Things You'll Need
Instructions
Go to Pacificlog town.
Visit the house on the bottom right.
Talk to the old man staring out of the window. Each pokemon on your team has an assigned ID number, as does Mirage Island. If one of your pokemon's ID number matches that of Mirage Island, the old man will tell you he sees the island. If none of the ID numbers match, the old man will tell you he doesn't see the island.
Surf to Mirage Island on Route 130, if the old man states that he can see it.
Go to a pokemon center and insert some of your pokemon into the computer. Each time you do, your pokemon will receive new ID numbers. Take the pokemon out and return to the old man to see if the numbers match with Mirage Island. This can be tedious, but well worth it when you finally acquire the Liechi berry that is present there.