# The Packing Chromatic Number Is 15

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On a square lattice, place 1s so that all 1s have a taxicab distance greater than 1 from each other. Next, add 2s so that the 2s all have a taxicab distance greater than 2 from each other. And so on. If the entire square lattice is filled with values, what is the maximal value in the lattice?

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Contributed by: Ed Pegg Jr (June 13)

Open content licensed under CC BY-NC-SA

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References

[1] B. Martin, F. Raimondi, T. Chen and J. Martin, "The Packing Chromatic Number of the Infinite Square Lattice Is between 13 and 15." arxiv.org/abs/1510.02374.

[2] B. Subercaseaux and M. J. H. Heule, "The Packing Chromatic Number of the Infinite Square Grid Is 15." arxiv.org/abs/2301.09757.

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