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1,2,..,49 written into chessboard

Source: Turkish NMO 1st Round - 2013 - Problem 4

April 19, 2013
number theoryprime numberscombinatorics proposedcombinatorics

Problem Statement

The numbers 1,2,…,491,2,\dots, 49 are written on unit squares of a 7×77\times 7 chessboard such that consequtive numbers are on unit squares sharing a common edge. At most how many prime numbers can a row have?
<spanclass=′latex−bold′>(A)</span> 7<spanclass=′latex−bold′>(B)</span> 6<spanclass=′latex−bold′>(C)</span> 5<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> 3 <span class='latex-bold'>(A)</span>\ 7 \qquad<span class='latex-bold'>(B)</span>\ 6 \qquad<span class='latex-bold'>(C)</span>\ 5 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ 3
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