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# Convex Subsets in Space

Suppose that $$C$$ is a convex subset of $$\mathbb{R}^3$$ with positive volume. Suppose that $$C_1, C_2,\dots C_n$$ are $$n$$ translated (not rotated) copies of $$C$$ such that $$C_i \cap C \neq 0$$, but $$C_i$$ and $$C_j$$ intersect at most on the boundary for $$i\neq j$$. Prove that $$n \leq 27$$ and that 27 is the best bound.

Note by Finn Hulse
3 years, 8 months ago

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