Here's a brainteaser:

[TiefBlau]

How's this:

In the first round, everyone looks around to see what the color on everyone else's head is. Afterwards, their attention shifts to specifically the people with red balls on their heads, because they want to see whether or not they'll move when the master tells them to. The people with red balls on their heads notice that people are looking at them, and deduce that they must have a red ball on their head. They look at all the people with red balls and move when they move.

I really don't know how else you can do this without determining the number of balls or something like that.

 

[MR.Spartacus]

They took the balls off and looked? They just got bored and were going home, thus making any relations to his challenge coincidental?

 

[glodud]

all of the balls were red

EDIT: they realized that the color of a ball on your head doesn't determine how wise you are

 

[Graevan]

I'd have taken a red ball from the head of another and stepped forth.
Wisdom isn't granted by another, it is something you gain yourself, and if the man in possession of wisdom doesn't act on it then he is a fool.

 

[Duffeknol]

I liked my answer better. I hate mathematical riddles

 

[Ekonk]

They looked in the reflection of the white balls.

Nah, I've got nothing.

 

[sms_117b]

That seems more like a test of modesty than anything else, anyone that would have stepped forward would be arrogent and probably not wise, as they all stayed back acting modest, they passed.

 

[Spoonius]

It doesn't matter if they had white or red balls. Every man who is willing to 'take a step further' is a wise man.

That's what I figured.

I third that.

I don't think so... the head guy specifically stated that only those with red balls upon their heads were wise.

EDIT: To be honest, there isn't really enough info to go on. There could be multiple solutions (some of which have already been discussed).

 

[SultanP]

Still none of them stepped forward, and only the wise know that they aren't truly wise. So they were all wise by not stepping forward.

Or not. Doesn't make sense in the context of the riddle.

 

[nuba km]

It doesn't matter if they had white or red balls. Every man who is willing to 'take a step further' is a wise man.

That's what I figured.

I third that.

I don't think so... the head guy specifically stated that only those with red balls upon their heads were wise.

EDIT: To be honest, there isn't really enough info to go on. There could be multiple solutions (some of which have already been discussed).

The same thing happens the third time, yet the fourth time when the master asks the wise men to move they do. And the master congratulates them.

the wise men step forward it doesn't say that they had red balls on their head it only says that the master said the men with red balls on their head were wise.

 

[Grouchy Imp_v1legacy]

So there's this wise man which has an unknown number of apprentices. One day he gathers all of them and tells them: "Today I will separate the wise from the foolish." He brings out a bag of red balls and a bag of white balls (their number is also unknown). "Those which are wise will receive a red ball and those which are not will receive a white ball." after which he starts to put the balls on their heads. Catch is every apprentice can see the balls on the others heads but not his own. The master then says: "All of the wise men take a step further!" The apprentices start looking at each other but no one moves. The master repeats: "All of the wise men take a step further!" The apprentices have the same reaction. The same thing happens the third time, yet the fourth time when the master asks the wise men to move they do. And the master congratulates them.

How did the wise men know they had red balls on their heads?

A truly wise man would take the ball off his head and look at it.

 

[Tekkawarrior]

Every time a guy comes in here, with less than 20 posts, gives us a riddle, and leaves. I'm getting tired of this crap.

 

[karplas]

The answer is in the number of times he asked them.

The apprentices know that there is at least one wise person and at least one unwise person in their crowd. But they don't know if they themselves are wise or not at first.

If the master had only given one of the apprentices a red ball, he would immediately seen that no one else had one and would have stepped forward the first time the master called.

If the mastr had given two of them red balls, they would both have seen one other apprentice with a red ball. So they still wouldn't know if they were wise or not.
The first time the master would call, they would both notice that the other wise apprentice didn't move, which could only mean that the other apprentice could also see a red ball. Therefore, both apprentices would know that they were wise and would step forward the second time the master asked.

Now imagine there are 4 apprentices with a red ball on their head:
the master asks a first time for the wise to step forward. The wise ones see 3 other apprentices with a red ball and so they don't step forward because they don't yet know if they are wise or not.
The second time the same thing happens, and the third time as well.
But the fourth time the master asks the wise to step forward, they realise that if there had only been 3 wise apprentices, they would all havce been sure of it the third time the master asked them to step forward, so they would know that there were four wise apprentices, and therefore that they were wise.

There, sorry for the wall of text but it is a bit complicated to explain :/

I don't think your explanation completely holds:

"The apprentices know that there is at least one wise person"- This assumption is required for your solution to be valid (and to be honest, I think assuming this is the only way to solve the problem), but it's exactly that: an assumption: I can't see where this is given in the problem.

"and at least one unwise person in their crowd."- This assumption I think is false.

See, let's reduce this problem to two apprentices, who are both given a red ball. Assuming they were both told up front that at least one red ball was given, each apprentice could think the first time: "The other apprentice has a red ball, so he is wise. If he saw I had a white ball, he'd immediately know he'd have a red one. Yet he doesn't step forward, so he must see I have a red ball as well". The second time both apprentices would step forward (and you see, it doesn't require that there is at least one unwise person in their crowd). This solution can be expanded to an arbitrarily large crowd with an arbitrarily large part of apprentices with a red ball. But it requires that all apprentices somehow know there has to be at least one apprentice with a red ball.

 

[awesomebillfromdawsonville]

The answer is simple. They all like balls on their heads.

 

[Habakkuk]

It doent state that people with white balls on their heads didnt move.

Perhaps everyone moved including the ones with white balls on their heads but only the ones with red balls were congratulated.

 

[GaijinAndrew]

Every time a guy comes in here, with less than 20 posts, gives us a riddle, and leaves. I'm getting tired of this crap.

I am truly sorry if I have offended you, but the motive for which I have not given the answer yet is because I do not spend all my time on the internet and I usually check these sort of things once in a while. Also I myself did not know the answer when I posted this riddle, and that is because I had an argument with my psychology teacher about the solution. Apparently the answer is that no wise man would think that he is wise just by having a ball on his head and actually all the people who decided to take a step forward even without knowing the color of their ball were indeed wise.I am not particularly satisfied about that answer...but still. Also I think the number of posts I have on this site is totally irrelevant. Yes I do not dedicate myself to this community much as others do but that doesn't mean that I posted this riddle just to amuse myself at your mental strain. I apologize again for causing you any sort of discomfort.

 

[CheesusCrust]

Snip

Well that was pretty anti-climatic

 

[Outright Villainy]

Snip

Well that was pretty anti-climatic

You're damn right it is!

Here's one with some more mathematical rigour:
http://xkcd.com/blue_eyes.html

To be honest I was expecting some variation of that, and most of the Op's riddle makes no sense with a philosophical answer.

Why did the all do at the same time for one thing?

Wouldn't a couple have done it the first, second or third time?

 

[Habakkuk]

Every time a guy comes in here, with less than 20 posts, gives us a riddle, and leaves. I'm getting tired of this crap.

No one asked you to do this.

 

[Tekkawarrior]

Every time a guy comes in here, with less than 20 posts, gives us a riddle, and leaves. I'm getting tired of this crap.

No one asked you to do this.

Yea no one "asks" you to do this either, no one asks you get up from your bed in the morning, but you do it because you want to. I like brainteasers that isn't my problem, my problem is people coming in asking a question and then bailing on us. This forum is mine as much as it is anyone else.

Doesn't it annoy you too? oh wait, you've been here less than 10 days.
This is my last post in this thread.