During Chapter 11, you will find yourself coming face to face with a wheel of sorts that will have the pirate captains' sigils on them. Your goal is to turn these plaques with the sigils on them a certain way, so that the stars adorning the sides of them will line up with one another. There will be a total of four sets, but the problem lies with that only the first set will actually have the stars on them.
After solving each set, a door will open up, allowing you to reach a room with paintings of the captains. You will need to find a square pattern on each painting that shows the stars, after which, you can play around with the papers inside your journal to find out the correct alignment. This will work with all of the sets, although you will have two unknown entities with the final set, meaning you'll have to play around a bit with those.
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