Pangrammatic Window


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

Generally, according to the law of probability, the shorter the work, the longer the pangrammatic window will be. Using the frequencies of the letters, it is easy to show this. For a sequence length m, the probability it will contain all 26 letters is P(a)P(b)…P(y)P(z) where P(n)=1-(1-p(n))m. Inputting the letter frequencies, the probability that a 1,700-letter sequence will contain all 26 letters is about 50%. At 1000, there is about a 19.5% chance, and at 2,500, there is about a 73% chance. Technically, the probability of a perfect pangrammatic window, i.e. one 26 letters long, is about 556 billion to one.

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