Pangrammatic window

A pangrammatic window is a stretch of naturally occurring text that contains all the letters in the alphabet.

Shortest examples

The shortest known naturally occurring pangrammatic window was discovered in October 2014 through an automated processing of Google's indexed webcorpus, found in a review of the movie ''Magnolia'' written by Todd Manlow on the website PopMatters, at 36 letters:

The shortest known window in a published work is found in Piers Anthony's book ''Cube Route'', at 42 letters:

Prior to that, the shortest known window in a published work was found in Lillie de Hegermann-Lindencrone's 1912 book ''In the Courts of Memory'', at 56 letters:"Sub-60-Letter Pangrammatic Windows" in the February 2006 edition of Word Ways: The Journal of Recreational Linguistics

Probability of occurrence

Generally, according to the law of probability, the shorter the work, the longer the minimal pangrammatic window (if any) will be.

Some estimates can be made using the frequencies of the letters. Assuming that the incidence of each letter in a passage is independent of the incidence of the other letters, and provided ''m'' is much larger than 26, the probability that a sequence of length ''m'' will contain all 26 letters is approximately
P(a)P(b)...P(y)P(z), where P(''letter'') = 1 − (1 − p(''letter''))^''m'' and p(''letter'') is the frequency of the letter as a fraction (e.g. 5% is 0.05). Inputting the letter frequencies for the English language, the probability that a 1,700-letter sequence will contain all 26 letters is about 50%. At 1,000, there is about a 19.5% chance, and at 2,500, there is about a 73% chance.

For example, the shortest pangrammatic window in ''Around the World in Eighty Days'', by Jules Verne, is 150 letters:

The shortest pangrammatic window in the United States Declaration of Independence, a significantly shorter work, is 592 letters:

{{blockquote, We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.—That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed,—That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed.

See also

* Panalphabetic window

References

Pangrams