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Quandaries & Queries
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 Topic: divides
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 abc,abc 2002-11-20 From Pam:Prove or disprove that "every number of the form abc,abc (where a, b, and c represent digits) is divisible by 7,11, and 13"Answered by Penny Nom. A Place Value Curiosity 1998-05-25 From Ed:I was visiting with an elderly gentleman this afternoon. He showed me this curiosity and then asked if I could explain it to him. Can you provide an explanation of why the 9 or multiple of 9 keeps occurring in this procedure? Choose any number, say 125 and add the digits to get 8. subtract the 8 from the 125 and the result is 117. Add the digits in 117 to get 9. Subtract the 9 from the 117 to get 108. Add the digits in 108 to get 9. If this procedure continues a 9 or a multiple of 9 reoccurs. What is the mathematical explanation behind this happening? Answered by Denis Hanson.

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