That's the beautiful part of the problem. Apparently, there's no info gain from one day to another. So, apparently, there's no way to solve the problem in the 2nd day if it was not solved in the 1st day, and so on.

Somebody already explained the induction inference for this problem in a previous message.

The problem can be "thought" like this:

1. The smurfs solve the problem in the first day. This means there's one red because the red one sees that everyone else has green, so... But they don't solve it in the first day, so, there are at least 2 reds. (Now, the info gain/change is almost obvious, isn't it?)
2. The smurfs solve it in the second day. This means there are 2 reds because there are at least 2 and the red ones can see that there are at most 2, etc. But they don't solve it in the 2nd day, so, there are at least 3.
3. So on and on...

I belive this is the most beautiful problem of this type I have ever heard. It's true that I heard it for the first time about 20 years ago... :)

The 2nd wonderful part of the problem (IMHO) is that each smurf trusts completly all remaining smurfs that each of them will think the best rekoning. That's a real team spirit! :)

I may have switched the colors in the above. This is good if the king asked the reds to come to the meeting place.

Vlad

>Then I must have misread the original question. If I use information from the previous day, those information must be different from todays information, otherwise I've an infinite loop. And this requires that the number of green or red smurfs decreases over the time. But since for every green smurf the situation is the same, no-one can start saying "I'm a green smurf". WHat did I miss?
>
>Christof