# Tiling a Chessboard with Dominoes (Opposite Colors Removed)

DevFeed: [Tiling a Chessboard with Dominoes (Opposite Colors Removed)](<https://devfeed.tech/articles/tiling-a-chessboard-with-dominoes-opposite-colors-removed-40248.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2011/11/18/tiling-a-chessboard-2/>)

Published: 2011-11-18T10:32:54Z

Content type: tutorial

Language: en

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

Topics: [Algorithm](<https://devfeed.tech/topics/algorithm.md>)

Tags: [algorithm](<https://devfeed.tech/tags/algorithm.md>), [analysis](<https://devfeed.tech/tags/analysis.md>), [chessboard](<https://devfeed.tech/tags/chessboard.md>), [color](<https://devfeed.tech/tags/color.md>), [dominoes](<https://devfeed.tech/tags/dominoes.md>), [proofs-without-words](<https://devfeed.tech/tags/proofs-without-words.md>), [tiling](<https://devfeed.tech/tags/tiling.md>)

## 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").