Kvant Math Problem 883

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Problem

Fig. 1

Fig. 1

What is the smallest number of colors needed to color the cells of an infinite sheet of square grid paper so that

  1. any two cells at distance 6 are colored differently? (The distance between two cells is the smallest number of horizontal and vertical grid lines that a rook must cross on a path from one cell to the other.)

  2. any four cells forming an L-shaped figure (Fig. 1) are colored in four different colors?

A. G. Pechkovsky, I. V. Itenberg

Leningrad City Mathematical Olympiad (50, 1984)

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