Imagine an island where 100 people are imprisoned by a dictator. These prisoners are all perfect logicians, meaning they are exceptionally good at reasoning and problem-solving. There’s only one way to escape: a prisoner can approach the guards at night and ask to leave. If they have green eyes, they are set free; if not, they face severe consequences. Interestingly, all 100 prisoners have green eyes, but they have lived on the island since birth and have no way of knowing their own eye color. There are no mirrors or reflective surfaces, and the water containers are opaque. Additionally, they are not allowed to communicate with each other, although they see one another during daily head counts.
Despite these restrictions, the prisoners understand that no one would risk trying to leave without being absolutely certain of their success. After pressure from human rights groups, the dictator allows you to visit the island. You are permitted to make only one statement, and it cannot provide any new information.
After careful thought, you tell the prisoners, “At least one of you has green eyes.” The dictator is suspicious but reassures himself that your statement couldn’t change anything. You leave, and life on the island seems to continue as usual. However, on the hundredth morning after your visit, all the prisoners are gone, each having asked to leave the previous night.
To understand how this happened, let’s consider a simpler scenario with just two prisoners, Adria and Bill. Each sees one person with green eyes, and for all they know, that could be the only one. On the first night, each stays put. But when they see each other still there in the morning, they gain new information. Adria realizes that if Bill had seen a non-green-eyed person, he would have left the first night, concluding that the statement could only refer to himself. Bill simultaneously realizes the same about Adria. The fact that the other person waited tells each prisoner that their own eyes must be green. On the second morning, they both leave.
Now imagine a third prisoner, Carl, who sees Adria and Bill. Each of them sees two green-eyed people but isn’t sure if the others see the same. They wait through the first night, but on the second morning, they still can’t be sure. Carl thinks, “If I have non-green eyes, Adria and Bill would have left on the second night.” When he sees both of them still there on the third morning, he realizes they must have been watching him, too. They all leave on the third night.
This pattern continues regardless of how many prisoners are added. The key concept here is common knowledge. While your statement itself didn’t contain new information, it created a shared understanding among all the prisoners. They now know that at least one of them has green eyes, and they also know that everyone else is aware of the green-eyed people they can see, and so on.
What any given prisoner doesn’t know is whether they themselves are one of the green-eyed individuals until as many nights have passed as the number of prisoners on the island. While you could have provided more specific information to expedite their escape, in situations involving strict authority, it’s often wise to proceed with caution.
Form small groups and discuss the logical steps each prisoner must take to deduce their own eye color. Consider how the concept of common knowledge plays a role in their reasoning. Share your insights with the class, focusing on how the prisoners’ thought processes evolve over time.
Participate in a role-playing exercise where each of you acts as a prisoner on the island. Use props to represent eye colors and simulate the daily head counts. Experience firsthand how the prisoners’ knowledge changes over time and how they eventually reach a conclusion.
Work individually or in pairs to create a mathematical model of the puzzle. Use logical reasoning and set theory to represent the prisoners’ knowledge and the progression of their deductions. Present your model to the class, highlighting key insights and any assumptions made.
Engage in a debate about the ethical implications of the dictator’s rules and your role in the prisoners’ escape. Consider the balance between providing information and respecting the prisoners’ autonomy. Discuss whether there could be alternative solutions to the puzzle.
Write a short story or script that reimagines the ending of the puzzle. Consider different scenarios, such as the introduction of new rules or the presence of an unexpected variable. Share your creative work with the class and discuss how these changes affect the outcome.
Imagine an island where 100 people, all perfect logicians, are imprisoned by a dictator. There’s no escape, except for one unusual rule: any prisoner can approach the guards at night and ask to leave. If they have green eyes, they’ll be released; if not, they’ll face severe consequences. All 100 prisoners have green eyes, but they’ve lived there since birth and cannot learn their own eye color due to the lack of reflective surfaces and opaque water containers. Most importantly, they are not allowed to communicate with each other, although they see one another during daily head counts.
Despite this, they all understand that no one would risk trying to leave without absolute certainty of success. After pressure from human rights groups, the dictator reluctantly allows you to visit the island and speak to the prisoners under strict conditions: you may only make one statement, and you cannot provide any new information.
After careful consideration, you tell the crowd, “At least one of you has green eyes.” The dictator is suspicious but reassures himself that your statement couldn’t change anything. You leave, and life on the island seems to continue as usual. However, on the hundredth morning after your visit, all the prisoners are gone, each having asked to leave the previous night.
To understand how this happened, consider a simpler scenario with just two prisoners, Adria and Bill. Each sees one person with green eyes, and for all they know, that could be the only one. On the first night, each stays put. But when they see each other still there in the morning, they gain new information. Adria realizes that if Bill had seen a non-green-eyed person, he would have left the first night, concluding that the statement could only refer to himself. Bill simultaneously realizes the same about Adria. The fact that the other person waited tells each prisoner that their own eyes must be green. On the second morning, they both leave.
Now imagine a third prisoner, Carl, who sees Adria and Bill. Each of them sees two green-eyed people but isn’t sure if the others see the same. They wait through the first night, but on the second morning, they still can’t be sure. Carl thinks, “If I have non-green eyes, Adria and Bill would have left on the second night.” When he sees both of them still there on the third morning, he realizes they must have been watching him, too. They all leave on the third night.
This pattern continues regardless of how many prisoners are added. The key concept here is common knowledge, which means that while your statement itself didn’t contain new information, it created a shared understanding among all the prisoners. They now know that at least one of them has green eyes, and they also know that everyone else is aware of the green-eyed people they can see, and so on.
What any given prisoner doesn’t know is whether they themselves are one of the green-eyed individuals until as many nights have passed as the number of prisoners on the island. While you could have provided more specific information to expedite their escape, in situations involving strict authority, it’s often wise to proceed with caution.
Logic – The systematic study of the principles of valid inference and correct reasoning. – In his philosophy class, John learned how logic is used to construct sound arguments and identify fallacies.
Reasoning – The action of thinking about something in a logical, sensible way. – Her reasoning was clear and concise, leading to a well-supported conclusion in her essay on ethical dilemmas.
Problem-solving – The process of finding solutions to difficult or complex issues. – The seminar focused on developing critical thinking skills to enhance students’ problem-solving abilities in real-world scenarios.
Knowledge – Facts, information, and skills acquired through experience or education; the theoretical or practical understanding of a subject. – The philosopher emphasized that true knowledge requires both empirical evidence and rational thought.
Understanding – The ability to comprehend or grasp the meaning of something. – Achieving a deep understanding of existentialism requires studying both its historical context and its philosophical implications.
Communication – The imparting or exchanging of information or news. – Effective communication is essential in philosophy to clearly articulate complex ideas and engage in meaningful dialogue.
Certainty – Firm conviction that something is the case. – Descartes sought certainty in knowledge by doubting everything that could possibly be doubted.
Information – Data that is processed or organized in a meaningful way. – The philosopher argued that information alone does not constitute knowledge without critical analysis and interpretation.
Authority – The power or right to give orders, make decisions, and enforce obedience. – In his critique of traditional authority, the philosopher questioned the legitimacy of power structures that suppress individual autonomy.
Escape – The act of breaking free from confinement or control. – The allegory of the cave in Plato’s Republic illustrates the philosopher’s escape from ignorance to enlightenment.
