A few tricks that are quite important to know in the rotation game present in all the newer Nokia cellular phones (these rules apply for level 1-4):

A sequence can be used to swap columns/rows of three. Without this, you'll be circling around for hours.

Let's say we want to rotate this:
12
34
56

Into this:
21
43
65

Then we'll have to follow these steps:
```1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
12 31 31 53 53 34 34 34 13 21
34 42 54 41 64 56 25 12 24 43
56 56 62 62 21 21 16 65 65 65
```
What you can use this for: Everything!
If we do the following instead then we save two whole moves and consequentally score more all-important points:

```  1. 2. 3. 4. 5. 6. 7. 8.
12 31 43 43 32 32 21 21
34 42 21 52 45 51 35 43
56 56 56 61 61 46 46 65
```

Another useful move to know is how to rotate this:

```  1 2 3                1 2 3
4 5 6   into this:   4 5 6   .
7 8 9                8 9 7
```

The most efficient way to do that is as follows:

```   1.  2.  3.  4.  5.  6.  7.
123 413 413 153 136 136 123
456 526 756 476 457 425 456
789 789 829 829 829 897 897
```

In the three-by-three game, there are 9! (362,880) different ways of arranging the 9 numbers. All 9! arrangements are reachable. Of the 362,880 different possible starting positions:

• 1 can be solved in 0 moves (the goal position).
• 8 can be solved in 1 move (by rotating each of the 4 corners either clockwise or anticlockwise).
• 52 can be solved in a minimum of 2 moves.
• 328 can be solved in a minimum of 3 moves.
• 1,996 can be solved in 4 moves.
• 11,336 can be solved in 5 moves.
• 51,582 can be solved in 6 moves.
• 130,042 can be solved in 7 moves.
• 125,929 can be solved in 8 moves.
• 39,706 can be solved in 9 moves.
• 1,880 can be solved in 10 moves.
• 20 can be solved in a minimum of 11 moves.
• 0 can be solved in a minimum of 12 or more moves.

So the 'hardest' possible 3x3 rotation puzzles can be solved in 11 moves. Since there are only 20 of them, I will show them below. Can you find the sequence of 11 moves for any of them?

```  387   687   789   897   927
654   954   654   654   654
921   321   321   321   381

947   957   967   978   981
852   684   258   654   654
361   321   341   321   327

984   987   987   987   987
657   354   456   564   624
321   621   321   321   351

987   987   987   987   987
645   651   654   654   654
321   324   123   231   312
```

I will leave the discovery of the 11-move sequences as an exercise for the reader.

Finally, here is how to reverse the entire playfield in 10 moves:

```     1.  2.  3.  4.  5.  6.  7.  8.  9. 10.
987 697 567 574 574 546 546 546 436 413 123
654 584 894 869 826 872 382 132 512 526 456
321 321 321 321 319 319 179 789 789 789 789
```

This game is not hard. It keeps frustrating people who don't know how to solve it, but it is very easy to learn. If you haven't figured it out yourself, just read the writeups above and you'll know how to play it. After that it is easy, your highscores will be getting higher and higher. I believe that Level 2 is the best one for reaching high scores. On the first one, I was able to reach something over 1000 one time, but on the second level, it is much easier to reach 1000+. The levels 3 + 4 are a bit bigger (5x5, 6x6) and take more time to solve, so your scores won't be as high as on the second level. The levels 5, 6 and 7 are different, because . Just take a look at them on your phone, and you'll understand. I have to admit that I have never solved one of those, though I didn't really try.

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