9.3. There are 2004 small boxes on the table, each containing 1 ball. It is known that some of the balls are white, and there are an even number of white balls. You are allowed to point to any 2 boxes and ask: "Do they contain at least 1 white ball?" How many times do you need to ask, at a minimum, to determine 2 boxes that both contain white balls?

将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。
9.3. 4005.

We will number the boxes (and the balls inside them) from 1 to 2004, and refer to the problems by the numbers of the box pairs. We will call all non-white balls black balls.

First, we prove that 2 white balls can be found with 4005 questions. We ask the questions $(1,2),(1,3), \cdots,(1,2004)$, $(2,3),(2,4), \cdots,(2,2004)$. If all the answers are affirmative, then balls 1 and 2 are white (in fact, if ball 1 is black, then at least one more black ball can be found, which forms a black ball pair with ball 1). If at least one of the answers is negative (let's assume it is a question involving ball 1), then ball 1 is black. In this case, the other ball in the questions that include ball 1 and yield an affirmative answer must be white. Thus, we have found all the white balls, and there are at least 2.

Second, we prove that fewer than 4005 questions cannot suffice. Suppose there exists a strategy that ensures finding 2 white balls with fewer questions. We can give affirmative answers to all the questions. In this case, after at most 4004 questions, we must identify 2 balls (for definiteness, let's say the 1st and 2nd balls) and assert that they are both white. At this point, there must be a question of the form $(1, n)$ or $(2, n)$ that has not been asked, for example, the question $(1, k)$, otherwise, 4005 questions would be needed. If we place black balls in the 1st and $k$-th boxes and white balls in all the other boxes, then all the answers we gave are correct. However, the first ball identified by the player is black, which is a contradiction.