The winning ID number changes daily, and the game looks for matches by examining the IDs of all Pokémon in the player's party and in all PC boxes (but not Pokémon in the Day Care).
In Pokémon Diamond and Pearl, the player may only check for matches once a day, and this occurs at the same time that they are told what the winning ID is.
This is changed in Pokémon Platinum so that the player may check for matches multiple times in one day; however, after winning a prize, they may not participate again for the rest of the day.
So, it depends on how many Pokemon you have from different people. Start Trading!!!