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P26 [Number Theory] - Turkish NMO 1st Round - 2003

Source:

May 18, 2014

Problem Statement

Each of the numbers nn, n+1n+1, n+2n+2, n+3n+3 is divisible by its sum of digits in its decimal representation. How many different values can the tens column of nn have, if the number in ones column of nn is 88?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> 5 <span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ 5
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