MathDB
Turkey NMO 2008 1st Round - P20 (Combinatorics)

Source:

August 25, 2012
ceiling function

Problem Statement

Each of the integers a1,a2,a3,,a2008a_1,a_2,a_3,\dots,a_{2008} is at least 11 and at most 55. If an<an+1a_n < a_{n+1}, the pair (an,an+1)(a_n, a_{n+1}) will be called as an increasing pair. If an>an+1a_n > a_{n+1}, the pair (an,an+1)(a_n, a_{n+1}) will be called as an decreasing pair. If the sequence contains 103103 increasing pairs, at least how many decreasing pairs are there?
<spanclass=latexbold>(A)</span> 21<spanclass=latexbold>(B)</span> 24<spanclass=latexbold>(C)</span> 36<spanclass=latexbold>(D)</span> 102<spanclass=latexbold>(E)</span> None of the above <span class='latex-bold'>(A)</span>\ 21 \qquad<span class='latex-bold'>(B)</span>\ 24 \qquad<span class='latex-bold'>(C)</span>\ 36 \qquad<span class='latex-bold'>(D)</span>\ 102 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}