Typewriter

[AuSmith]

"A secretary, eager to try out a new typrewriter, thought of a sentence shorter than one typed line, set the controls for the first 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 in the remaining space on the 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?"

Thanks to T. Robert Scott for the problem and Martin Gardner for spreading it.