Track / Stage 7 / 2 of 300 #1402 of 1964

Problem 1402

National Olympiad second round; IMO P1/P4

Algebra Difficulty 7.0 Prove it KöMaL problem A · Hungary · 2020

Let $H \subseteq \mathbb{R}^3$ such that if we reflect any point in $H$ across another point of $H$ , the resulting point is also in $H$ . Prove that either $H$ is dense in $\mathbb{R}^3$ or one can find equidistant parallel planes which cover $H$ .

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