[

Several points were marked on a line. After that, a point was added between each pair of adjacent points. This operation was repeated three times, and as a result, there were 65 points on the line. How many points were there initially?

#
If there were $n$ points on a line, then in one operation, $n-1$ points were added.

## Solution

If there were 65 points at the end, then there were 33 (and 32 were added) points before that. Similarly, there were 17 points after the first operation, and 9 before it.

## Answer

9 points.