Question

Some points were initially placed on a line. After that, a point was inserted between each pair of neighboring points. After that, such an insertion was repeated two more times. 113 points are on the line as a result. How many points were placed on the line initially?

Answer 1

Answer: The initial number of points on the line was 15.

Explanation:

8n-7=113

8n=120

n=15

Answer 2

15 points

Explanation:

Initial number of points= x

It can be added 1 less points between the existing ones, so:

Step 1

• added x-1, and number of points become x+x-1= 2x- 1

Step 2

• added 2x-1-1= 2x-2 and number of points become 2x-1+2x-2= 4x-3

Step 3

• added 4x-3-1= 4x-4 and finally we have 4x-3 + 4x-4= 8x -7 points

Now,

• 8x-7= 113
• 8x= 120
• x=120/8
• x=15

Number of initial points is 15