MathDB
Turkey NMO 2007 1st Round - P28 (Combinatorics)

Source:

October 5, 2012
absolute value

Problem Statement

nn integers are arranged along a circle in such a way that each number is equal to the absolute value of the difference of the two numbers following that number in clockwise direction. If the sum of all numbers is 278278, how many different values can nn take?
<spanclass=latexbold>(A)</span> 1<spanclass=latexbold>(B)</span> 2<spanclass=latexbold>(C)</span> 4<spanclass=latexbold>(D)</span> 139<spanclass=latexbold>(E)</span> None of the above <span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 4 \qquad<span class='latex-bold'>(D)</span>\ 139 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}