Problem 193

Erdős Problem #193: declared status 'open'. Formalized: yes. Let $S\subseteq \mathbb{Z}^3$ be a finite set and let $A=\{a_1,a_2,\ldots,\}\subset \mathbb{Z}^3$ be an infinite $S$-walk, so that $a_{i+1}-a_i\in S$ for all $i$. Must $A$ contain three collinear points? Prize: no. OEIS: A231255. Tags: geometry.