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:
[![Bang][1]][1]
(Snapshot from Bang's paper.)
Does anyone know if this problem has been solved? I am especially interested in $\mathbb{R}^2$.
> Bang, Thøger (1951), "[A solution of the 'plank problem'](https://doi.org/10.1090/S0002-9939-1951-0046672-4 )", *Proc. Amer. Math. Soc.* 2 (6): 990–993, doi:10.2307/2031721, [JSTOR 2031721](http://www.jstor.org/stable/2031721), MR 0046672.
