MathDB

27

Part of 2004 National Olympiad First Round

Problems(1)

P27 [Combinatorics] - Turkish NMO 1st Round - 2004

Source:

11/15/2013
We have 3131 pieces where 11 is written on two of them, 22 is written on eight of them, 33 is written on twelve of them, 44 is written on four of them, and 55 is written on five of them. We place 3030 of them into a 5×65\times 6 chessboard such that the sum of numbers on any row is equal to a fixed number and the sum of numbers on any column is equal to a fixed number. What is the number written on the piece which is not placed?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> 5 <span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ 5