Finding The Right Row

Logic Level 3

1223434664589856101212106\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,,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,,2,4,6,8,\ldots, which begins at 2 and each number after the first is two larger than the previous number.

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

In which horizontal row does the number 2016 first appear?

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