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10

Part of 2000 National Olympiad First Round

Problems(1)

Turkey NMO 2000 1st Round - P10 (Number Theory)

Source:

7/24/2012
NN is a 50−50-digit number (in the decimal scale). All digits except the 26th26^{\text{th}} digit (from the left) are 11. If NN is divisible by 1313, what is the 26th26^{\text{th}} digit?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 6<spanclass=′latex−bold′>(D)</span> 8<spanclass=′latex−bold′>(E)</span> More information is needed <span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 3 \qquad<span class='latex-bold'>(C)</span>\ 6 \qquad<span class='latex-bold'>(D)</span>\ 8 \qquad<span class='latex-bold'>(E)</span>\ \text{More information is needed}