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Turkey NMO 2007 1st Round - P16 (Combinatorics)

Source:

October 4, 2012

Problem Statement

The sum of the largest number and the smallest number of a triple of positive integers (x,y,z)(x,y,z) is called to be the power of the triple. What is the sum of powers of all triples (x,y,z)(x,y,z) where x,y,z9x,y,z \leq 9?
<spanclass=latexbold>(A)</span> 9000<spanclass=latexbold>(B)</span> 8460<spanclass=latexbold>(C)</span> 7290<spanclass=latexbold>(D)</span> 6150<spanclass=latexbold>(E)</span> 6000 <span class='latex-bold'>(A)</span>\ 9000 \qquad<span class='latex-bold'>(B)</span>\ 8460 \qquad<span class='latex-bold'>(C)</span>\ 7290 \qquad<span class='latex-bold'>(D)</span>\ 6150 \qquad<span class='latex-bold'>(E)</span>\ 6000