Finding The Right Row

Logic Level 3

\[\begin{array} {ccccccccc} 1 \\ 2 \quad 2 \\ 3 \quad 4 \quad 3 \\ 4 \quad 6 \quad 6 \quad 4 \\ 5 \quad 8 \quad 9 \quad 8 \quad 5 \\ 6 \hspace{0.32cm} 10 \hspace{0.32cm} 12 \hspace{0.32cm} 12 \hspace{0.32cm} 10 \hspace{0.32cm} 6 \\ \vdots \end{array} \]

In the triangle above, the outer diagonal lines are \(1,2,3,4,\ldots,\) which begins at 1 and each number after the first is one larger than the previous number.

The next diagonal lines are \(2,4,6,8,\ldots,\) which begins at 2 and each number after the first is two larger than the previous number.

SImiarly, the \(n^\text{th}\) diagonal begins at \(n\) and each number after the first is \(n\) larger than the previous number.

In which horizontal row does the number 2016 first appear?

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