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Trophy symbol - corresponds to the trophy cup for collecting event items (Museum | Achievements tab)
Check mark - corresponds to finishing all quests in the main event story line
Chest symbol - corresponds to the event treasure (Museum | Treasures tab)
If the Chest still indicates it is incomplete, go to the Museum. Choose the Treasures tab, then click on the 8th Birthday "MegaCake." It may be darkened because it is incomplete. The next pop-up will show you which pieces you do not have. You can click on an individual piece, and it will tell you the location name where you can find it.