# Tiling a Chessboard

DevFeed: [Tiling a Chessboard](<https://devfeed.tech/articles/tiling-a-chessboard-40213.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2011/06/26/tiling-a-chessboard/>)

Published: 2011-06-26T20:24:09Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [color](<https://devfeed.tech/topics/color.md>), [standard](<https://devfeed.tech/topics/standard.md>)

Tags: [chessboard](<https://devfeed.tech/tags/chessboard.md>), [color](<https://devfeed.tech/tags/color.md>), [dominoes](<https://devfeed.tech/tags/dominoes.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [standard](<https://devfeed.tech/tags/standard.md>), [tiling](<https://devfeed.tech/tags/tiling.md>)

## 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.