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Magic Multiplications with Digits

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See some patterns generated by arithmetic involving numbers whose digits increase, decrease, or are repeated, or by multiples of some digit. Try to figure out why these curious patterns appear.

Contributed by: Enrique Zeleny (March 2011)
Open content licensed under CC BY-NC-SA

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A. H. Beiler, Recreations in the Theory of Numbers: The Queen of Mathematics Entertains, New York: Dover Publications, 1964.

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