MathDB

28

Part of 2010 National Olympiad First Round

Problems(1)

Turkey NMO 2010 1st Round - P28 (Combinatorics)

Source:

7/26/2012
Only AA and BB have nn friends in a village of 20102010 people. The other 20082008 people have all different numbers of friends. How many possible values of nn are there?
<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> None <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>\ \text{None}