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Math Help - Arithmetic puzzle help

  1. #1
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    Arithmetic puzzle help

    I do not understand the solution to this problem. Please help!

    The Problem:

    "The integer A consists of 666 threes, and the integer B has 666 sixes. What digits appear in the product AB?"

    The (partial) Solution:

    "Since 6 = 3 x 2, the product in question will be the same as that obtained by multiplying the integer A1 composed of 666 digits 9 by the integer B1 composed of 666 digits 2. etc."

    Does anyone understand what this means? This is problem #72 from the USSR Olympiad Problem Book.
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  2. #2
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    Here's the rest of the solution if it helps explain the previous sentence:

    ...But A1 is 1 less than 10^666; and so if B1 is multiplied by A1, the result is the same as multiplying B1 by 10^666 (which yields an integer composed of 666 digits 2 followed by 666 zeros) and subtracting the integer B1. It clearly follows that the result will be a number of form:

    {22.....21} {77.....78}
    __665________665__

    I really dont understand what the original line means:

    "Since 6 = 3 x 2, the product in question will be the same as that obtained by multiplying the integer A1 composed of 666 digits 9 by the integer B1 composed of 666 digits 2"
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  3. #3
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    Ah I understand. They mean that 666 #9's times 666 #2's is equivalent to 666 #3's times 666 #6's. The grammar was just weird.
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