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11 to 99 in square grid 9x9

Source: 1992 Swedish Mathematical Competition p2

April 2, 2021
combinatorics

Problem Statement

The squares in a 9×99\times 9 grid are numbered from 1111 to 9999, where the first digit is the row and the second the column. Each square is colored black or white. Squares 4444 and 4949 are black. Every black square shares an edge with at most one other black square, and each white square shares an edge with at most one other white square. What color is square 9999?
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