Chef and Card Game

Chef is playing a card game with his friend Morty Smith. The rules of the game are as follows: - There are two piles of cards, pile $A$ and pile $B$, each with $N$ cards in it. Pile $A$ belongs to Chef and pile $B$ belongs to Morty. - Each card has one positive integer on it - The ‘power’ of a card is defined as the sum of digits of the integer on that card - The game consists of $N$ r