Abstract: If we cover a convex body K with planks (strips of space between two parallel yperplanes), does it follow that the sum of the widths of the planks is at least the minimal width of K? This question was posed by Alfred Tarski in 1932, and answered in the affirmative by Bang in 1951. It leads to numerous related questions. I will present a few such results and one or two proofs in the talk. However, many related questions are still unsolved.