Blue eyes: logic puzzle

about one or two weeks back, while scrolling through XKCD comics I have bumped into Blue Eyes logic puzzle, that Randall (the author of XKCD) heard in Boston from some random guy named Joel. Randall titles the puzzle as the “hardest logic puzzle”. It was not the case for me so I would title it as “most interesting (and hard) logic puzzle”. Here is why:

I wont rewrite the setup for the puzzle, you can just read the original here.

So now you know what this is about… if you want to solve it yourself (it might take some time) stop reading.

Why I find this puzzle so interesting is that from the first view it does not make any sense, it shouldn’t be solvable. What the sear (the one with green eyes) says shouldn’t make any difference right? Because everybody knows that there is other person with blue eyes, they can see it, yet when everybody hears it, it makes a difference and in the induction that proves the solution, this information is totally crucial.

If you start with less people like one, then two and so on, it becomes way more obvious that what the sear says actually does make a difference.

It took me together about 2 hours to solve the puzzle and I think it is perfect example of something quite simple working in non-intuitive ways and how our brains still have hard time grasping it.