Cards for Dice

Nine cards can be numbered, so that the sum of the numbers on a randomly chosen pair of cards gives an integer from 2 to 12 with the same frequency of occurence as rolling that sum on two standard dice. What are the numbers on the nine cards? Are there multiple solutions?

Are there other sets of cards that give the same results? In a previous POTW (Alternat ive Dice), we showed that we can use multiple sets and choose 1 card from each set (by rolling dice). Are there any other solutions in which we choose multiple cards from the set(s), as in the above question?

Source: Based on a puzzle from the USA Mathematical Talent Search.

Solutions were received from several people. The 9 cards are: 1/2, 3/2, 5/2, 5/2, 7/2, 9/2, 9/2, 11/2, 13/2. Nick Baxter showed this is unique.

For the second question, one answer, choosing 2 cards each from the sets (0,1,2,4)(0,1,2,4) will have the same result as rolling 2 dice.

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