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National and Regional Contests
Turkey Contests
National Olympiad First Round
2005 National Olympiad First Round
14
14
Part of
2005 National Olympiad First Round
Problems
(1)
P14 [Number Theory] - Turkish NMO 1st Round - 2005
Source:
10/26/2013
We call a number
1
0
3
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6
10^3 < n < 10^6
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a balanced number if the sum of its last three digits is equal to the sum of its other digits. What is the sum of all balanced numbers in
m
o
d
13
\bmod {13}
mod
13
?
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A
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5
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7
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D
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11
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E
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12
<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 5 \qquad<span class='latex-bold'>(C)</span>\ 7 \qquad<span class='latex-bold'>(D)</span>\ 11 \qquad<span class='latex-bold'>(E)</span>\ 12
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7
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11
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12