Packing problem

Packing problems are one area where mathematics meets puzzles. Many of these problems stem from real-life packing problems.

In a packing problem you are given

one or more (usually two-or three-dimensional) containers
several 'goods' some or all of which have to be packed into this container

Usually the packing requires to be without gaps and overlaps, but in some packing problems the overlapping (of goods with each other and/or with the boundary of the container) is allowed and has to be minimised. Hence we can discern several categories of packing problems:

Table of contents

1 Categories of packing problems
2 Examples of 'gaps, but no overlaps' packing problems:

2.1 Example 1
2.2 Example 2

3 Literature

Categories of packing problems

No gaps or overlaps allowed
- many polycube puzzles fit into this category
- many polysquare puzzles fit into this category
- many tiling puzzles fit into this category
Gaps allowed, but no overlaps. Usually the total area of gaps has to be minimised. See below for an example.
Gaps and overlaps allowed. Here usually the total area of overlaps has to be minimised.

Examples of 'gaps, but no overlaps' packing problems:

Journal of Recreational Mathematics - easy read, many articles.

See also: Tetris