MathDB

8

Part of 2007 National Olympiad First Round

Problems(1)

Turkey NMO 2007 1st Round - P08 (Combinatorics)

Source:

10/4/2012
Starting from the number 123456789123456789, at each step, we are swaping two adjacent numbers which are different from zero, and then decreasing the two numbers by 11. What is the sum of digits of the least number that can be get after finite steps?
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 5<spanclass=′latex−bold′>(E)</span> 9 <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 5 \qquad<span class='latex-bold'>(E)</span>\ 9