The Chosen Ones

The puzzle
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


Solution
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:

Spoiler (hover to show)

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:

Spoiler (hover to show)

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:

Spoiler (hover to show)

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:

Spoiler (hover to show)

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:

Spoiler (hover to show)

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

Tip 6:

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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 =]]]]

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();
    }
}

Solution:

Spoiler (hover to show)

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 :]

Yeah