MathDB

20

Part of 2014 National Olympiad First Round

Problems(1)

Set contains powers of 2 or 3

Source: P20 [Combinatorics] - Turkish NMO 1st Round - 2014

5/23/2014
How many distinct sets are there such that each set contains only non-negative powers of 22 or 33 and sum of its elements is 20142014?
<spanclass=′latex−bold′>(A)</span> 64<spanclass=′latex−bold′>(B)</span> 60<spanclass=′latex−bold′>(C)</span> 54<spanclass=′latex−bold′>(D)</span> 48<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 64 \qquad<span class='latex-bold'>(B)</span>\ 60 \qquad<span class='latex-bold'>(C)</span>\ 54 \qquad<span class='latex-bold'>(D)</span>\ 48 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
modular arithmeticcombinatorics proposedcombinatorics