Self-enumerating Pangrams
A self-enumerating pangram, or a pangrammic autogram, is one which describes exactly the number of letters it itself contains. The task of finding such a pangram is complicated because changing the description changes the numbers of letters used in the description. The most trivial discovery technique is the generate and test technique.
This kind of pangram arose from some verbal horseplay between Douglas Hofstadter, 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 is not a complete pangram as it lacks 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. The Pangram Machine, as Sallows called his device, accepted a description of the initial sentence fragment and tried to fill in the blanks. The result was published in Scientific American in October 1984:
This Pangram contains four as, one b, two cs, one d, thirty es, six fs, five gs, seven hs, eleven is, one j, one k, two ls, two ms, eighteen ns, fifteen os, two ps, one q, five rs, twenty-seven ss, eighteen ts, two us, seven vs, eight ws, two xs, three ys, & one z.
There are exhaustive lists online of self-enumerating sentences and thus also of certain pangrams, in English, Italian and Latin. These were computed using binary decision diagrams.
Read more about this topic: Pangram