Problem: The Century Puzzle

Can you write $100$ in the form of a mixed number, using all the nine digits once, and only once? The late distinguished French mathematician, Edouard Lucas, found seven different ways of doing it and expressed his doubts as to there being any other ways. As a matter of fact, there are just eleven ways and no more. Here is one of them, $91 \frac{5742}{638}.$ Nine of the other ways have similarly two figures in an integral part of the number, but the eleventh expression has only one figure there. Can the reader find this last form?

Solutions: 1

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Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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