A pangrammatic window is a stretch of naturally occurring text that contains all the letters in the alphabet.
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:[1]
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:[2]
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 approximatelyP(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: