Thank you for accepting my work as an 'Honorable Mention'. Although no good ideas occurred to me on first seeing the problem, I am glad I did not give up at that point.
As for the algorithm, I settled on a simple one, where the cards are arranged heuristically, and a search is made for better answers by exchanging pairs of cards. I feel that there must be a more systematic way to solve the problem, so I am thinking of trying again.