Tarski's Planks problem, solved by Thøger Bang in 1951, says (in a simplified $\mathbb{R}^2$ version) that it requires "planks" (parallel strips) of total width $\ge d$ in order to completely cover a disk of diameter $d$. The last paragraph of Bang's short paper poses an open problem:

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          [![Bang][1]][1]
          ^{(Snapshot from Bang's paper.)}

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Does anyone know if this problem has been solved? I am especially interested in $\mathbb{R}^2$.

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> Bang, Thøger (1951), "A solution of the 'plank problem'", *Proc. Amer. Math. Soc.* 2 (6): 990–993, doi:10.2307/2031721, [JSTOR 2031721](http://www.jstor.org.libproxy.smith.edu:2048/stable/2031721), MR 0046672.