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P08 [Combinatorics] - Turkish NMO 1st Round - 2005

Source:

November 8, 2013
countingdistinguishability

Problem Statement

How many natural number triples (x,y,z)(x,y,z) are there such that xyz=106xyz = 10^6?
<spanclass=′latex−bold′>(A)</span> 568<spanclass=′latex−bold′>(B)</span> 784<spanclass=′latex−bold′>(C)</span> 812<spanclass=′latex−bold′>(D)</span> 816<spanclass=′latex−bold′>(E)</span> 824 <span class='latex-bold'>(A)</span>\ 568 \qquad<span class='latex-bold'>(B)</span>\ 784 \qquad<span class='latex-bold'>(C)</span>\ 812 \qquad<span class='latex-bold'>(D)</span>\ 816 \qquad<span class='latex-bold'>(E)</span>\ 824
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