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>
       
 
       
// return the unique n-digit number with a predefined last digit
       
// which after multiplication with a multiplier is a right-rotation of itself
       
// return only that value modulo some power-of-10
       
// if there is no such number, then return 0

       
unsigned int search(unsigned int numDigits, unsigned int multiplier, unsigned int lastDigit, unsigned int modulo)
       
{
       
  // will be 10, 100, 1000, 10000, ...
       
  unsigned int shift = 10;
       
  // first digit of last iteration
       
  unsigned int carry =  0;
       
 
       
  // set last digit
       
  unsigned int current = lastDigit;
       
  unsigned int result  = lastDigit;
       
 
       
  while (--numDigits)
       
  {
       
    // process next digit
       
    auto next = multiplier * current + carry;
       
    // "next" has at most two digits, carry over the first digit to next iteration
       
    carry     = next / 10;
       
    // and its second digit becomes part of "result"
       
    current   = next % 10;
       
 
       
    // current digit relevant for result ?
       
    if (shift < modulo)
       
    {
       
      result += current * shift;
       
      shift  *= 10;
       
    }
       
  }
       
 
       
  // left-most digit
       
  auto first = multiplier * current + carry;
       
  // failed ? (no leading zero, product's first digit must match last digit of factor)
       
  if (current == 0 || first != lastDigit)
       
    return 0;
       
 
       
  return result;
       
}
       
 
       
int main()
       
{
       
  unsigned int maxDigits = 100;
       
  std::cin >> maxDigits;
       
 
       
  // last five digits
       
  const unsigned int Modulo = 100000;
       
 
       
  unsigned int result = 0;
       
  // from 2 to 100 digits
       
  for (unsigned int numDigits = 2; numDigits <= maxDigits; numDigits++)
       
    // each multiplier between 1 and 9
       
    for (unsigned int multiplier = 1; multiplier <= 9; multiplier++)
       
      // last digit can't be zero, therefore 1 to 9 only
       
      for (unsigned int lastDigit = 1; lastDigit <= 9; lastDigit++)
       
        result += search(numDigits, multiplier, lastDigit, Modulo);
       
 
       
  std::cout << result % Modulo << std::endl;
       
  return 0;
       
}

This solution contains 10 empty lines, 17 comments and 1 preprocessor command.