Pangram

A pangram (Greek: pan gramma, "every letter"), or holoalphabetic sentence, is a sentence which uses every letter of the alphabet at least once. Pangrams are used to display typefaces and test equipment. For example, the pangram The quick brown fox jumps over the lazy dog was utilized by Western Union to test Telex/TWX data communication equipment for accuracy and reliability.

Interesting pangrams are generally short; constructing a sentence that includes the fewest repeat letters possible is a challenging task. Longer pangrams that are enlightening, humorous, or eccentric can be noteworthy in their own right. In a sense, the pangram is the opposite of the lipogram, where the aim is to omit one or more letters.

Ideographic scripts

Ideographic scripts, that is, writing systems composed principally of logograms, cannot be used to produce pangrams in the literal sense, since they are radically different from alphabets or other phonetic writing systems. In such scripts, the total number of signs is large and imprecisely defined, so producing a text with every possible sign is impossible. However, various analogies to pangrams are feasible, including traditional pangrams in a romanization. In addition, it is possible to create pangrams that demonstrate certain aspects of ideographic characters.

• Chinese:
  • The Thousand Character Classic is a one-thousand-character poem in which each character is used exactly once, but it does not include all Chinese characters.
  • The single character 永 (permanence) incorporates every basic stroke used to write Chinese characters exactly once, as described in the Eight Principles of Yong.

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 of 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 here and thus also of certain pangrams, in English, Italian and Latin. These were computed using BDD's (binary decision diagrams).

See also

• Pangrammatic window
• Pangrammatic lipogram
• Lorem ipsum

External links

• Pangrams at rec.puzzles
• Pangrams at Word Oddities
• A list of pangrams in several languages
• Another account of Lee Sallow's efforts
• Pangrams at Fun with Words
• A pangram list
• Pangram contest winners
• Pangrams at AskOxford
• A list of Russian pangrams