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>
       
 
       
unsigned long long search(unsigned int cards, unsigned int rooms)
       
{
       
  // need one card to exit the right-most room
       
  unsigned long long need = 1;
       
 
       
  // I need one card to enter the next room and one to come back, thus I can transport "cards - 2" to the next room in one step
       
  const auto Transport = cards - (1 + 1); // these 2 cards are "wasted"
       
 
       
  // compute in each room how many cards I need to exit, beginning with the right-most room
       
  for (auto currentRoom = rooms; currentRoom > 0; currentRoom--)
       
  {
       
    // how many cards are required to satisfy "need", including cards wasted moving forth and back
       
    auto consumed = 0ULL;
       
 
       
#define FAST
       
#ifdef  FAST
       
    // all iterations of the following "while"-loop are basically the same, let's process them quickly
       
    if (need >= cards)
       
    {
       
      // determine number of iterations
       
      auto moves = (need - cards) / Transport;
       
 
       
      // do I need one more to ensure need < cards at the end ?
       
      if (need - moves * Transport >= cards)
       
        moves++;
       
 
       
      // compute all iterations at once
       
      need     -= moves * Transport;
       
      consumed += moves * cards;
       
    }
       
#else
       
    // the basic algorithm becomes slow if needing many cards and Transport is small
       
    while (need >= cards)
       
    {
       
      need     -= Transport;
       
      consumed += cards;
       
    }
       
#endif
       
 
       
    // carry the remaining cards in the last move, including a card to enter the next room
       
    auto previous = need + consumed + 1;
       
    // ... and continue with the previous room (the one on the left side of the current room)
       
    need = previous;
       
  }
       
 
       
  return need;
       
}
       
 
       
int main()
       
{
       
  unsigned int rooms = 30;
       
  unsigned int cards = 40;
       
  std::cin >> rooms >> cards;
       
 
       
  unsigned long long result = 0;
       
  for (unsigned int i = 3; i <= cards; i++)
       
    result += search(i, rooms);
       
 
       
  std::cout << result << std::endl;
       
  return 0;
       
}

This solution contains 11 empty lines, 11 comments and 5 preprocessor commands.