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nydus/The Canterbury Puzzles, and Other Curious ProblemsPublic

Henry Ernest Dudeney collects a wide variety of original mathematical and mental puzzles into this volume. The book features an introductory essay on the nature of puzzles and provides solutions for all problems at the end.

Page 128 of 307
Table of Contents

83 .— The Ribbon Problem.

A ring diagram displaying a sequence of numbers from 0 to 9 in a circle, with an arrow pointing to the number 2.

If we take the ribbon by the ends and pull it out straight, we have the number 0588235294117647. This number has the peculiarity that, if we multiply it by any one of the numbers, 2, 3, 4, 5, 6, 7, 8, or 9, we get exactly the same number in the circle, starting from a different place. For example, multiply by 4, and the product is 2352941176470588, which starts from the dart in the circle. So, if we multiply by 3, we get the same result starting from the star. Now, the puzzle is to place a different arrangement of figures on the ribbon that will produce similar results when so multiplied; only the 0 and the 7 appearing at the ends of the ribbon must not be removed.

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