Project Euler

Problem

6

What is the difference between the sum of the squares and the square of the sums?

The sum of the squares of the first ten natural numbers is 1² + 2² + … + 10² = 385

The square of the sum of the first ten natural numbers is (1 + 2 + … + 10)² = 55² = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Solution

function difference(limit) {
    function squareSum(limit) {
        var i, s = 1,
            e = Math.log(limit) / Math.LN10;
        // special case: limit is a power of 10
        if (e - (e << 0) === 0) {
            s = limit * (limit >> 1) + (limit >> 1);
        }
        else {
            for (i = 2; i <= limit; i += 1) {
                s += i;
            }
        }
        return s * s;
    }

    function sumSquare(limit) {
        var i, s = 1;
        for (i = 2; i <= limit; i += 1) {
            s += i * i;
        }
        return s;
    }

    return squareSum(limit) - sumSquare(limit);
}

console.log(difference(100));