# Klarner’s theorem

*How do I fit as many boxes and suitcases as possible into my much too small car? How are container ships loaded in the most space-saving way possible? How can I cut out as many biscuits as possible from a sheet of dough? How does the layout artist fill a newspaper page with as many advertisements as possible without gaps?*

Such questions, which play a major role in everyday life and in business, are what mathematicians call *packing problems*. They were a speciality of the American mathematician *David A. Klarner* (†1999).

A puzzle in the Maths Adventure Land refers to one of its central statements. *Klarner’s theorem* states: A rectangle of dimension , which consists of squares with side length 1, can be filled without gaps with -sized strips if at least one of the side lengths or is divisible by . The rectangle in the Maths Adventure Land is divided into , or squares. The strips with which this area is to be filled consist of four squares of the same size arranged in a row one behind the other. of these strips also make squares.