[Guest]

5 leaders of 5 tribes gather to split their island into 5 areas each for a tribe, the splitting must satisfy these following conditions:

Each tribe's land must be continues (as in one piece)...

Each tribe must be adjudicate to all 4 other tribes land so that in case of war two allied tribes can provide support for each other, by being adjudicate that means each two tribes must share a piece of the same wall, meanning you have room to put in a gate there, if two tribes meet at only a single point that doesn't count (see picture)

The island can't have any "public" areas, meaning you can't create a path between two tribes that doesn't belong to any tribe, also the sea doesn't count as well...

For the sake of this puzzle the island can be in any shape you want and it doesn't matter if one tribe got more land than another...

[Guest]

Let's assume the island is circular. Draw an interior circle. One tribe owns the land between the sea and the inner circle, surrounding the remaining land. Then simply bisect the inner circle twice creating the other four areas. Voila!

[Guest]

Let's assume the island is circular. Draw an interior circle. One tribe owns the land between the sea and the inner circle, surrounding the remaining land. Then simply bisect the inner circle twice creating the other four areas. Voila!

The 4 in the inner circle won't have connections between them, think of each two facing each other...

Try drawing it...

[araver]

Well,

assuming you want a 2D map of the island, that is impossible.

5 regions, each adjacent to the other (border, not point) cannot be colored by 4 colors so that no two adjacent regions have the same color (pigeon hole principle).

Hence, if such a map existed, it would contradict the Four color theorem.

[Aaryan]

if the island is any shape... just make the island shaped in five pieces, each with four "arms". Twits and curl them so that one arm of Tribe A connects with one of Tribe B, one with Tribe C, one with D, and one with E. Repeat.

[Molly Mae]

I agree with Araver. Two dimensionally, it is impossible. Only by adding a third dimension (say an arch over a canyon, where one tribe owns the arch while another tribe owns the land in the canyon directly below the arch) can this be achieved.

[curr3nt]

For the sake of this puzzle the island can be in any shape you want and it doesn't matter if one tribe got more land than another...

I want the island to be a Möbius strip.

-------------------

+   1   |    2    x

-------------------

=  3  | 4 | 5 | 3 =   

-------------------

x   sea     |  1  +

-------------------

The plane wraps around and connects on x, = and +.

edit - fixed layout

Edited February 11, 2011 by curr3nt

[curr3nt]

Guess that isn't technically an island...

This one is surrounded by the same body of water.

-------------------

------------------- 

+   1   |    2    x 

------------------- 

=  3  | 4 | 5 | 3 =    

------------------- 

x   sea     |  1  + 

            -------

-------------------

[Guest]

Here's one take:

I like the arch solution. I'll try to illustrate here with letters, but I don't know if it will work.

AAAAAAAAAA

AABBCCDDEE

AABBCCDDEE

AABBFFDDEE

AABBCCDDEE

AABBCCDDEE

EEEEEEEEEE

The FF section in the middle is an archway connecting the DD tribe to the BB tribe, with the resulting valley beneath belonging to the CC tribe. Thus connections are maintained between all tribes.

Here's another take

Still working within the constraints of the riddle wording itself, consider the FF section not as a public area owned by no tribe, but as a shared area owned by DD and CC. It is not common to all and is thus not in violation of the riddle, but probably isn't in the spirit of the riddle.

Edited February 11, 2011 by jpar1983

[Guest]

araver was the first to get it right...

[curr3nt]

araver was the first to get it right...

bah... I liked my answer. I am going to build my island when I get home. They do not let me play with anything sharp (like colored pencils) at work.

[Guest]

bah... I liked my answer. I am going to build my island when I get home. They do not let me play with anything sharp (like colored pencils) at work.

So the correct answer is that it is impossible?

[Molly Mae]

So the correct answer is that it is impossible?

It is impossible if the island can only be represented in two dimensions. If there were a system of caves beneath the island (and some tribes owned some of the caves [or just one tunnel]), it would be possible. In order to connect the fourth tribe to the first three, you'll always be isolating one tribe. The fifth tribe would have to tunnel under (or over, in the case of the arch over canyon model) into the isolated tribe's territory.

[curr3nt]

It is impossible if the island can only be represented in two dimensions.

My solution is two dimensional...

[Guest]

My answer is a picture. See attachment.