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Posted: **Tue Oct 30, 2012 7:51 pm**

If it's allowed, could anyone tell, how large high levels are (maybe width, height or number of colors)? I mean level, for example 40-45 and further ones. Currently I have some ideas but they will be useless for too large levels, so it's interesting to me, is it reasonable to implement them.

Posted: **Tue Oct 30, 2012 9:20 pm**

I am currently at level 54 and you can easily find levels like 8x10 or 7x11.. number of colors varies from 2 to 4 (I can't remember viewing a level with depth 5). number of pieces is around 22
I am not being very accurate because I don't want to look at real numbers, since I am solving the current level for a while.

Posted: **Wed Oct 31, 2012 7:30 pm**

Oh, I've thought they are about 20x20 or so. Thanks, it seems a bit more doable now.

Posted: **Wed Oct 31, 2012 8:03 pm**

how do you (portal) go about solving the level? brute force with early outs? or do you model the levels as equations?

Posted: **Thu Nov 01, 2012 12:57 am**

basically early outs..
all my attempts with mathematical modeling failed, although I think it is much more beautiful

Posted: **Thu Nov 01, 2012 9:21 am**

i have so many ideas about early out conditions but i think i am still missing the game changing ones. currently i try to implement recursion. using big tiles first, calculating the minimum "flipping count" that is still required to solve the level ... so i can rule out many positions of big tiles that increase the required "flipping count" beyond what is provided by the remaining tiles. also for depth=3 and up it would make sense to keep track of the tile with the highest flipping count still required ... if that is 3 for example and i only got 2 tiles left i can ignore the solution up to the current piece. i am also trying to figure out a mathematical way to calculate if remaining pieces provide too much flipping power. i. e. you can not solve a level with 3 remaining flips with 3 remaining pieces with a flipping power of 9, 3 and 2. you will end up with an "overflipped" board

but i guess you are doing it completely different and laugh about my thoughts right now

Posted: **Fri Nov 02, 2012 1:14 am**

not laughing, don't worry..
the method around seems to be self-learning, so we should be careful in discussions.. this may be a little frustrating sometimes, but also much more rewarding..
so, I will not reveal what I am doing, but a little of methodology should be fine. I spent quite a while trying to estimate how long my solution would take to solve the level. this is good to determine if I am going to wait, if optimization in some factor would be enough or I have really to think about something new.. a week is fine, a month possibly ok, an year is usually not fine, a decade almost sure not fine. But it surely depends on the patience of each one.
another thing that helped was devising a checkpointing strategy.. this turned out to be necessary after some frustrating progress-loss a couple of times.. this ended up being interesting since it is a concern of "real-world" applications..

Posted: **Sat Nov 24, 2012 12:23 pm**

I made some statistics about the available levels.
The numbers are generated by examining 100 instances of each level.

Code: Select all

Level   #Colors   #Pieces   Game size     Fields per piece
 1      2          3        3x3  - 3x3    1 - 3
 2      2          4        3x3  - 3x3    1 - 3
 3      2          5        3x3  - 3x3    1 - 3
 4      2          5        3x3  - 3x4    1 - 4
 5      2          6        3x3  - 4x4    1 - 4
 6      2          6        3x3  - 4x3    1 - 4
 7      2          6        3x3  - 4x5    1 - 5
 8      2          7        3x3  - 4x5    1 - 5
 9      2          7        3x3  - 4x5    1 - 5
10      2          7        3x3  - 5x5    1 - 6
11      2          8        3x3  - 5x6    2 - 6
12      3          8        3x3  - 5x5    2 - 6
13      2          8        3x4  - 6x5    2 - 7
14      3          9        4x3  - 5x6    2 - 7
15      2          9        4x3  - 7x5    2 - 7
16      3          9        3x5  - 6x5    3 - 8
17      2         10        4x4  - 5x6    3 - 8
18      3         10        5x3  - 5x6    3 - 7
19      2         10        5x4  - 7x5    3 - 9
20      3         11        5x4  - 5x7    3 - 9
21      2         11        6x3  - 6x6    3 - 7
22      3         11        4x5  - 6x6    3 - 10
23      2         12        6x4  - 6x6    3 - 10
24      3         12        4x5  - 7x5    3 - 7
25      4         12        5x4  - 7x6    3 - 11
26      3         13        5x4  - 5x6    3 - 6
27      2         13        6x4  - 7x5    3 - 7
28      3         13        5x6  - 7x7    3 - 12
29      2         14        5x6  - 7x7    3 - 12
30      4         14        5x4  - 7x5    3 - 7
31      2         14        7x5  - 7x7    3 - 13
32      3         15        6x6  - 8x7    3 - 13
33      2         15        5x5  - 6x6    3 - 7
34      3         15        6x6  - 9x7    3 - 14
35      4         16        6x7  - 7x9    3 - 14
36      3         16        4x7  - 6x6    3 - 7
37      2         16        6x7  - 7x10   3 - 15
38      3         17        6x8  - 9x8    3 - 15
39      2         17        5x5  - 6x6    3 - 6
40      4         17        6x8  - 9x9    3 - 16
41      2         18        7x7  - 9x9    3 - 16
42      3         18        6x5  - 6x7    3 - 7
43      2         18        6x8  - 9x9    3 - 17
44      3         19        8x7  - 10x9   3 - 17
45      4         19        7x5  - 7x6    3 - 7
46      3         19        9x7  - 10x9   3 - 18
47      2         20        7x9  - 9x10   3 - 18
48      3         20        5x7  - 8x6    3 - 7
49      2         20        9x7  - 10x11  3 - 19
50      4         21        7x9  - 9x12   3 - 19
51      2         21        6x6  - 7x7    3 - 7
52      3         21        7x5  - 6x7    3 - 6
53      2         22        9x8  - 12x10  3 - 20
54      3         22        6x6  - 7x7    3 - 7
55      4         22        10x8 - 11x11  3 - 21
56      3         23        9x9  - 11x11  3 - 21
57      2         23        5x8  - 9x6    3 - 7
58      3         23        8x11 - 13x10  3 - 22
59      2         24        9x10 - 12x12  3 - 22
60      4         24        8x5  - 6x9    3 - 7
61      2         24        8x11 - 12x12  3 - 23
62      3         25        11x9 - 12x12  3 - 23

Posted: **Mon Dec 03, 2012 12:21 am**

Nice.
What do you mean by "Fields per piece"?
And for "game size", I suppose your metric for min and max is the area. Is this right?

Posted: **Sun Dec 16, 2012 6:28 pm**

portal wrote:What do you mean by "Fields per piece"?

Hm, maybe the term "fields" is misleading in this context.
"Fields per piece" should denote the number of colored squares per piece, e.g. 4 for all pieces occurring in Tetris.

portal wrote:And for "game size", I suppose your metric for min and max is the area. Is this right?

Exactly.

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How large the high-levels are

How large the high-levels are

Level statistics