039.js

// 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 maximised?

function findTriplets(sum) {
    var triplets = [];
    var max = Math.ceil( sum/2 );
    var a, b, c;
    for (a = 3; a < max; a++) {
        for (b = a+1; b < max; b++) {
            if (Math.pow(sum-b-a, 2) === (Math.pow(a, 2) + Math.pow(b, 2))) {
                triplets.push( [a, b, sum-b-a] );
            }
        }
    }
    return triplets;
}

function tripletsMax(max) {
    var p, number, maxNumber = 0;
    for (var i = 12; i <= max; i++) {
        number = findTriplets(i).length;
        if (number > maxNumber) {
            maxNumber = number;
            p = i;
        }
    }
    return p;
}

console.log( tripletsMax(1000) );