To explain we will take an Island of 4 instead of 100, it's Melody, Eton, Fredy, and MC.
Thinking as Melody:
There are only two options. Either we all have green eyes or only I have blue eyes.
I, Melody am going to *imagine* that out of four of us, I do have blue eyes.
If I have blue eyes, then Eton knows that I have blue eyes and Fredy and MC have Green eyes. In this case, Eton is trying to determine whether only him and I have blue eyes / only Fredy and MC have green eyes, or only I have blue eyes and Fredy, MC, and Eton himself have green eyes.
Eton also knows that I know Fredy and MC can see me (with my blue eyes), so I know Eton is considering:
"if both Melody and I have blue eyes and MC and Fredy have Green eyes, then MC is trying to figure out whether just Fredy has green eyes, or both her and Fredy have Green eyes while Mel and I have blue eyes. In a case where MC is imagining she has blue eyes, like both Mel and I, (Eton) she is going to watch to see what Fredy does tonight, for if the three of did have blue eyes then Fredy will leave, knowing he must have green eyes.
(The next day)
Fredy is still here. Therefore, if I (Eton) actually do have blue eyes like Mel, then MC will leave tonight."
The alternate applies between MC and Fredy.
(The next day)
MC is also still here.
Melody: "That means in this case where I have blue eyes, Eton must know he does not have blue eyes, and will leave tonight."
(The next day)
Because Eton did not leave, Melody knows she must not have blue eyes, and therefore her eyes are green.
Published Jan 8, 2025
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