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Getting the multiplier, multiplicand and the product with U’s

  1. Jan 28, 2009 #1
    In the following long multiplication puzzle, each of the U’s represents a decimal digit from 0 to 9, whether same or different.

    Each digit from 0-9 must appear precisely 2 times in the following multiplication.

    None of the numbers can contain any leading zero.

    ......U U U
    ......U U U
    ......U U U
    ...U U U
    U U U
    U U U U U

    Determine the multiplier, multiplicand and the product.

    Note: The dots are present merely for the sake of formatting, and none of the dots represent a decimal point.
    Last edited: Jan 29, 2009
  2. jcsd
  3. Jan 29, 2009 #2
    I don't follow. Why couldn't the answer be:

    111 * 111 = 12321
    111 * 222 = 24642
    123 * 321 = 39483

    Clearly if all the U's represent the SAME digit, the puzzle is impossible, unless U=0. And if U's are different digits, there are seemingly a plethora of answers, so long as each digit in the 2nd number times the 1st number is smaller than 1000, and obviously the product is less than 100000. What am I missing?

  4. Jan 29, 2009 #3
    You’re right, davee123.

    I really goofed up the problem statement and forgot to add that:

    ”Each digit from 0-9 must appear precisely 2 times in the following multiplication.”

    I have now incorporated the said amendments in the problem text.

    I sincerely apologize for the inconvenience caused due to the foregoing.
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