MathDB
P27 [Combinatorics] - Turkish NMO 1st Round - 2003

Source:

May 18, 2014
geometryperimeter

Problem Statement

A finite number of circles are placed into a 1×11 \times 1 square. Let CC be the sum of the perimeters of the circles. For how many CCs from C=435C=\dfrac {43}5, 99, 9110\dfrac{91}{10}, 192\dfrac{19}{2}, 1010, we can definitely say there exists a line cutting four of the circles?
<spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 1<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 3<spanclass=latexbold>(E)</span> 4 <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ 4