MathDB

24

Part of 2012 National Olympiad First Round

Problems(1)

Turkish NMO First Round - 2012 Problem - 24 {Combinatorics}

Source:

7/1/2012
There are 20122012 backgammon checkers (stones, pieces) with one side is black and the other side is white. These checkers are arranged into a line such that no two consequtive checkers are in same color. At each move, we are chosing two checkers. And we are turning upside down of the two checkers and all of the checkers between the two. At least how many moves are required to make all checkers same color?
<spanclass=′latex−bold′>(A)</span> 1006<spanclass=′latex−bold′>(B)</span> 1204<spanclass=′latex−bold′>(C)</span> 1340<spanclass=′latex−bold′>(D)</span> 2011<spanclass=′latex−bold′>(E)</span> None <span class='latex-bold'>(A)</span>\ 1006 \qquad <span class='latex-bold'>(B)</span>\ 1204 \qquad <span class='latex-bold'>(C)</span>\ 1340 \qquad <span class='latex-bold'>(D)</span>\ 2011 \qquad <span class='latex-bold'>(E)</span>\ \text{None}