List of Pangrams - Self-enumerating Pangrams

Self-enumerating Pangrams

A self-enumerating pangram, or a pangrammic autogram, is one which describes exactly the number of letters it itself contains. Because changing the description changes the numbers of letters used in the description, the task of finding such a pangram is exceedingly complex.

This particularly interesting kind of pangram arose from some verbal horseplay between Douglas Hofstadter, an AI researcher and writer for Scientific American, Rudy Kousbroek, a Dutch linguist and essayist, and Lee Sallows, a British electronics engineer. Hofstadter posed the problem of sentences that describe themselves, prompting Sallows to devise the following:

Only the fool would take trouble to verify that his sentence was composed of ten a's, three b's, four c's, four d's, forty-six e's, sixteen f's, four g's, thirteen h's, fifteen i's, two k's, nine l's, four m's, twenty-five n's, twenty-four o's, five p's, sixteen r's, forty-one s's, thirty-seven t's, ten u's, eight v's, eight w's, four x's, eleven y's, twenty-seven commas, twenty-three apostrophes, seven hyphens and, last but not least, a single !

This, while interesting, is not a complete pangram as it lacks a j, q, and z. Kousbroek published a Dutch equivalent, which spurred Sallows, who lives in the Netherlands and reads the paper where Kousbroek writes his essays, to think harder about this problem in order to solve it more generally. Initial attempts to write a program for this came to naught, but, in 1984, he decided to construct a dedicated piece of hardware for this task, the Pangram Machine. This accepts a description of the initial sentence fragment, and tries to fill in the blanks. The result was later published in Scientific American in October 1984, as follows:

This Pangram contains four a's, one b, two c's, one d, thirty e's, six f's, five g's, seven h's, eleven i's, one j, one k, two l's, two m's, eighteen n's, fifteen o's, two p's, one q, five r's, twenty-seven s's, eighteen t's, two u's, seven v's, eight w's, two x's, three y's, & one z.

There are exhaustive lists of some self-enumerating sentences, and thus also of certain pangrams, in English, Italian and Latin. These were computed using BDDs (binary decision diagrams).