Magazine article Word Ways

The Printer's Paradox

Magazine article Word Ways

The Printer's Paradox

Article excerpt

A printer "has a block of 100 spaces, each of which can be filled with any of 27 different type symbols: the 26 letters of the alphabet (upper case) and a null for spacing purposes. The number of intelligible messages that can be printed under these restrictions is staggeringly large, but obviously finite, since the number of ways of filling 100 spaces with any of 27 symbols is the 100th power of 27.

Among these messages there are some which characterize or define positive integers, sometimes in any of several ways. For instance 7 is characterized by SEVEN, FIVE PLUS TWO, THE SQUARE ROOT OF FORTY NINE, THE NUMBER OF DAYS IN A WEEK, and many other ways the reader can think of Most of the possible "messages" are nonsense. Most of those that are not do not refer to integers. It follows, of course, that the number of integers that can be characterized in no more than 100 spaces is also finite, anti that being true, there must be a largest one. …

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