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Turkey Contests
National Olympiad First Round
2008 National Olympiad First Round
6
6
Part of
2008 National Olympiad First Round
Problems
(1)
Turkey NMO 2008 1st Round - P06 (Number Theory)
Source:
8/24/2012
A positive integer
n
n
n
is called a good number if every integer multiple of
n
n
n
is divisible by
n
n
n
however its digits are rearranged. How many good numbers are there?
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3
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B
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4
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C
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6
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D
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12
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Infinitely many
<span class='latex-bold'>(A)</span>\ 3 \qquad<span class='latex-bold'>(B)</span>\ 4 \qquad<span class='latex-bold'>(C)</span>\ 6 \qquad<span class='latex-bold'>(D)</span>\ 12 \qquad<span class='latex-bold'>(E)</span>\ \text{Infinitely many}
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3
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B
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4
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6
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12
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Infinitely many
modular arithmetic