>>>The king smurf gathered all the smurfs of his land to play a game. 100 smurfs assembled in his great hall and listened attentively to the king. "I will either place a red hat or a green hat on each of your heads. I am relying on your honor. You are not to attempt in any way shape or form to look at your hat or ask others what color your hat is. You must figure it out. One thing. Their must be at least one red had and at least on green hat." He then blindfolded them and randomly picked hats from two sacks until he had placed hats on all of their heads. When he was done he removed their blindfolds.
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>>>He further explained that there were to meet each day at his hall for one hour at noon. At the end of the hour, if they had figured out the color of their hat, they were to announce it to the king and return the hat. They would then not need to return to the hall. "Good luck to you all."
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>>>At the end of the 13th day, a number of smurfs approached the king and all announced they had green hats. The following day the remainder announced they had red hats.
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>>>How many green hats and how many red hats were their and most importantly how did they figure it out?
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>>It´s a nice inductive solution, and here it goes:
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>>If there had been only one green hat, on the first day that smurf, seeing 99 red hats, would have known his hat was green. Since it didn´t happen, there were at least 2 green hats.
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>>If there had been only two green hats, on the second day the green hat smurfs, seeing 98 red ones and 1 green (and reasoning that there had to be at least 2 green hats as seen previously) would have known that they had green hats. Since it didn't happen, there were at least 3 green hats.
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>>Do I need to go on?
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>>Nice problem!
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>Okay I will be the stupid one to ask the dumb question. Why couldn't it have been 13 red hats and 87 green hats????
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>I feel stupid, but if you have an answer to that question, please let me know how you did it? Did I miss the obvious as usual?

The problem states there has to be at least 1 Red and 1 Green hat. The problem also states that after 13 days, a number said they had green hats. The next day the rest said they had red hats.

Then follow the logic provided above.