IT-CESENATICO 2006 Problem 1

Two people play the following game: there are $40$ cards numbered from $1$ to $10$ with $4$ different signs. At the beginning they are given $20$ cards each. Each turn one player either puts a card on the table or removes some cards from the table, whose sum is $15$ . At the end of the game, one player has a $5$ and a $3$ in his hand, on the table there's a $9$ , the other player has a card in his hand. What is it's value?