"Did you just...." present or past tense?

Consider the following two statements, and the tenses.

• Did you win?
• You just won.

But what about *Did you just __ a camera*? Would it be followed by win or won?

Did you win? is asking about the past. It is the past tense of do. Rearranging the words yields you did win, which is, essentially, you won. There is no need for a double of the past tense (you did won).

You just won is the same as the above, with the simple addition of a slight modifier, just.

Did you just win a camera? Rearranging the words: You did just win a camera = (remember, there is no need for a double past tense) you just won a camera.

Did you just won is two simple past tenses. There is no construction with did such as this in English. The correct construction is in the bold above.