Several points are marked on the line. After that, a point was added between every two adjacent points.

Several points are marked on the line. After that, a point was added between every two adjacent points. This operation was repeated 3 times, and as a result, there were 73 points on the line. How many points were there at the beginning?

Let the initial number of points on the line be X.
If you add one point between each two points of this set of points, the number of points on the straight line will increase by X – 1, thus, the points on the straight line will become X + X – 1 = 2X – 1.
After the second repetition of the operation of placing points, they will become:
(2X – 1) + (2X – 1 – 1) = 4X – 3.
After adding points for the third time, they become:
(4X – 3) + (4X – 3 – 1) = 8X -7.
According to the condition, now there are 73 points on the straight line, that is
8X – 7 = 73;
8X = 80;
X = 10.
Answer: there were 10 points on the line.