EXPLANATION: imagine there is only 1 person on the island, he will look around and see that there are no blue eyed people, he will then know his eye color in 1 day, if there are two, each will see that there is 1 blue eyed person, of this person doesn't leave on the 1st day, that means that he must also have blue eyes so that the same rules apply to the other man's perspective, following this logic, n= blue eyed people and d= days so d=n because for each person added, one more day is needed to know their own eye color.
No one is allowed to speak or gesture to one another in any way. As more and more people come to see the light, they will start trying to help the rest of the group. 1 thought 2 and 3 needed to leave together, 2 thought 1 and 3 needed to leave together, and 3 thought 1 and 2 needed to leave together. Before the guru speaks, I think it is implied everyone knows that there are 100 + 99 + 1 + ? All the rest of the chain of reasoning is based on "The n blue-eyed people I can see can't deduce it yet, therefore there must actually be n+1 blue-eyed people of which I am one", which all falls apart if, in the n=1 case, it.You're right. Each person is highly devout, and there is no way that any of them would try and cheat this process. Everyone on the island knows all the rules in this paragraph.On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). 4.2 Answers. Every night at midnight, a ferry stops at the island. On day 3, I see 2 people with blue eyes, who are still there.

These candidates are known to be excellent logicians - in fact, the best logicians in the whole kingdom. If there were just one blue-eyed person, she would leave on the first night, so if nobody leaves on the first night, then everybody will know there are at least two blue-eyed people, so there’s no need for the guru to announce this on the second day. The king rejoices and says, "Correct! Header Menu Menu . However, he doesn’t know about their eye-colour superstitions, and opens his speech with “It’s incredible to see one or more people with blue eyes in this part of the world”.The question is - what effect, if any, does his faux pas have on the island?”.Remember that your formulation of the question must:As with all puzzles of any fame, there exist a few other slightly different formulations [0][1], but Terence Tao’s is my favourite and I believe the most precise one.

Since, he knows that at least one person has blue eyes, he must conclude that it is he who has blue eyes. I can't quite put my finger on the difference it makes* but it does seem to be necessary to create a concrete starting point where, if there were only 1 person with blue eyes, they would figure it out. Using the simple brown-blue model (two genes; a brown gene dominates blue gene), what are the chances of my first child having blue eyes. Welcome back to Popular Mechanics' Riddle of the Week. I have found that characterising the people in the explanation as you and your companions makes things easier to visualise. All three candidates can see all 5 hats and their colors as they are placed on the table. Everyone can already see that there are multiple people with blue eyes.All 100 blue-eyed people will kill themselves on day 100 after the speech.Pretend that I am the only person on the island with blue eyes.

There is an island with exactly 201 residents, 100 with blue eyes, 100 with brown eyes, and the island leader (who has green eyes). Leave them below for our users to try and solve.Both of my parents have brown eyes, as do I. ).Day one: 1, 2 and 3 are here. They are all perfect logicians — if a conclusion can be logically deduced, they will do it instantly. Thus, there is a 2/3 chance that I carry a blue gene. I know there are either 99 or 100 blue eyed people on the island. Blue eyes - no one has to kill themselves. I already knew that there were blue-eyed islanders. Then he puts the hats back in the chest where they can't be seen.The king says "these five hats that I have just shown you will be used exclusively for this test.

Do we just have to assume no one has ever made eye contact with a blue eyed person while the entire island was watching?Thanks in advance, sorry If I am making the wrong assumptions or misunderstanding the riddle.Does the riddle hinge on the face that everyone in the village hears the base case at the same time?When the Guru says "I see at least one person with blue eyes" nobody is learning the fact that at least one person has blue eyes. The people without brown eyes cannot figure it out, because as they wait that last day to see whether they had blue eyes or not, everyone with blue eyes leaves.
So my answer would have been everyone guesses they have blue eyes on the first night and 100 of them get off the island on the first night.Your email address will not be published. Nobody leaves.Day three: 1, 2 and 3 are still here. Finally, after what felt like ages to the king, Candidate #1 raises his hand and announces: "I have a white hat." Explanations left as exercise for the reader. New information IS being introduced to the island, and so common sense answer 1 is wrong.Pretend again that I am the only person with blue eyes. (Add references to proof by induction and base cases according to mathematicality of your audience.

If you have never seen the Blue-Eyed Islanders Puzzle before, then hold onto your hats and stand near some sterilised plastic sheeting because your brain is about to explode. I know there are either 98 or 99 blue eyed people on the island. Proof: Or 100 brown, 99 blue, and he could have red eyes.The Guru is allowed to speak once (let’s say at noon), on one day in all their endless years on the island. Interspersed are opportunities to sit back and watch in smug satisfaction as the minds of your dining companions are mangled more and more with every second they spend in your island world.If you want to completely obliterate someone’s standing in your group (for example a rival alpha male or a romantic enemy), try and tempt them into venturing another, infinitely inferior brainteaser that you can use as a segue into stomping them mercilessly into the ground. Feel free to use content on this page for your website or blog, we only ask that you reference content back to us.


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