Behind one of the secure doorways outside the mansion in Blue Prince is the Gemstone Cavern that will give you two Gems a day. To unlock it though you'll need to solve a puzzle related to a colored sequence.
In this guide to unlock the Gemstone Cavern in Blue Prince we'll give you the solution hint by hint, so if you're looking for a nudge in the correct direction but not the solution be sure to scroll down this guide slowly.
Gemstone Cavern Hints
The first hint is that unlocking the Gemstone Cavern has to do with the colored lights on the panel in the Utility Room. You might also be aware of this as the V.A.C System lights.
The second hint is that there's ways to get colors in additional to the light being off, green, and red. You can learn more about how to trigger additional colors by visiting the Mail Room.
In order to unlock the Gemstone Cavern you need to have the lights all set in a specific way. More information can be found about this in the emails of the Office computer.

The solution to this puzzle is that you need to have the sequence of lights on the Utility Box set to OFF - BLUE - GREEN - WHITE - RED - PURPLE. You can do this by selecting the lights in the following order
Once you've entered in the code correctly the room will expand giving you access to a large switch. Flipping this switch will open the door to the Gemstone Cavern. Once in the Gemstone Cavern look for a valve tied to another secret of the Mt. Holly exterior.