Question 15
Positive integers are arranged in the left-aligned triangular array below. The header labels the columns; the labels before the vertical line number the rows.
$$\begin{array}{c|rrrrrr} &1&2&3&4&5&6\\\hline 1&1&&&&&\\2&2&3&&&&\\3&4&5&6&&&\\4&7&8&9&10&&\\5&11&12&13&14&15&\\6&16&17&18&19&20&21\end{array}$$
Continue in the same way. How many entries smaller than 2000 lie in its column?
$$\begin{array}{c|rrrrrr} &1&2&3&4&5&6\\\hline 1&1&&&&&\\2&2&3&&&&\\3&4&5&6&&&\\4&7&8&9&10&&\\5&11&12&13&14&15&\\6&16&17&18&19&20&21\end{array}$$
Continue in the same way. How many entries smaller than 2000 lie in its column?