My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too. Or just jump to my GitHub repository.

       
#include <iostream>
       
#include <set>
       
#include <cmath>
       
 
       
// a square is described by its lower left corner (x,y) and its index along x and y axis

       
struct Square
       
{
       
  Square(double x_, double y_, unsigned int left_, unsigned int below_)
       
  : x(x_), y(y_), left(left_), below(below_)
       
  {
       
    setSideLength();
       
  }
       
 
       
  // lower-left corner
       
  double x;
       
  double y;
       
  // number of squares on the left side
       
  unsigned int left;
       
  // number of squares below
       
  unsigned int below;
       
 
       
  // length of a side
       
  double side;
       
 
       
  // note: sort in reverse, therefore return true if it's the larger (!) value
       
  bool operator<(const Square& other) const
       
  {
       
    return side > other.side;
       
  }
       
 
       
private:
       
  // find length of edges of the largest square whose lower-left corner is at x,y
       
  void setSideLength()
       
  {
       
    // see my explanations above
       
    side = 0.5 * (sqrt((x - y) * (x - y) + 4) - x - y);
       
  }
       
};
       
 
       
int main()
       
{
       
  unsigned int indexLeft  = 3;
       
  unsigned int indexBelow = 3;
       
  std::cin >> indexLeft >> indexBelow;
       
 
       
  // square's number
       
  unsigned int result     = 0;
       
 
       
  // create first square with lower-left corner at (1,0) and no other squares on its left or bottom side
       
  std::set<Square> todo = { Square(1, 0, 0, 0) };
       
  unsigned int candidates = 1; // => the first square is left of and below all other squares
       
  while (candidates > 0)
       
  {
       
    result++;
       
 
       
    // pick first (= largest) square
       
    auto current = *(todo.begin());
       
    // and remove it
       
    todo.erase(todo.begin());
       
 
       
    // create a new square on top of the current square
       
    Square top  (current.x,    current.y + current.side,
       
                 current.left, current.below + 1);
       
    todo.insert(top);
       
    // and a square on the right side
       
    Square right(current.x + current.side, current.y,
       
                 current.left + 1, current.below);
       
    todo.insert(right);
       
 
       
    // count how many squares could be on the left or bottom side of a square with index (3, 3)
       
    if (top    .left <= indexLeft && top    .below <= indexBelow)
       
      candidates++;
       
    if (right  .left <= indexLeft && right  .below <= indexBelow)
       
      candidates++;
       
    if (current.left <= indexLeft && current.below <= indexBelow)
       
      candidates--;
       
  }
       
 
       
  // show ID of last square with index (3, 3)
       
  std::cout << result << std::endl;
       
  return 0;
       
}

This solution contains 12 empty lines, 16 comments and 3 preprocessor commands.