MathDB
Arranging Numbers into Columns

Source:

March 3, 2009

Problem Statement

The odd positive integers 1,3,5,7,,1,3,5,7,\cdots, are arranged into in five columns continuing with the pattern shown on the right. Counting from the left, the column in which 1985 1985 appears in is the
[asy] int i,j; for(i=0; i<4; i=i+1) { label(string(16*i+1), (2*1,-2*i)); label(string(16*i+3), (2*2,-2*i)); label(string(16*i+5), (2*3,-2*i)); label(string(16*i+7), (2*4,-2*i)); } for(i=0; i<3; i=i+1) { for(j=0; j<4; j=j+1) { label(string(16*i+15-2*j), (2*j,-2*i-1)); }} dot((0,-7)^^(0,-9)^^(2*4,-8)^^(2*4,-10)); for(i=-10; i<-6; i=i+1) { for(j=1; j<4; j=j+1) { dot((2*j,i)); }} [/asy]
<spanclass=latexbold>(A)</span> first<spanclass=latexbold>(B)</span> second<spanclass=latexbold>(C)</span> third<spanclass=latexbold>(D)</span> fourth<spanclass=latexbold>(E)</span> fifth <span class='latex-bold'>(A)</span> \text{ first} \qquad <span class='latex-bold'>(B)</span> \text{ second} \qquad <span class='latex-bold'>(C)</span> \text{ third} \qquad <span class='latex-bold'>(D)</span> \text{ fourth} \qquad <span class='latex-bold'>(E)</span> \text{ fifth}