MathDB

16

Part of 2007 National Olympiad First Round

Problems(1)

Turkey NMO 2007 1st Round - P16 (Combinatorics)

Source:

10/4/2012
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,z≤9x,y,z \leq 9?
<spanclass=′latex−bold′>(A)</span> 9000<spanclass=′latex−bold′>(B)</span> 8460<spanclass=′latex−bold′>(C)</span> 7290<spanclass=′latex−bold′>(D)</span> 6150<spanclass=′latex−bold′>(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