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Coloring square

Source: St Petersburg Olympiad 2008, Grade 11, P1

August 30, 2017
combinatorics

Problem Statement

We color some cells in 10000×1000010000 \times 10000 square, such that every 10×1010 \times 10 square and every 1×1001 \times 100 line have at least one coloring cell. What minimum number of cells we should color ?
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