MathDB
P30 [Combinatorics] - Turkish NMO 1st Round - 2001

Source:

April 23, 2014

Problem Statement

There are nn airports which form a regular nn-gon. In the beginnig, there is exactly one plane at only kk airports. Each of the planes flies to one of the nearest airport each day. For which of the following ordered pairs (n,k)(n,k), it is impossible to gather all planes at a airport on one day however the planes are arranged initially?
<spanclass=latexbold>(A)</span> (10,6)<spanclass=latexbold>(B)</span> (10,4)<spanclass=latexbold>(C)</span> (11,3)<spanclass=latexbold>(D)</span> (11,5)<spanclass=latexbold>(E)</span> (13,8) <span class='latex-bold'>(A)</span>\ (10,6) \qquad<span class='latex-bold'>(B)</span>\ (10,4) \qquad<span class='latex-bold'>(C)</span>\ (11,3) \qquad<span class='latex-bold'>(D)</span>\ (11,5) \qquad<span class='latex-bold'>(E)</span>\ (13,8)