MathDB

B6

Part of 2019 Putnam

Problems(1)

Putnam 2019 B6

Source:

12/10/2019
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.
Putnam 2019