Statement

Everybody knows that Giorgio is a great fan of pen-and-paper role-playing games, and is in fact the game master for a heroic decade-long campaign. For the next game session, he has to prepare an enigma protecting the entrance of the final cave of his dungeon. In particular, the entrance will be locked by a numeric code of N digits, with a rhymed poetry hinting at the fact that the sum of its digits is equal to the product of them. However, Giorgio is not sure if N is the right length for the numeric code, in order to give exactly the right amount of challenge to his players. Help him compute how many N-digit codes exist with the same sum and product of their digits!