Math Puzzle - The Ribbon Problem

This is the debt I pay Just for one riotous day, Years of regret and grief. Sorrow without relief. Pay it I will to the end-- Until the grave, my friend, Gives me a true release-- Gives me the clasp of peace. Slight was the thing I bou... Read more of The Debt at Martin Luther King.ca

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The Ribbon Problem

(MISCELLANEOUS PUZZLES)

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.