Question

I have solved the project Euler problem 16 but discovered this rather novel approach but I cannot get my head around the technique employed (from http://www.mathblog.dk/project-euler-16/):

int result = 0;

BigInteger number = BigInteger.Pow(2, 1000);

while (number > 0) {
    result += (int) (number % 10);
    number /= 10;
}

My version seems more conventional but I think the above approach is cooler.

var result = BigInteger
    .Pow(2, 1000)
    .ToString()
    .Aggregate(0, (total, next) => total + (int) Char.GetNumericValue(next));

How does the mathematics work on the first approach, it is cool, but I need some explanation to help me understand, so if someone would be so kind to explain to me I would really appreciate it.

NOTE: If I have posted in the wrong section please let me know the better place to ask.

Answer 1

value % 10 will return the last digit (remainder after dividing by 10). Dividing the integer by 10 will remove this number.

Think of the number as a list, and you’re just dequeuing the list and summing the values.