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P06 [Number Theory] - Turkish NMO 1st Round - 2013

Source:

April 17, 2013

Problem Statement

What is the 111st111^{\text{st}} smallest positive integer which does not have 33 and 44 in its base-55 representation?
<spanclass=′latex−bold′>(A)</span> 760<spanclass=′latex−bold′>(B)</span> 756<spanclass=′latex−bold′>(C)</span> 755<spanclass=′latex−bold′>(D)</span> 752<spanclass=′latex−bold′>(E)</span> 750 <span class='latex-bold'>(A)</span>\ 760 \qquad<span class='latex-bold'>(B)</span>\ 756 \qquad<span class='latex-bold'>(C)</span>\ 755 \qquad<span class='latex-bold'>(D)</span>\ 752 \qquad<span class='latex-bold'>(E)</span>\ 750
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