28.214 On the back of 2005 cards, 2005 different real numbers are written. Each time a question is asked, you can point to any three cards and ask about the set of three numbers written on them. How many times at least must you ask to be sure to know what numbers are written on the back of each card?

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Parse at least 1003 questions.
Assume that $N$ questions have already been asked. Clearly, each card should participate in at least one question, otherwise it would be impossible to determine the number on that card. Suppose that $k$ cards each participate in exactly one question. Then, in the same question, it is impossible to encounter two such cards. In fact, if two such cards participate in the same question, then if the numbers written on these two cards are swapped, the answer we receive would not change at all, thus making it impossible to determine which number is written on each card. Therefore, $k \leqslant N$. The remaining cards each participate in at least two questions. If we sum up the number of questions each card participates in, then we have $3N \geqslant k + 2(2005 - k) = 4010 - k \geqslant 4010 - N$, which means $2N \geqslant 2005$, and thus $N \geqslant 1003$.

Next, we will explain how to achieve the goal with 1003 questions. Remove one card and divide the remaining cards into 344 groups, each containing 6 cards. Number the cards in each group from 1 to 6, and ask three questions for each group: $(1,2,3)$, $(3,4,5)$, and $(5,6,1)$. In this way, in each group, the cards numbered $1, 3, 5$ each appear in two questions, so they can be uniquely determined; while the numbers written on the cards numbered $2, 4, 6$ each appear in one question. Thus, through $\frac{2004}{6} \times 3 = 1002$ questions, we can determine the numbers on 2004 cards. The remaining one question is used to determine the number on the card that was set aside (just ask it together with any other two cards once).