During Genshin Impact's Summertime Odyssey event from July 15, 2022, to August 24, 2022, you can loot hundreds of Chests hidden across the Golden Apple Archipelago. Making the right changes to each island's topography will merit you even more Chests—including one Common Chest and three Precious Chests underneath the Broken Isle.
Prerequisite for the Precious Chest puzzle under the Broken Isle in Genshin Impact
Before you can unlock this puzzle, you first need to unlock The Islands' Stirring Strings Waypoint by completing Xinyan's Blazin' Trails! World Quest. Once that's done, you need to complete two Pyro torch puzzles (which lead to a hidden Phantasmal Conch). While solving the Pyro torch puzzle, it's important to make sure that you interact with the switch to open the gate beside the last Pyro torch, as that will serve as the entryway for the Precious Chest puzzle.
How to solve the underground Precious Chest puzzle in the Broken Isle in Genshin Impact
Start by heading to Xinyan's island north of the Broken Isle and interact with the drum to Change Mountain Style. Look to your left and make sure that you see a tall mountain. Once that's done, head to the area circled in the image above to find a cave entrance.
Enter the cave and go through the door. You will be back to the location of the previous Pyro torch puzzle, but the placement of the plantation inside the cave will be slightly different. This small change will allow you to solve the puzzle to claim the Chests.
Assuming that the Melodic Harp is behind you, rotate the Melodic Bloom circled in the image above once so that it's facing the Melodic Bloom at the center of the platform. Play the Melodic Harp. This will unlock the Common Chest at the center (not pictured above). After looting the Common Chest, play the Melodic Harp again. The barrier blocking the three Precious Chests at the edge of the room will disperse, allowing you to claim the loot.
Keep in mind that if you have the short mountain style, you won't be able to break the barrier blocking the Precious Chests. So make sure to switch to the tall style before coming! Apart from a ton of Primogems, you'll also get a Serenitea Pot Furnishing called Allegro Bloom: Special Tuning.
Check out our guide on Where to find the hidden Phantasmal Conch (Misplaced Conch 3) in Twinning Isle in Genshin Impact to unlock more hidden objectives in the Golden Apple Archipelago.