MathDB
Turkey NMO 2007 1st Round - P36 (Combinatorics)

Source:

October 5, 2012

Problem Statement

Five points, no three of which are collinear, are given. What is the least possible value of the numbers of convex polygons whose some corners are from these five points?
<spanclass=latexbold>(A)</span> 10<spanclass=latexbold>(B)</span> 11<spanclass=latexbold>(C)</span> 12<spanclass=latexbold>(D)</span> 15<spanclass=latexbold>(E)</span> 16 <span class='latex-bold'>(A)</span>\ 10 \qquad<span class='latex-bold'>(B)</span>\ 11 \qquad<span class='latex-bold'>(C)</span>\ 12 \qquad<span class='latex-bold'>(D)</span>\ 15 \qquad<span class='latex-bold'>(E)</span>\ 16