Here's what you're missing: The smurfs trust their king completly. If the king asked them to do somthing, it means that something can be done!

Besides the other approach in my reply to Christof, here's another one:

1. How many reds should be so the problem can be solved in the 1st day. Solution: one. This situation is almost obvious. If it's not solved in the 1st day, there are at least 2 reds.
2. How many reds should be, etc. Solution: 2. If not solved, there are at least 3 reds.
3. Etc.

Vlad


>Agree with everything you say. Having read all the replies I too have
>been wondering if I'd missed something !
>
>Michel.
>
>====================== Original message follows ====================
>
>>Hi Vlad,
>>
>>>You use the info from the previous days to distinguish. The inductive method works.
>>
>>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