Abstract: If we cover a convex body K with planks (strips of space
between two parallel hyperplanes), 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.