# Solution for 7 circle puzzle

#### Aeroblyctos

Level 37
By Tears

[size=12pt]The puzzle[/size]
There're 9 circles, which fall into 3 categories: corners (C), edges (E) and center (X) just as below

C - E - C
E - X - E
C - E - C

Game rule:
- Every circle has its "power", when it's power increases, it's color changes.
- All circles' starting power is 1 and the maximum power is the current puzzle level (L) + 1. (On level 1, maximum power is 2 and so on)
- When you tap on a circle, it and all its adjacent circles (horizontal and vertical only) will increase power by 1
- After extends maximum power, the power will return back to 1.

Game goal:
Make all the circle to the maximum power

[size=12pt]Solution[/size]
I'll give you some tips so you can solve it on your own. Don't blame me if you just click on the last spoiler to see the solutions.

Tip 1:
To solve this puzzle, you have to tap all the circles in the same category(C / E / X) by the same amount. Example: You cannot tap southeast corner 3 times while northeast corner 4 times. If you tap a corner twice then you have to tap all the others by the same amount.

Tip 2:
Assume that you tap on corner circles C times, edge circles E times and center circle X times. Try to think how the power of each category will change.

Tip 3:
Still stuck? I see. I'll give you an example. The power of each corner is 1 at the beginning, you tap each corner C times, its power will increase by C, each corner has 2 edges so if you tap on each edge E times, the power of each corner will increase by 2E

Tip 4:
I have a feeling that you don't want to solve this on your own, right?
OK, the power of each category is this:
PowerC = 1 + C + 2E (each corner has 2 edges)
PowerE = 1 + 2C + E + X (each edge has 2 corners and 1 center)
PowerX = 1 + 4E + X (the center is adjacent to 4 edges)

Tip 5:
You have the power, you're very near. Think about the relationship between the power and current level.

Tip 6:
That relationship is mentioned in Game Rule. After maximum power is L + 1, so in order to solve this puzzle, PowerX, PowerC and PowerE must be divisible by (L + 1). Finally, we have this math =]]]]]

Find C, E, X that:
(1 + C + 2E) % (L + 1) == 0
(1 + 2C + E + X) % (L + 1) == 0
(1 + 4Y + Z) % (L + 1) == 0

To be honest, I don't have any better solution and try and wrong, but I'm a developer, I can simply just write some lines of code and let the computer do that job for me. This is that f*cking code, keep it if in the future, Aero create more level =]]]]

[size=8pt]public class HelloWorld {

public static void main(String []args) {
int MAXLEVEL = 3;
int MAXTRY = 5;
for(int level = 1; level <= MAXLEVEL; level++) {
find(level, MAXTRY);
}
}

private static void find(int level, int max) {
System.out.println("Level " + level + ": ");
for(int X = 0; X <= max; X++) {
for(int C = 0; C <= max; C++) {
for(int E = 0; E <= max; E++) {
int powerC = 1 + C + 2 * E;
int powerE = 1 + 2 * C + E + X;
int powerX = 1 + 4 * E + X;
int L = level + 1;

if(powerC % L == 0 && powerE % L == 0 && powerX % L == 0) {
System.out.println(String.format("C = %d, E = %d, X = %d", C, E, X));
}
}
}
}
System.out.println();
}
}

[/size]

Solution:
Level 1: Tap X once and each C once.
Level 2: Tap X once and each E once.
Level 3: Tap X thrice, each C thrice and each E twice.

Congrats!!! You solved the puzzle.

I played this puzzle before, even before TCO. There's a map dedicated for this puzzle and it has about ten or more level. I forgot the name of that map, I don't know if Aero played that map or not. It took me half a day to figure out the solution for that map so when I see it in TCO, I just laugh =]]]]]

@Aero, I love puzzles, make more puzzles please :]