Proposed by Felix Ulrich-Oltean

The Bookshelves Problem

We are given a set of planks of wood, all of the same width and thickness but with a variety of lengths and we are attempting to construct some bookshelves in such a way that we can accommodate as many books as possible. This entry is based on a real problem of trying to make some bookshelves out of some old skirting boards.

diagram showing a basic set of bookshelves

Assumptions and restrictions:

Information given:

Decisions or outputs required:

The decision is where to cut each plank: i.e. a (potentially) empty list of cut points for each plank

In addition the solution should make clear: