Project Euler 91: Right triangles with integer coordinates

Project Euler 91 Problem Description

Project Euler 91: The points P (x₁, y₁) and Q (x₂, y₂) are plotted at integer co-ordinates and are joined to the origin, O(0,0), to form ΔOPQ.

There are exactly fourteen triangles containing a right angle that can be formed when each co-ordinate lies between 0 and 2 inclusive; that is,
0 ≤ x₁, y₁, x₂, y₂ ≤ 2.

Given that 0 ≤ x₁, y₁, x₂, y₂ ≤ 50, how many right triangles can be formed?

Analysis

There is a hyper series here…somewhere.
Data Table 1. Number of triangles from 0 ≤ x₁, y₁, x₂, y₂ ≤ {1..10}.

Now, we can remove 3n² known triangles that have an edge on either axis.

Data Table 2. Number of triangles as above but with 3n² contributing to sum

Data Table 3. Number of triangles as above but with N²/2 contributing to sum

Well, brute force until I figure out the series, which seems trivial but so far elusive. Still, good enough for even a more challenging problem set from HackerRank.

This program and method
solves all test cases
on HackerRank

Project Euler 91 Solution

Afterthoughts

No afterthoughts yet.