# Maximum number of line intersections formed through intersection of N planes

Given N planes. The task is to find the maximum number of line intersections that can be formed through the intersections of N planes.**Examples:**

Input:N = 3Output:3Input:N = 5Output:10

**Approach:**

Let there be N planes such that no 3 planes intersect in a single line of intersection and no 2 planes are parallel to each other. Adding ‘N+1’th plane to this space should be possible while retaining the above two conditions. In that case, this plane would intersect each of the N planes in ‘N’ distinct lines.

Thus, the ‘N+1’th plane could atmost add ‘N’ new lines to the total count of lines of intersection. Similarly, the Nth plane could add at most “N-1′ distinct lines of intersection. It is easy therefore to see that, for ‘N’ planes, the maximum number of lines of intersection could be:

(N-1) + (N-2) +...+ 1 = N*(N-1)/2

Below is the implementation of the above approach:

## C++

`// C++ implementation of the above pproach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to count maximum number of` `// intersections possible` `int` `countIntersections(` `int` `n)` `{` ` ` `return` `n * (n - 1) / 2;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 3;` ` ` `cout << countIntersections(n);` ` ` `return` `0;` `}` |

## Java

`// Java implementation of the approach` `class` `GFG` `{` ` ` ` ` `// Function to count maximum number of` ` ` `// intersections possible` ` ` `static` `int` `countIntersections(` `int` `n)` ` ` `{` ` ` `return` `n * (n - ` `1` `) / ` `2` `;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `int` `n = ` `3` `;` ` ` ` ` `System.out.println(countIntersections(n));` ` ` `}` `}` `// This code is contributed by AnkitRai01` |

## Python3

`# Python3 implementation of the above pproach` `# Function to count maximum number of` `# intersections possible` `def` `countIntersections(n):` ` ` `return` `n ` `*` `(n ` `-` `1` `) ` `/` `/` `2` `# Driver Code` `n ` `=` `3` `print` `(countIntersections(n))` `# This code is contributed by mohit kumar` |

## C#

`// C# implementation of the approach` `using` `System;` `class` `GFG` `{` ` ` ` ` `// Function to count maximum number of` ` ` `// intersections possible` ` ` `static` `int` `countIntersections(` `int` `n)` ` ` `{` ` ` `return` `n * (n - 1) / 2;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `Main (String[] args)` ` ` `{` ` ` `int` `n = 3;` ` ` ` ` `Console.WriteLine(countIntersections(n));` ` ` `}` `}` `// This code is contributed by 29AjayKumar` |

## Javascript

`<script>` `// Javascript implementation of the above approach` `// Function to count maximum number of` `// intersections possible` `function` `countIntersections(n)` `{` ` ` `return` `n * (n - 1) / 2;` `}` `// Driver Code` `var` `n = 3;` `document.write(countIntersections(n));` `</script>` |

**Output:**

3

**Time Complexity:** O(1)

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