Word Ways

Article Title

Planet Packing


A. Ross Eckler


Suppose that one has a list of words. What is the smallest string of letters needed to exhibit all of these words, each spelled out in order but not necessarily using adjacent letters in the string? For example, one, two, and three can be embedded in the eight-letter string thrwonee (or several others), but no seven-letter string is possible. It is easy to see that seven is the theoretical minimum, for six different letters appear once in any word, and one letter appears twice in a word. For longer lists, however, letter counts of individual words yield only a lower bound for the minimum achievable string length.