A Problem Based On A Unique Concept Of Counting

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A Problem Based On A Unique Concept Of Counting

image containing math problem statement

This problem is based on an unique method of counting number of regions created by cutting a plane using straight lines.

We can minimize the number of cuts by ensuring that no cut passes through an intersection point of two previous cuts. In other words we maximize the number of regions per cut.

This is a problem of dividing a plane into regions using straight lines, as described .

Let the number of cuts be $n$. Therefore, the maximum number of regions these $n$ cuts can form is $\xacomb{n+1}{2} + 1$.

Therefore,

$\xacomb{n+1}{2} + 1 \ge 29$

$\Rightarrow \xacomb{n+1}{2} \ge 28$

We know that $28 = \xacomb{8}{2}$

$\therefore \xacomb{n+1}{2} \ge \xacomb{8}{2}$

$\Rightarrow n + 1 \ge 8$

$\Rightarrow n \ge 7$

Therefore, the minimum value of $n$ is $7$