MathDB

8

Part of 2008 National Olympiad First Round

Problems(1)

Turkey NMO 2008 1st Round - P08 (Combinatorics)

Source:

8/25/2012
Numbers 0,1,2,…,90,1,2,\dots,9 are placed left to right into the squares of the first row of 10×1010 \times 10 chessboard. Similarly, 10,11,…,1910,11,\dots,19 are placed into the second row, and so on. We are changing signs of exactly five numbers into the squares of each row and each column. What is the minimum value of the sum of the numbers on the chessboard?
<spanclass=′latex−bold′>(A)</span> −10<spanclass=′latex−bold′>(B)</span> −2<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> 10<spanclass=′latex−bold′>(E)</span> None of the above <span class='latex-bold'>(A)</span>\ -10 \qquad<span class='latex-bold'>(B)</span>\ -2 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 10 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}