Suppose X is one, then the brown eyed person appears to be stuckYes, the problem specifically doesn't work if the number of people with an eye colour is below a certain amount.
The case for X>2 seems similar to the case for X=2, there's no magical point at which they can suddenly all say
In a scenario where there is, say, just brown and green (regardless of whether they know this or not), then X>3 is enough.
Where X=3 or less there is not enough information to go on (you successfully point out the flaws) and they could conceivably be any other eye colour. But above that you know it is impossible for there to be an individual who can see only one or two browns, therefore it can be inferred properly.
One of the main problems comes from the explanation of the issue which involves the suggestion that you recurse the problem back to X=1, this is inaccurate because there is always a known absolute minimum people that could have brown eyes (n, the brown eyed people you can see) and a known minimum number that any one person could see (n - 1). So long as for a brown eyed person (n - 1) > 2 the the inference is possible.
Remember; it does not matter what alternative eye colour they might be (and whether they can see it or not). Only that they are either brown or not brown. The logical inference is based on what the others must be seeing.
Try jotting it down and then reasoning it out as an individual in the tribe. Once it clicks it will seem simple :)
Yes, the problem specifically doesn't work if the number of people with an eye colour is below a certain amount.
The case for X>2 seems similar to the case for X=2, there's no magical point at which they can suddenly all say
In a scenario where there is, say, just brown and green (regardless of whether they know this or not), then X>3 is enough.
Where X=3 or less there is not enough information to go on (you successfully point out the flaws) and they could conceivably be any other eye colour. But above that you know it is impossible for there to be an individual who can see only one or two browns, therefore it can be inferred properly.
One of the main problems comes from the explanation of the issue which involves the suggestion that you recurse the problem back to X=1, this is inaccurate because there is always a known absolute minimum people that could have brown eyes (n, the brown eyed people you can see) and a known minimum number that any one person could see (n - 1). So long as for a brown eyed person (n - 1) > 2 the the inference is possible.
Remember; it does not matter what alternative eye colour they might be (and whether they can see it or not). Only that they are either brown or not brown. The logical inference is based on what the others must be seeing.
Try jotting it down and then reasoning it out as an individual in the tribe. Once it clicks it will seem simple :)