Nice game! I think I found an alternate solution for the exam puzzle:
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Everything is the same except the island location and the lines:
32 days ago(+1)
Looking at this again this is a valid alternate solution, nice job. Idk why I didn't see it earlier. However, as it has the same underlying numbers as the intended solution, it doesn't break the puzzle. I'd still prefer if the exam had a fully unique solution but I'm happy leaving this alternate in.