# Water island puzzle

On a planet called T, there exists a continent called P, which is surrounded on all sides by water. The continent comprises eight countries – A, R, B, C, D, E, G and K – located contiguously on it, i.e., the total area of the eight countries is the same as the area of the continent.

Each country is exactly in the shape of a square, with the four edges of the square as its boundaries. The areas of the eight countries are all equal. Any country is said to be a neighbour of another country if the two countries have one edge as a common boundary.

Further, one can travel by land between two countries only if the two countries are neighbours and it is known that one can reach any country from any of the other countries by travelling by land (passing through one or more countries, if required).

It is also known that

• R and E are the only neighbours of D, while K is the only neighbour of B, but K is not to the west of B.
• A and D are the only neighbours of E, while K is the only neighbour of C.
• E is directly to the north of R.
• G is directly to the east of D and no country is present directly to the south of G.

Source: time

What is the approach for this puzzle? Q:

Which of the following countries is to the immediate South of K?
a) B
b) C
c) G
d) No country is to the immediate South of K.

I have the same solution as already posted. Without following its reasoning, here is mine:

Quickly establish that E - D - R must run north to south. Now G is somewhere east of D but not adjacent


E
|
D       G
|
R

G must be approached from the north.
Only A or K can touch G.
Only A or K can touch E.
Suppose it is E - K - A - G

E - K - A
|       |
D       G
|
R

Now B and C must touch K but one of them would have to join D and G.
But both B and C only have one neighbour K.
So it must be E - A - K - G and as K is not to the west of B it must be:

B
|
E - A - K - C
|       |
D       G
|
R


c) G is to the immediate South of K.

• Weather Vane How did you deduct that G must be approached from the North only. There is a possibility of approaching G from west or east also. Pls explain
– sam
Oct 20, 2018 at 14:09
• @sam cannot approach G from the east because there are not enough (only A and K) remaining pieces. B and C cannot be used as links because they both have only one neighbour (K). Cannot approach from the west because D too can't have any more neighours. Oct 20, 2018 at 14:12
• Yes Thanks, It got this. But there is a logical error i found. It is mentioned A and D are the only neighbors of E. So only A and D can touch E. K cannot touch E. So E-K is faulty anyways. :)
– sam
Oct 20, 2018 at 14:30
• Ah thanks yes, but I ruled out E - K - A - G for a different reason. Oct 20, 2018 at 14:32

Given the backstory, we know that we are basically dealing with a connected square-shaped 2D objects that are of equal areas.

First of all, I would go through each and every condition that they provided, and draft it out first, with each of the possibilities there could be. (This is the tedious effort of thinking up of all possibilities - Without this step, we will have issues when trying to connect up everything, as we could possibly miss something out)

Then, for the conditions which have overlapping variables (In this case, overlapping countries, such as K is the only neighbour of C and K is the only neighbour of B, combine them one by one, and draft out the possibilities of them being connected to other pieces as you do so. (This potentially grows exponential, but you'll have to keep at it)

Once all the condition is met, and you know what moves you can and cannot make, all there's left is to connect them together where they logically fit.

(If you need further clarification, please let me know :) )

P.S look up brute force and back-tracking, this method is heavily related to those concepts

My solution:


B
|
E - A - K - C
|       |
D       G
|
R


• Please give a reference to look up on backtracking and brute-force. I need the approach for such puzzles.
– sam
Oct 14, 2018 at 8:09
• Welcome to Puzzling.SE, @Lippy! Nice Answer! Oct 14, 2018 at 8:11
• @sam Look up N-Queens on backtracking, it basically only has 1 condition: Queens shouldn't be able to attack each other on the board. Regarding backtracking, most, if not all, approaches which considers ALL possibilities are considered as brute force. Also, regarding whether there are any "approaches" to such puzzles, I guess one of the approach is already described in the answer, which is identify constraints, combine what makes sense logically until you build a whole picture. Oct 14, 2018 at 9:02
• Thanks Lippy for addressing my queries and nice explanation as well.
– sam
Oct 14, 2018 at 9:14
• @Lippy, I got just 10 mins to solve this puzzle. Looking at your solution, I feel using brute-force will make it impossible to solve this in 10 mins.Can you tell how many possibilities you made in the beginning?
– sam
Oct 14, 2018 at 11:39