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Turkey NMO 2008 1st Round - P34 (Number Theory)

Source:

August 27, 2012

Problem Statement

We call a positive integer "special" if the number is divided by all of its digits (except the 00s). At most how many consequtive special numbers are there?
<spanclass=′latex−bold′>(A)</span> 9<spanclass=′latex−bold′>(B)</span> 10<spanclass=′latex−bold′>(C)</span> 12<spanclass=′latex−bold′>(D)</span> 13<spanclass=′latex−bold′>(E)</span> 14 <span class='latex-bold'>(A)</span>\ 9 \qquad<span class='latex-bold'>(B)</span>\ 10 \qquad<span class='latex-bold'>(C)</span>\ 12 \qquad<span class='latex-bold'>(D)</span>\ 13 \qquad<span class='latex-bold'>(E)</span>\ 14
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