Question 9
The positive integers are arranged in rows and columns as shown below.
Row 1: 1
Row 2: 2 3
Row 3: 4 5 6
Row 4: 7 8 9 10
Row 5: 11 12 13 14 15
Row 6: 17 18 19 20 21 22
$\vdots$
More rows continue to list the positive integers in order, with each new row containing one more integer than the previous row. How many integers less than 2000 are in the column that contains the number 2000?
**Editorial note for this self-study exercise:** Follow the verbal rule of consecutive positive integers in left-aligned rows. The displayed sixth row has a source error: for this exercise replace it by 16, 17, 18, 19, 20, 21, and continue without omissions. Count only entries strictly less than 2000.
Row 1: 1
Row 2: 2 3
Row 3: 4 5 6
Row 4: 7 8 9 10
Row 5: 11 12 13 14 15
Row 6: 17 18 19 20 21 22
$\vdots$
More rows continue to list the positive integers in order, with each new row containing one more integer than the previous row. How many integers less than 2000 are in the column that contains the number 2000?
**Editorial note for this self-study exercise:** Follow the verbal rule of consecutive positive integers in left-aligned rows. The displayed sixth row has a source error: for this exercise replace it by 16, 17, 18, 19, 20, 21, and continue without omissions. Count only entries strictly less than 2000.