Question 119
There are some cards with positive integers on them, and the sum of these integers is $2007$. For any integer $1 \le k \le 2006$ we can choose some cards so that the sum of the numbers written on those cards is $k$, and there is only one way (if cards with the same number are considered to be the same) to do so for each $k$. How many kinds of such a set of cards are possible?