Ah, Intuition takes me there
Intuition takes me everywhere
Not exactly everywhere. But whatever, there’s a problem in this post, and to avoid me spoiling the solution with my continuous babbling, I would suggest that you skip directly to the part called “The problem” below.
Here I continue my discussion from this post regarding logic, the downfalls of intuition, and the benefits of looking at the boundary solutions for a given problem (or the small cases, if you prefer to call them that way in this context). This time, it seems, the problem under investigation is a bit harder.
I. The problem
So, there’s an island, and there are people on it: 100 of them have blue eyes, 100 have brown eyes, and one has green eyes. Nobody knows the color of their own eyes or the distribution of eye colors on the island. Every night at midnight, a ship comes to the island and takes away all the people who know for sure the color of their eyes. Everyone wants to find out the color of their own eyes and get away from the island. People on the island are not allowed to communicate in any way, and can’t use silly tricks like looking at their reflections in the water. They can only look at each other, and in particular a person with blue eyes will observe 99 people with blue eyes, 100 people with brown eyes and 1 person with green eyes.
Finally, and as usual, all the people on the island are wise men/women, and if there is some logical argument that can be made, they make it instantaneously.
The only thing that happens on the island for all eternity (I know, I’m breaking the law of non-communication here, but that’s the only violation) is that one day at noon, the green-eyed person gathers all the other 200 people so that they can all see each other and says, “I can see a person with blue eyes.” All the other people know he’s telling the truth : ) (after all, these are decent wise people).
The question is the following: who is going to leave the island, and when?
Now think about it (while listening to this, perhaps? : ) )
The dominating feeling people get from this problem is confusion. Many bring up the following argument: “What difference does it make that the green-eyed person says so and so? They can all see that there are people with blue eyes!” and then try to extract something more from the statement of the problem by asking questions about it. But it tells you everything you need to know, and there are no tricks involved: the solution is a logical argument. Of about twenty people, three managed to get to the answer. And getting to the answer seems to be the easier part – proving it rigorously and making sense of it on a more intuitive level is actually harder.
But I feel that the real issue here is not that people are unable to solve the problem – rather, they refuse to approach it, especially after they get confused by the fact that the words of the green-eyed person seemingly “don’t provide any new information”, whatever that means. It’s as if they close their minds, even though I tell them that there is a logical argument in support of the claim that his words actually change something. It’s just so counter-intuitive.
Another reason for not really thinking about the problem seems to be low self-confidence when it comes to logic puzzles (and this problem of low self-confidence applies to all of us in many other contexts …). People say things like, “I’m terrible at such problems!”, or “I’m not that smart, I can’t solve it!”, etc. I find this attitude really harmful! After thinking about this for a while, it seems to me that this is such a bad (and sort of ironic) misunderstanding. It does take intelligence to solve this problem – but I believe that what demonstrates intelligence even more is the way you approach it. Even if you can’t solve it, if you continue to think hard about it you surely increase your chances – that’s sort of obvious, right? And thinking hard is always good – in fact, it is the best way to increase your intelligence. So… it might seem strange, but the quality of not giving up and working towards improving your current situation seems to be a premise – and thus, later in your life, a sign – for being smart; and given the fact that people can often achieve more than they think, increased self-confidence seems to be one other such sign : ) But enough with the psychology stuff for today.
This puzzle is shamelessly advertised as “The hardest logic puzzle in the world” here at xkcd. Their (his) explanation of the parts that are hardest to grasp was sort of “OK, see – I’m right!” and a bit unsatisfactory – indeed, it’s hard to discuss it in depth (and I’m not sure if I can provide a more insightful explanation, but I’ll try).
A discussion on the answer will follow in a subsequent blog post : )