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Erdős problem 193

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Let S⊆Z3S \subseteq \mathbb{Z}^3 be a finite set and let A={a1,a2,…}A = \lbrace a_1, a_2, \ldots \rbrace be an infinite SS-walk, so that ai+1−ai∈Sa_{i+1} - a_i \in S for all ii. Must AA contain three collinear points?

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Problem row
sha256:6c37cbbd87e6d753ae83a85705f6c5e74fdde82ab4389a0a750ef1c2a17fb2b0
Metadata
sha256:4bcd53e2e3fbd8b4a015f6a94bd1c6d6e390dca2d1d7947f8506a1c6ab035ee3
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:97dfcd543aec6a297493928dcbe58e3afd0e253c985386c530a6fcecf33df3d3
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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