MathDB
Putnam 2019 B6

Source:

December 10, 2019
Putnam 2019

Problem Statement

Let Zn\mathbb{Z}^n be the integer lattice in Rn\mathbb{R}^n. Two points in Zn\mathbb{Z}^n are called {\em neighbors} if they differ by exactly 1 in one coordinate and are equal in all other coordinates. For which integers n≥1n \geq 1 does there exist a set of points S⊂ZnS \subset \mathbb{Z}^n satisfying the following two conditions? \\ (1) If pp is in SS, then none of the neighbors of pp is in SS. \\ (2) If p∈Znp \in \mathbb{Z}^n is not in SS, then exactly one of the neighbors of pp is in SS.
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