The Blank Column

A secretary, eager to try out a new typewriter, thought of a sentence shorter than one typed line, set the controls for the two margins and then, starting at the left and near the top of a sheet of paper, proceeded to type the sentence repeatedly. She typed the sentence exactly the same way each time, with a period at the end followed by the usual two spaces. She did not, however, hyphenate any words at the end of a line: When she saw that the next word (including whatever punctuation marks may have followed it) would not fit the remaining space on a line, she shifted to the next line. Each line, therefore, started flush at the left with a word of her sentence. She finished the page after typing 50 single-spaced lines.

Without experimenting on a typewriter, answer this question: Is there sure to be at least one perfectly straight column of blank spaces on the sheet, between the margins, running all the way from top to bottom? (T. Robert Scott originated this problem, which was sent to me by his friend W. Lloyd Milligan of Columbia, S.C.)

A: "What are the ages, in years only, of your three children?"

B: "The product of their ages is 36."

A: "Not enough information."

B: "The sum of their ages equals your house number."

A: "Still not enough information."

B: "My oldest child—and he's at least a year older than either of the others—has a wart on his left thumb."

A: "That's enough, thank you. Their ages are. . . ."

Complete A's sentence. (Mel Stover of Winnipeg was the first of several readers to send this problem, the origin of which I do not know.)

1. The shortest knotted chain known that meets all the conditions specified has 36 links [see Figure 13]. It is reproduced from Max Delbriick's paper, "Knotting Problems in Biology,"

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