaccounted for. So no such tiling is possible. Problem: Cut one corner off a chessboard.