A little history of the problem, culled from the pages of Metamagical Themas, Hofstadter's collection of his Scientific American columns. First mention of it is in the Jan. '82 column. Lee Sallows opened the field with a sentence that began "Only the fool would take trouble to verify that his sentence was composed of ten a's ...." etc.

Then in the addendum to the Jan.'83 column on viral sentences, Hofstadter quotes Sallows describing his Pangram Machine, "a clock-driven cascade of

sixteen Johnson-counters," to tackle the problem. An early success was

"This pangram tallies five a's, one b, one c, two d's, twenty- eight e's, eight f's, six g's, eight h's, thirteen i's, one j, one k, three l's, two m's, eighteen n's, fifteen o's, two p's, one q, seven r's, twenty-five s's, twenty-two t's, four u's, four v's, nine w's, two x's, four y's, and one z."

Sallows wagered ten guilders that no-one could create a perfect self- documenting sentence beginning, "This computer-generated pangram contains ...." within ten years.

It was solved very quickly, after Sallows' challenge appeared in Dewdney's Oct. '84 SA column. Larry Tesler solved it by a method Hofstadter calls "Robinsonizing," which involves starting with an arbitrary set of values for each letter, getting the true values when the sentence is made, and plugging the new values back in, making a feedback loop. Eventually, you

can zero in on a set of values that work. Tesler's sentence

This computer-generated pangram contains six a's, one b, three c's, three d's, thirty-seven e's, six f's, three g's, nine h's, twelve i's, one j, one k, two l's, three m's, twenty-two n's, thirteen o's, three p's, one q, fourteen r's, twenty-nine s's, twenty-four t's, five u's, six v's, seven w's, four x's, five y's, and one z.

The method of solution (called "Robinsonizing," after the logician Raphael

Robinson) is as follows
1) Fix the count of a's. 2) Fix the count of b's. 3) Fix the count of c's. ... 26) Fix the count of z's.

Then, if the sentence is still wrong, go back to step 1.

Most attempts will fall into long loops (what Hofstadter calls attractive orbits), but with a good computer program, it's not too hard to find a Robinsonizing sequence that zeros in on a fixed set of values.

The February and May 1992 Word Ways have articles on this subject, titled "In Quest of a Pangram, (Part 1)" by Lee Sallows. It tells of his search for a self-referential pangram of the form, "This pangram contains _ a's, ..., and one z." (He built special hardware to search

for them.) Two such pangrams given in the article are

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

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.

It also contains one in Dutch by Rudy Kousbroek
Dit pangram bevat vijf a's, twee b's, twee c's, drie d's, zesenveertig e's, vijf f's, vier g's, twee h's, vijftien i's, vier j's, een k, twee l's, twee m's, zeventien n's, een o, twee p's, een q, zeven r's, vierentwintig s's, zestien t's, een u, elf v's, acht w's, een x, een y, and zes z's.
Dewdney, A.K. Scientific American, Oct. 1984, pp 18-22. Sallows, L.C.F. Abacus, Vol.2, No.3, Spring 1985, pp 22-40. Sallows, L.C.F. Word Ways, Feb. & May 1992 Hofstadter, D. Scientific American, Jan. 1982, pp 12-17.

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