Big-chief little horn's dilemma.

[Admin]

Big-chief little horn has 3 sons. He needs to decide who to give his chiefdom to. He has 5 feathers: 3 yellow and 2 red. He gives each of his 3 sons a feather, and puts it on their head. They can't see their own feather, but they can see each others.

He actually gives each of his sons a yellow feather, but they don't know that.

They're not allowed to tell each other what colours they can see and they have to work it out for themselves. All they know is how many feathers of each colour there are in total, and which colour feather each of the other brothers have. They cannot see the remaining feathers.

The first one to tell the chief what colour feather he has on his own head and how he knows wins the chiefdom.

Could one of them answer first and how do they know the answer?

[Lord Muck oGentry]

Big-chief little horn has 3 sons. He needs to decide who to give his chiefdom to. He has 5 feathers: 3 yellow and 2 red. He gives each of his 3 sons a feather, and puts it on their head. They can't see their own feather, but they can see each others.

He actually gives each of his sons a yellow feather, but they don't know that.

They're not allowed to tell each other what colours they can see and they have to work it out for themselves. All they know is how many feathers of each colour there are in total, and which colour feather each of the other brothers have. They cannot see the remaining feathers.

The first one to tell the chief what colour feather he has on his own head and how he knows wins the chiefdom.

Could one of them answer first and how do they know the answer?



Ummm...one them is likely to think " If I had a red feather, one of the others would have cracked this first, so..."

[brianp]

Could one of them answer first and how do they know the answer?

One of them might argue as follows:

1) My father is a fair man so he's likely to make things equally difficult for all of us.

2) The only way he could do that is by giving us all the same colour feather.

3) He only has two red feathers but he has three yellow ones, hence to treat us all alike he must give us all yellow feathers.

4) The available evidence - ie my brothers both having yellow feathers - is not proof, but is certainly consistent with my hypothesis. I'll go with it!

5) Hey dad - my feather is yellow.
i

[vbloke]

All one of them has to do is dip his head into some paint or dye and tell the chief that his feather is whatever the colour of the paint is.

[Lord Muck oGentry]

A thinks: if B could see Y and R, he'd be wondering why C hadn't cracked it, and coming to the conclusion that C hadn't cracked it because C couldn't see 2R . Since B hasn't spoken, he can't be looking at Y and R. So...

[Matt]

The first brother to recive a feather hypothesises that his feather is red.

He sees the second brother recieve a yellow feather and knows that under his hypothesis the second brother could know that his feather was yellow if the third brother also recieved a red feather.

The third brother would also know this and when he recieved his feather would know that if the second brother didn't imediately react then his own feather must be yellow.

However neither second nor third brother react so the first brother knows that his initial hypothesis was wrong and declares that he must therefore have a yellow feather.

There's a lot of second guessing bout what the other brothers are thinking but that's the way of these logic puzzles.

The second brother could make a similar assessment, perhaps the third also.

[Lord Muck oGentry]

I think we've got pretty much the same answer, Matt.

[Allo Allo]

The one who kills Dad (the old sod) will get the Chiefdom. ;D

[Cuddles]

I'm with Vbloke and Allo Allo here. Logic problems are so much easier if you cheat.:cheesy:

[Admin]

A son who could see two red feathers would know for certain that his was yellow (and claim the chiefdom).

A son who could see one red feather would know his was yellow if the third son didn't see two red feathers (and claim the chiefdom).

If they all have yellow feathers then it's impossible for any son to work out their own colour directly or via the others' responses.

So, the first son who realises that he can't work out the answer and the other two can't work out the answer either, means they must all have yellow feathers will be the winner.

[vbloke]

I still prefer my answer.

[Allo Allo]

A son who could see two red feathers would know for certain that his was yellow (and claim the chiefdom).

A son who could see one red feather would know his was yellow if the third son didn't see two red feathers (and claim the chiefdom).

If they all have yellow feathers then it's impossible for any son to work out their own colour directly or via the others' responses.

So, the first son who realises that he can't work out the answer and the other two can't work out the answer either, means they must all have yellow feathers will be the winner.

Hey! I could have worked that out! :smiley: But it didn't occur to me!!!!!;D

[Matt]

I think we've got pretty much the same answer, Matt.

Yes except that you explained it better. Your explanation was so concise I actually missed it. If I'd have read it before going to bed I wouldn't have stayed awake trying to figure it out and then make a late night post trying to get down what I'd figured out.

Darn you!

[Lord Muck oGentry]

All one of them has to do is dip his head into some paint or dye and tell the chief that his feather is whatever the colour of the paint is.

Well, direct methods are sometimes best:

http://www.giantitp.com/comics/oots0327.html

[tkingdoll]

This extremely unfair. One of the sons has a stutter, and the other one had chilli for lunch and has been suffering from terrible hiccups. The whole thing is biased in favour of the third son who can speak more quickly than the other two.

Um big heap unfair.

[SKIRRID5]

To veer from the topic a little, my favourite Native American joke concerns a rich chief with three squaws. He was able to afford expensive skins for them to sit on. Two squaws each weighed 150 lbs, and sat, one on an antelope hide, the other on a bear skin. The third squaw was very fat, weighing 300 lbs. She sat on a hippopotamus hide.
The moral is: The squaw on the hippopotamus is equal to the sum of the squaws on the other two hides.
Aren't you glad I told you that?