Geometry or Combinatorics ?

Probability Level 4

Find the maximum number of regions into which 50 lines can divide a plane into. Details :- All of the lines lie on a single plane.


The answer is 1276.

Venkata Karthik Bandaru by Venkata Karthik Bandaru , 20, India

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2 solutions

The above shows the proof of the general formula for the maximum number of regions k lines can divide a plane into. Hence, substituting k = 50 in the above derived formula, we get the answer to be 1276.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Think of it from this perspective, each new line drawn will add another region for each existing line on the plane. Hence, we can derive the formula that the number of regions divided by n lines is the nth triangle number+1.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Yeah, it is the crux idea.

Venkata Karthik Bandaru - 5 years, 4 months ago

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