# Project Euler

## Integer right triangles

### Problem 39

If *p* is the perimeter of a right angle triangle with integral length sides, {*a*,*b*,*c*}, there are exactly three solutions for *p* = 120.

{20,48,52}, {24,45,51}, {30,40,50}

For which value of *p* ≤ 1000, is the number of solutions maximized?

Again, the larger the number, the number of solutions should also increase in general. Therefore, we’ll start will the maximum number ( *p* ≤ 1000) and count backward.

We can cut the search space smaller by recognize the following triangle with a, b, c.

Therefore, search a between 1 to and search b between a+1 to in a nested loop to ensure no repeat combination of a and b. Then, increment the number of solution for a specific c by solving c base on a and b using the equations from above. Since p ≤ 1000, then c ≤ 998. At the end, find the c with the most solution.