Int32 CentreOfGravity(int[] arr) {

    // get "total mass" of input:
    Int32 total = 0;
    for(int i = 0; i < arr.Length; i++ ) total += arr[i]; // or just arr.Sum( e => e ); if using Linq

    // Work from left-to-right such that Min( Mass(left) - Mass(right) ) is found:
    Int32 left = 0;
    Int32 minDelta = Int32.MaxValue;
    Int32 minDeltaIdx = -1;
    for(int i = 0; i < arr.Length; i++ ) {

        left += arr[i];

        Int32 delta = left - (total - left);
        if( delta < minDelta ) {
            minDelta = delta;
            minDeltaIdx = i;
        }
    }

    return minDeltaIdx;
}