The New Sudoku Players' Forum

by **z666zz666z** » Thu Mar 07, 2013 2:11 pm

Pat, thanks a lot for the "direct link" to a the file, that way i could find it very easy, just click on the link and download it to my HDD.

Pat wrote:
z666zz666z wrote:
Each row has to be of exact same length 225*3=675 charactes

i almost got it into your format
except my file (attached) has an extra TAB separating cells -- sorry

Pat, it does not matter at all that extra TABs, i can use Notepad++ to remove them... as easy a Find&replace "\t" to "".

I have downloaded the file just perfect, thanks at all.

On previous post when i said i did not see it when i go to...:
http://www.setbb.com/sudoku/viewtopic.php?t=1830&mforum=sudoku
I did not see it, just because my Browser show the numbers as one pixel per digit (like it it where an image) and i did not try to select all (i did not even think it could be text), sorry for that... in other words the text was shown as a font with a size too small to be able to read anything of it and no scrollbars at all.

On previous post when i said i did not see it when i go to...:
http://forum.enjoysudoku.com/a-new-100x100-t6395.html
I did not see it, just because i did not understand the format and so not see it as a sudoku (if it would have scrollbas so each row of sudoku would be on a line maybe i would understand the format).

Again, thanks to Pat for putting the file as an Atatachment (a file in a Plain Text format so any text viewer, notepad, etc can read it)... in that way it is very easy to find it... just with one click can be downloaded.

Note for those that says they have no problems to find it on:
http://www.setbb.com/sudoku/viewtopic.php?t=1830&mforum=sudoku
http://forum.enjoysudoku.com/a-new-100x100-t6395.html
I went again to them and i still do no see a download link there, where is it?
As i said i do not see any link where i can download any file, like Pat has done on his post, so in my opinion it is not trivial to find it there, at least not as trivial as on Pat post... a direct link... correct that there is a lot of text i can Copy&Paste, but my browser (Google Chrome) show it with a so small font size i can not even notice that was the text of sudoku cells, so i never think on doing a Copy&Paste.

Again thanks to Pat for putting a "direct link" to a "Plain Text format file" (no matter that tabs, i can remove them or adapt my algorithm to suport them)...

Note about the format and why i choose that one:
The format is a very common and standar format for "Information Exchange" on all over the world... a Plain text format, each cell with a fixed size... so the format is formally called a "ASCII fixed column", the Pat ones is also "tab delimited format".
I used that other format (similar to Pats one but without Tabs) since i want to test my program not only with 225x225 ones, also with 10000x10000 and whit a "OneMillon x OneMillon" one
Just for a Madnness extreme i did a test with a "OneMillon x OneMillon" one... i did not let it to finish since it was only just to check if it would work of just hang, crash, etc...

Note about the size of the file for that one, the total madness "OneMillon x OneMillon" one:
The file on plain text without Tabs has a size of 5.457TB, yes TeraBytes... so no PC has enough ram to hold it fully on RAM on "ASCII Plain text" format... neither on binary format since it takes at least 2.73TeraBytes.
If i include such tabs the file goes up to 6.366TB, so the tabs will take One TeraByte extra, that matters a lot...
I know it was a Really Full Madness One ... it needs a big rack of HDDs to hold the info... near 6 extrenal 2TB HDD (USB3.0/Sata-III) on Raid stripping ... and for solving it and extra 2TB HDD for temporal info ... i also calculated that if i was too madnees to try to print it on paper it would maybe need more paper than there is on the world, well not really so much, but something really near 400 millon ( yes, 400000000 ) pages of paper... i am not as mad to print that, je je... neither to try to solve it manually of course, just to check the algorithms... i neither let it to finish... when it solved up to 25% i shut it down, takes too, too much time... estimated more or less a month of a High speed home-super-computer with a 4x4 (four quadcore computers).

Yes, i know i am a little paranoid when testing my own made algorithms... why prove it with small amunt of data if i can test it with huge branch of huge data!!! ... with that ultra-madness-high-amount of data you can also check extrange and rare conditions where data is not readed on time, bottlenecks, etc... and one very important thing... how much more time needed for extra size.

Oh! i am also more madness...
I did some cals for a 100 times that (a ten millon x ten millon one) but unfortunatly i do not have enought HDDs to aford that... a faked estimation tells me it would took to "find a valid one & solve it" about a full year of computer... i am not as mad to pay the cost of electricity for that task... so i desist on trying that one... but just do a simple Maths... since values can go from 0000000 to 9999999, that is 7 chars per cell, 10 millon cells per row (i removed the line breaks, more easy to process with direct file access) and ten millon rows, so 7*10^7*10^7 Bytes... that is 700TeraBytes, wow!!! that much just to hold one step.
Actually i have on External 2TB HDDs near 20Terabytes... (ten 2TB HDDs)... for huge test tasks like this ones, but i would need about 40 times what i have... i am not so rich, i can not even pay for that... maybe someone give them to me as a gift or let me free a "cluster super-computer"... but then where could i "storage" the "solution", je je... nowhere near me!!!
So finally i desist trying it, je je... with that Maths i saw the bigger one i could try was near "One millon x One Millon", so i test it not to end!!! It was great to see it did not crash and was really fast on getting some cells values... at least my algorith works with such huge data, je je... maybe it can not solve some of 9x9 but at least i think i had done things well so it can solve any one of any size if have enought HDD and time, it does not works on RAM, it uses HDD direct file access... a huge file working as RAM does (you can read/write any byte at any time) but slower of course, the file does not change on size, so never get fragmented, etc... speed is allways the same for the whole proccess... that is very important since if you let file get fragmented, read/write speed can decrease.

Well, again thanks a lot to Pat, now i have it... now i will try to solve it with pencil and paper... then after that, maybe i will pass it as input to my algorithm if i get "cycles" on the home-super-computer, now it is working on other tasks queues (and i am lot allow to use it till ends).

Thanks a lot to all of you.

by **m_b_metcalf** » Fri Mar 08, 2013 9:07 am

Well, thanks to z666zz666z, this topic has suddenly and unexpectedly been resurrected. I took the opportunity to do some regression testing on my old code, and produced the puzzle below, firstly in a 'standard'' format and then in z666zz666z's. This puzzle has more givens than previous attempts, but is much harder, probably around SE~7. Note that the first version of the puzzle has the value 100 where the second has 000, and allowance must be made for that in reading them. My early attempts used to take a day to produce and a few minutes to solve; this one took an hour to produce, but needs 1300s to solve (all at 2GHz).

[EDIT: The time to solve is now only 130s.]

When, z666zz666z, you have cracked these, I'd be fascinated to learn where your 10000x10000 puzzles come from, and what you mean by, for example, 50x50 and 250x250 (as opposed to 49x49 or 225x225: standard puzzles are of size N^2xN^2).

Regards,

Mike Metcalf

. 01 . 93 44 54 . 49 45 52100 16 24 . 09 80 51 . . . . 50 . . 18 . 91 . 15 40 06 . 85 . 05 . 69 12 87 . 53 . 62 . 29 78 . 25 81 75 88 64 . 72 . 28 33 41 . . 57 . . . . 56 07 31 76 . 90 10 74 . 13 . 55 58 98 26 60 96 86 14 . 68 59 61 39 30 27 . 92 77 20 82 47 11 . .
. 75 58 74 24 . . 20 25 03 29 64 94 . . . 99 89 83 60 44 27 90 02 . . 10 22 32 . . 42 54 31 36 30 52 96 13 . 66 . 12 71 41 43 . 18 07 . . . . . 48 65 21 . 34 . 87 . 23 06 . 61 78 . 59 . 33 86 67 . 76 . 38100 73 . . . 62 35 50 97 . 55 . . . . . 40 57 95 . . 81 17
95 97 99 . . 09 76 87 47 62 50 33 02 52 43 58 . . 49 78 89 19 63 60 . 61 . . 54 48 . 08 . 28 17 64 21 55 . 93 10 . . . 26 68 06 91 37 . 27 . . 92 38 53 23 81 . 40 16 . 72 88 03 . 66 . 12 98 . . 45 . 85 42 15 . 65 . 82 79 94 70 . 80 . . 77 84 14 . 01 35 36 41 . . 83 69
. . . . . . 68 48 82 69 . 87 . 63 . 39 66 67 34 41 . 78 85 08 13 . 58 56 38 06 . . . 94 53 92 84 43 98 . . 60 . 61 55 76 . 70 01 27 . 09 54 . . 51 77 42 19 93 . . . 30 95 26 36 52 80 . 97 . . . . 72 81 . 96 20 . . . 44 . . 11 . . 03 29 . . . . 12 04 18 73 90
38 12 91 33 21 . 19 92 07 . 95 . . . 55 69 . . . 17 . .100 . 37 86 67 . . 76 73 . 61 25 . . 03 39 02 77 . 83 . . . . 99 . 52 . 04 82 . 57 . . 29 16 14 32 90 71 74 20 49 01 45 60 27 64 . 51 80 75 . . . 87 54 94 78 . 36 26 08 63 13 65 10 98 42 85 34 09 96 56 50 68 . 84
08 . 23 59 50 36 31 . . . . 71 74 57 37 05 30 12 . 40 93 . 64 96 . 41 . 55 . 33 29 . 72 66 91 76 19 48 . . 80 04 95 65 . 28 73 44 79 21 . . . 97 87 . . 60 56 58 38 34 . 68 89 92 . 94 18 85 . . 77 24 . 01 62 09 84 . 06 90 20 . 67 . 27 45 . 43 61 52 . 13 32100 39 . 78 49
. 57 . 30 43 67 83 64 . . . 13 14 76 . 85 . 61 53 75 . . 42 92 25 98 52 . 09 59 . 74 24 95 41 . . . 18 . . 15 . 19 . 97 90 . 36 22 26 . 17 37 . . 12 70 11 62 08 . 81 96 . 63100 44 29 . 03 71 02 89 . 68 88 82 32 39 48 99 . . 69 . . 87 . 23 79 . 06 07 60 55 . . 46 16
51 . 86 46 . . 98100 . 90 96 73 . 56 91 07 . 18 25 23 97 77 69 39 84 43 04 . 28 . . 81 27 10 68 45 59 . . 35 . 16 54 74 . 14 50 63 57 92 06 30 71 75 61 . . . . . 13 09 62 40 99 05 . 47 11 24 48 44 52 66 . . 36 83 21 53 . 58 41 . 89 . . 49 19 72 93 76 38 37 03 02 64 . . .
. 40 29 72 . . . 81 37 35 04 . 54 82 86 79 10 . 68 90 . 16 . 07 95 . 94 87 30 03 80 . . 01 63 . 62100 32 . 20 49 . 56 11 67 47 02 . 38 . 50 96 . 44 . . 89 . 45 . 46 48 55 . 83 19 77 43 . 14 78 . 61 . . 22 31 . 60 . . 18 92 42 66 71 . 85 05 24 . . . 23 . 75 . 21 59
34 66 . . . 11 . . 65 84 . . . . 46 62 77 36 31 92 . . 99 21 . . 49 68 74 . . . . 60 90 15 47 79 75 26 08 58 . 85 13 59 94 87 . 42 98 83 52 03 76 67100 55 10 . 04 53 . 33 91 . 39 . 22 . 93 29 23 57 12 . . 37 06 63 . . 73 25 95 . . 16 . 02 05 54 30 89 88 44 . 86 71 97
. 34 22 . . 06 67 . 64 . . 84 18 59 05 . 91 . . 76 81 . . 95 . 77 98 . . 30 49 87 . . 74 46 07 60 55 16 40 02 . 15 . . 17 41 . 31 . 69 04 . . 01 . 96 08 29 70 85 26 57 . 90 . . 51 . . 82 . 36 79 . . 66 13 . 37100 80 . . . . 27 25 . 88 61 28 53 50 92 73 71 63 .
50 95 12 16 15 93 75 . 30 26 41 . 47 40 . 63 . 83 89 . 28 . . 03 44 78 . 97 29 . 08 . 14 . 88 . 20 81 39 25 . 48 77 . . 34 46 86 76 80 35 62 . . 10 84 19 79 51 . 37 59 . 21 52 67 55 69 06 87 27 18 24 94 91 . 73 65 . 90 56 36 . 01 . . . 98 . 92 09 58 . 82 64 . 99 66 23 .
41 74 . . 18 76 . . . 92 82 28 98 . . . . 06 36 . . 54 79 86 55 66 19 73 70 17 11 69 . . .100 72 05 80 91 . 47 52 . 04 . 58 30 . 24 56 . . . . . 95 46 75 60 . 44 35 13 71 . . . . . 62 53 . . 34 29 . 63 . 77 23 32 . . 97 67 14 40 12 . 57 . 37 . 59 90 . . . 01
57 70 61 35 45 59 43 . 04 27 14 44 13 07 03 19 . . 85 68 11 31 82 . . . . 05 12 . 89 18 . 29 . . 51 . . 01 42 . . 64 . . . 72 . 10 83 80 90 63 . 66 30 73 . . 60 . . 17 86 . . 54 84 . . . . 33 . . 47 97 37 . . 94 24 49 06 81 79 09 . . 76 67 46 62 93 . 32 . . 96
56 33 96 . . 23 77 47 . 98 . . 55 11 49 15 32 35 78 62 . 74 . . 88 . . 18 . 09 10 . 92 82 67 . . 75 90 03 14 12 . . . 63 13 73 . 66 . . . . 36 . 17 . 71 . 83 . . 24 01 95 .100 97 80 31 . . . 93 . 64 . 08 . 99 . . . . 61 89 . 51 68 69 05 41 70 25 81 . . . 07
. 54 . 48 51 88 . 19 03 17 . 67 95 12 33 08 93 64 . 53 26 84 36 27 . . . . 50 96 28 . 45 99 83 . 71 73 40 . 01 44 98 82 49 . 89 . 18 61 92 . . . 09 85 97 07 . 78 91 . . . 41 04 23 43 31 42 25 81 39 86 02 . . . . 70 . 05 60 34 . 65 72 63 62 . . 77 47 . 11 94 . . 24 06
. 37 . 91 86 . 82 78 58 01 75 34 90 99 . 87 38 . . 43 . 48 . 57 . 42 . 63 53 . 52 . . 22 95 59 . . 04 . 96 28 06 . . 26 20 . 45 55 . . . 94 05100 18 . 67 13 . 77 . 81 14 40 25 . . . 89 56 32 74 98 61 54 15 23 21 73 69 35 . . . 41 47 76 . 08 79 97 . 49 . 03 . 72 .
05 . . 38 20 90 32 . 36 60 65 . 57 66 . . . 79 73 86 04 94 . 13 15 . 46 76 49 . 84 98 43 09 . . . 58 . 62 81 97 . . 59 29 53 35 87 11 . . . . . . 37 34 31 . 61 27 02 64 92 72 74 28 . . 69 . . 96 . . 06 . .100 . 95 . 93 . . 30 18 07 50 51 44 19 . . . 14 . . 40
. 07 . 80 69 . . . 29 28 56 . 01 . . 96 24 54 . . . . . . 71 58 41 52 47 89 37 70 97 26 42 86 61 57 63 . 67 91 . 75 09 92 85 . . 43 . 40 27 20 15 76 . . 68 25 05 . 22 . 79 . 73 88 . . 51 . 78 . 84 . 49 48 72 44 53 10 66 . . 45 33 02 . 90 35 30 98 34 13 . 60 17 74 .
66 72 . 94 71 02 . . 46 . 80 . 88 97 50 27 . . . . 06 90 83 . . 20 . 93 67 75 79 15 76 . . . 44 . . 32 . 68 84 69 37 . 60 . 99 74 11 . 39 . 81 41 03 . 49 16 98 63 . 08 . . . 18 . 10 . 04 01 05 . 40 . 92 . . 19 . . . 91 17 . . 70 . 48 95 31 . 89 36 21 56100 65
18 94 48 . 62 57 . 37 67 . 63 26 35 84 38 . 13 34 52 91 19 . . 58 . 69 70 75 . 20 . 59 33 65 99 74 73 36 79 14 44 98 . 05 . 93 72 68 92 23 97 . 03 96 49 09 88 45 22 46 40 . . 32 60 21 50 51 85 17 . 87 42 . . 53 71 61 39 80 11 . . . 82 . 66 86 04 78 . 02 54 55 . . . 43 64 .
20 25 13 88 . . 41 28 35 80 83 89 93 18 14 . 36 55 39 10 92 . 76 . 78 . . 57 . 11 26 75 . 64 . 44 16 04 . 37 47 82 . 33 . 40 12 19 65 . 61 . . 17 . 62 71 02 59 . 06 . 46100 . . 22 . . 90 . 70 05 52 . 49 95 . 77 85 91 . . . 74 . 31 . 03 69 84 08 . . . 97 34 72 67 99
52 02 19 17 09 . 03 50 16 95 . . . . . 82 42 45 71 46 62 67 65 22 . 74 88 64 06 . . . . . . . . 69 . 27 85 13 . . 24 89 84 . . . 58 29 53 30 34 . 36 . 78 04 79 49 99 15 . . 72 37 . 56 75 . . 59100 11 18 . . . 41 08 57 . 21 . . 39 . 47 . . 66 90 . 40 . 92 60 .
54 96 . . 46 82 . 12 . 65 06 40 09 . 77 . 56 98 37 15 59 34 . . 97 68 25 95 . 44 92 21 . 05 51 . 30 47 . 53 43 80 74 52 27 . 16 31 55 18 70 60 . 86 69 48 . . 28 10 24 . . . . . . . . 08 36 66 . 78 72 94 . 93 19 . . . 87 29 58 . . 33 99 13 . 38100 . 81 61 . 14 . .
. 36 34 60 . 86 . 43 59 . 23 58 11 96 30 33 47 29 . 70 02 . 48 31 . 37 77 07 . . 94 35 40 89 . . . 20 57 98 06 .100 . 51 22 . . 46 56 68 . 42 87 67 75 64 93 52 41 88 . 38 28 54 25 03 . . . . . 99 82 . . . 84 01 08 . . 61 45 . 19 44 . . 10 . 16 39 83 17 71 . 49 . .
. 92 .100 . 14 49 58 53 71 . 81 19 . . 94 60 32 64 . . . 52 99 61 96 36 12 . 38 25 09 . 15 . 08 45 . 48 67 . 29 42 . . . 26 . 86 63 18 55 31 . 82 73 35 . 76 27 93 47 13 69 . 39 84 . 74 05 . 43 . 21 37 23 68 56 16 . . . . . . . 28 01 . . 20 80 11 . 70 . 78 . . 88
. 56 31 . 30 91 . 68 01 74 . 08 76 48 27100 04 . 67 97 . . 54 63 49 94 21 . 81 24 . 39 58 . . 78 . 06 28 . 60 17 38 99 95 88 . . . . 80 . . 98 13 12 40 90 92 . 77 . . 87 44 70 33 . . 18 . . 50 . 62 35 . 03 20 89 96 22 . 65 73 . 75 . . . . 37 10 . 82 52 05 36 09 .
32 . . . . 07 . . . 76 . 53 . 80 . . . . 16 20 . . 93 84 . 13 87 . 82 26 01 31 55 . 24 . . 10 34 11 54 . . . 48 90 . 15 . . . 25 72 . 95 81 47 57 . . . 43 66 . 75 86 63 14 09 96 . 22 33 . . . 45 41 58 . 36 . . 40 . 42 94 79 38 27 . 21 44 . . . 29 . . 03
06 08 45 27 93 10 . 75 23 55 . 72 99 74 78 . 95 59 . . 15 . 32 . . 09 28 04 01 39 82 . 38 . . 54 68 71 29 . 03 66 . 87 35 02 79 81 62 36 05 07 84 51 65 . 20 50100 77 . 16 57 83 94 53 64 76 48 12 . 17 . . 90 . 97 . 14 . 80 25 70 . . . 43 92 56 67 . 24 . . 46 63 42 96 31 26
99 87 64 . 61 24 . . 73 40 . 90 . 54 . . 03 25 65 22 . 91 27 . . . 80 60 98 . 77 . 84 . 13 66 02 72 . 46 58 20 97 07 45 . 57 39 67 76 89 37 . . 63 15 94 . . . . 82 . . 04 30 81 . . 92 12 79 . . . 44 29 . . 96 . 49 . 68 34 18 . . 05 32 86 . 85 47 53 06 93 74 . 41
74 . 16 . 19 71 . . . 10 52 . 77 . 65 09 44 05 82 96 23 . 81 61 67 87 02 43 14 83 . 95 . 04 . . 41 07 68 64 . . 92 . 15 58 91 80 34 93 32 03 06 33 . . 72 . 45 . . 26 39 . . . 53 38 57 . 63 48 35 . 27 66 59 79 50 75 97 62 37 90 24 70 73 . . 29 . 28 22 . 98 . . 69 20 .
24 68 . 58 38 13 . 33 49 . 45 78 41 . . 37 76 . . . 71 . 73 75 05 . 27 30 77 86 . 62 67 . 39 . . 88 51 . . 09 01 . . . 14 50 11 83 . 47 . . . . 84 . 97 23 56 . 95 . . 34 . 08 81 . 52 61 98 65 . 74 03 89 85 10 64 07 12 63 . . 40 48 . 44 . . 70 . 29 57 26 . 15 66
27 22 . 81 59 . 50 . 85 39 . 55 33 . . . . 47 . 63 29 70 96 . . . . 58 . 51 . 20 . . 21 89 35 . 12 34 61 . . 48 . . 97 03 . 54 87 44 . . 37 . 91 26 53 . 69 84 52 76 15 68 41 64 . . . . 07 83 . . 16 . 28 72 30 . 82 66 38 . 93 . 17 79 75 . 56 24 10 11 . 23 14 .
77 31 47 28 64 . . . 78 32 74 . 22 13 60 . . 72 87 . 82 20 46 41 . 63 42100 26 . . 96 . 80 30 . . 45 10 15 23 . 89 62 69 04 86 29 . 49 71 61 35 73 07 90 66 . 17 08 85 37 . 11 50 27 97 65 . . . 36 18 . . 76 84 . . . 39 . 14 83 03 . . 56 . 54 55 40 58 91 48 . . 01 52 12
. . . 18 . 66 54 . 75 . 15 94 . 62 64 06 53 . 07 38 . 10 57 . . 85 68 03 25 . . 13 48 . 40 69 36 . 16 90 99 27 37 41 . 55 08 26 59 . 52 . . . 01 22 . . 04 . . 05 77 61 . 42 . 58 19 14 . 33 . . . 60 12 . . 24 . 74 . 67 31 78 84100 . . 83 . . 95 47 80 87 . . 39
70 . 21 . . 97 45 04 12 . . 32 . 10 28 . 61 93 . . 50 09 07 48 . 52 . 39 . 79 . . . . 46 . 83 18 . 49 73 95 . 36 78 66 . 76 . 65 40 15 11 88100 16 98 25 77 . . . 89 62 . 06 35 . . . . 38 08 . 92 . . 47 31 87 86 72 58 05 43 . 80 81 . . 64 34 33 44 74 96 27 . . .
61 . . 55 . . . 41 44 93 . 48 . . . 14 54 01 .100 . 17 . . 45 . 47 98 69 18 75 . . 92 59 . . 24 82 . 12 19 43 46 52 42 81 94 63 25 13 20 . . . 39 . . 27 . 29 36 71 23 83 22 30 03 16 . 57 09 . . 26 32 67 64 68 40 28 87 . . 10 77 95 96 08 85 49 97 72 05 . . . 06 62 86
. 63 15 92 . . . 26 48 . 25 35 97 98 34 . 49 99 30 80 . 89 . . 28 88 . 44 24 12 57 .100 50 . 61 . 74 03 . 07 . . 38 39 . 32 . 72 45 14 . . 85 . . . . . . 54 01 40 93 . . 96 10 . . . 95 04 . 06 13 . 69 . . 27 20 76 21 36 51 . 22 16 . 71 42 94 41 78 18 37 . . 53
62 . 57 20 . . . . . . 39 . 66 24 . . 68 95 . . . 21 38 . 40 . 22 . 78 . 27 . 56 97 70 . 77 09 58 . 16 . 67 13 02 . 44 79 35 98 64 . 83 . 93 . . 10 94 12 . 48 31 . 63 . 80 87 72 . 71 45 14 54 51 . . 34 55 30 47 04 . 18 . . . 46 . 49 . 07 32 84 . . . 08 89 61
96 91 72 . 60 80 . . . 25 85 12 . 75 19 83 73 03 . . 31 92 35 . . 65 13 . . . 32 66 . . 78 93 . 28 26 54 64 . . . 87 51 . 22 71 33 82 . 56 . 57 . 48 74 41 24 18 . . 70 88 45 09 98100 20 81 15 46 42 . 39 43 62 02 . . 01 . . 53 23 69 . 34 . . 63 . 16 90 77 67 50 . 79
15 . . 62 88 18 12 . . . . .100 61 20 23 55 49 . 66 67 . 19 16 98 07 57 28 . 32 71 91 10 24 35 . 74 68 25 . . 22 . . 97 . . 27 64 29 . . 89 90 77 94 76 . 48 84 43 31 . 60 . 96 59 78 . 63 . 11 44 . 38 . 17 86 . . 13 73 39 75 54 37 83 80 87 53 52 . 95 46 14 08 85 . 33 .
31 11 41 51 . . . . 93 46 . 05 12 67 . 65 34 07 . 48 24 96 92 44 . 49 64 06 68 . 02 . 32 39 54 17 . 29 . . 83 75 55 . . . 04 40 53 . 63 . 28 82 21 20 52 09 79 26 27 . . . 25 57 76 97 13 94 88100 81 . 73 85 . . 60 23 71 . . 72 99 30 . . 45 42 74 35 . . 18 84 58 . 77 70
. 23 . . . 72 . . 17 . 11 54 96 70 68 . 45 37 60 50 . 81 86 20 02 . . . 83 31 . . 79 34 . . . 85 95 59 76 . 10 24 92 . 62 49 73 . 69 93 08 . 46 . 22 . 42 01 26 29 75 . . 71 44 82 58 . 80 03 . 39 14 . . . 25 57 . . 65 94 . 89 . 66 67 63 36 . . . 09 . 48 21 47 .
43 06 09 . . 27 . . 90 44 02 31 75 . 39 . . 33 . . 30 . 59 34 . . 56 . 10 . 62 26 . . 15 . . . 14 42 . 84 61 18 . 21 . 23 50 . 96 . 25 74 16 . 53 . 12 . 32 . 91 22 77 20 01 . 37 . . 67 72 58 45 99 98 68 47 51 24 . . 69 41 85 29 70 35 04 63 71 07 64 83 . . . 11 .
91 . 37 87 73 30 29 39 63 20 42 . 17 . 85 . 18 13 51 77 46 69 21 93 43 27 71 . 52 66 98 19 04 . . . 48 80 53 . 70 . 82 72 68 09 . . 14 . 95 05 .100 40 . . . 54 07 49 65 . 41 . 36 12 23 64 . 59 94 . . . 10 33 22 97 79 31 86 96 74 . 50 02 60 47 34 90 75 03 32 . 62 . . 92 44
76 84 54 . 42 25 . 45 . . 36 19 63 . . . . 73 38 08 75 . . . . 91 78 . 18 . . . . 11 64 . . . 47 . 46 74 . 77 17 39 02 . 43 . 49 88 . 35 55 . 62 04 87 50 86 52 . 92 40 24 . 15 30 68 96 89 26 48 28 82 56 53 34 31 81 21 . 33 . 03 61 . 06 22 . 41 12 97 . . 98 80 27 94
68 78 75 99 . 32 86 35 92 36 98 09 . . . 74 . 88 72 84 22 . 58 76 . 54 53 61 87 50 18 90 94 08 16 37 96 . . . . 89 66 01 . . . . . . . . . . 70 60 65 . 38 71 14 04 . . 46 80 95 33 . 51 . 40 12 . . . 83 . 64 02 15 11 19 43 28 27 . 26 97 25 82 06 67100 . 49 31 57 10 55
60 . 02 . . 70 24 . 14 50 . . 44 . . . 64 . . 52 . 33 77 40 . 39 97 11 . 73 . 28 . . . 05 . . . . 57 . 59 98 . . 19 .100 48 23 . 30 15 66 43 32 61 86 31 62 74 83 72 35 16 34 . . 47 91 . . 18 . 37 93 75 92 . 08 56 09 . 88 82 58 90 46 . . 87 68 76 . 17 20 . . 29
. . 67 34 85 94 . . 40 79 91 43 10 . 53 . 78 04 86 14 . 42 60 05 70 . . 88 65 63 45 82 . 23 . . 55 83 72 87 38 . 58 . 90 47 15 . . . 24 . 97 . . . 51 . . 44 . 07 61 03 73 . . 66 . 09 08 . 27 29 . 84 76 13 . 69 62 12 17100 77 57 . . . 59 50 . 81 . . 19 30 22 . .
. 47 53 64100 . . . 19 38 30 76 26 92 58 28 . . . . . 25 12 . . . . . 80 . 69 36 . 75 66 65 40 31 84 . 32 51 11 60 63 . 88 . . 35 34 33 29 59 . . . 67 39 . . 42 . 18 . 81 17 . 10 06 15 . . 01 46 . 52 71 90 61 16 . 48 . . 44 55 93 49 07 13 . 78 45 91 . 43 . 37 .
17 16 33 . . . 07 . 98 . 54 . 60 68 . . 35 50 . . 84 . 02 . 86 . 31 . 20 74 . . 12 . 61 95 34 . . . . . 49 . 76 24 30 10 41 . . . 46 . 08 . 27 22 93 . 44 . 28 29 58 82 . . 38 75 87 25 55 14 . 80 . . 03 78 . 89 63 32 . 91 67 64 52 65 . . 36 21 04 . 53 . 56 47
. . 38 . . 74 . . 22 . . 30 27 58 92 41 . 82 . . 95 14 . 80 12 03 . . . 72 66 77 36 40 69 . . 97 65 31 . 94 . 08 32 . 35 11 51 88 57 39 02 83 . 34 67 68 . 59 17 . 06 42 10 85 99 81 87 50 54 90 71 46 . 15 61 . 62 52 . 44 . . . 98 49 . 55 48 . . 13 73 86 43 24 . 05 .
40 . . . 28 . 34 94 . 67 43 91 86 53 06 78 . . . . . . . . 60 48 . 42 . . 33 49 . . 45 72 23 87 20 83 . 56 . 47 38 31 95 . 54 15 37 36 80 44 97 24 75 51 98 64 89 . 09 07 39 . . 11 73 . 84 74 . . 29 08 69 27 41 76100 57 . 62 68 . 18 . 92 . 81 26 50 . 01 30 . 25 93 02
26 88 82 12 . 03 62 18 15 56 99 . . 20 61 55 23 66100 49 07 28 98 36 19 . 32 41 16 57 35 . 91 74 . 25 . 21 01 68 . . 27 81 . . . 65 22 05 . 48 77 84 89 72 . 76 . . 59 60 . 31 . 78 43 96 70 79 . . 86 38 30 09 50 44 . 17 75 37 53 . . . . 54 . . 95 . 52 51 . 85 08 . 34 33
. 73 20 . . 39 87 30 91 37 24 . . 85 01 18 57 77 17 13 27 . 43 52 . . . 69 93 71 38 04 19 48 . 53 . 56 81 80 68 . 99 . 70 . 28 . . 67 45 54 . 07 . 95 11 . 05 . 12 . 88 65 . 23 . 36 08 55 . 97 22 35 16 59 79 . 94 33 . 50 . 31 60 . . 84 02 96 03 15 . . 75 . 62 32 44 92
92 48 36 86 78 35 99 32 68 . 09 . 72 79 29 59 . 84 81 88 54 . 62 . . 22 50 13 76 . 16 94 90 96 18 . 08 63 . . 91 42 85 44 . . 69 66 89 . . 38 70 71 . 17 56 . . 47 . 45 51 04 05 33 . . 46 93 24 64 21 . 20 77 02 . 40 83 43 27 25 15 26 11 97 28 . 19 . 39 82 57 . 31 49100 55 10
90 49 44 95 . 55 65 27 43 09 . 02 80 39 93 89 97 . 75 33 17 08 94 . 59 . 82 38 34 56 15 88 . 46 62 . 57 42 73 92 86 50 23 21 36 18 78 61 . 52 . 12 16 19 25 96 . . 81 74 . 22100 . 37 48 . 20 77 . . 47 68 45 58 05 51 . 67 98 69 85 . 24 70 . 35 41 29 . 07 83 63 60 71 66 . . . 11
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by **z666zz666z** » Fri Mar 08, 2013 3:55 pm

Thanks m_b_metcalf,

I have done a Copy&Paste of the 100x100 (second version), then i replaced '.' with spaces... and that is on what you call "z666zz666z format", to be perfectly strict... the format is "ASCII fixed column"... not any made by me...

It does not matter if when no digit you use "Space" or "." or "-", etc... just something different form a "number", but the important thing for a "standard fromat" is that such zeroes appear on numbers so if you use 1 up to 100, the format for each cell would be #### (four digits) since the least number of digits to represent a cell value would be four (just to hold the value 1000), so values would go as this: 0000 0001 0002 ...up to... 1000; but if you start on 0 and up to 999 then the format can have one digit less for each cell, as this 000 001 002 ...up to... 999.

Well that is the technical reason... the other important reason to have the "format" as a Fixed Length for each cell (each cell with same number of characters onto the file) comes from the need to hold the data on HDD since on RAM does not fit (for very huge ones, remember 1000 x 1000 and millon x millon), so for such huge data it is not practical to represent empty cells with a different number of characters than a non empty cell.

Anyone use the format that wants... i will still use a "standard format" that allows "direct access" to each cell without the need to read any other part of the file... imagine you have a DataBase on a plain text file and each record would have a different size, how do you read the record number one millon of a total of ten millon records? you would need to do a sequential read, not just a random read... etc etc ... that is the top most reason to have a "fixed record size", let the access to be direct, no need to read things that are before, just do a multiplication and read there... i think it is enough clear, else read WikiPedia or other medium that talks about "Fixed length records versus Variable length records"... etc...

Well, about the other point...

It is True that "Sudokus" normally are (sorry to correct you, but i must point it out for people that do not know about them that can not be perfect squares) N^2 * M^2 (N and M can not be the same number)...

But there are also come other that are not N^2 * M^2, for example you can make very simple rectangular Sudoku like this (rectangular, not square):

Code: Select all: 12. .3.

The solution to it is:

Code: Select all: 123 231

As you see the Sudoku is a 3x2 one, yes this one is too strange to be seen as a Sudoku, but it is... to express it perfectly detail it must be called a 1x1-3x2 Sudou... while normal 9x9 Sudoku must be expressed as 3x3-3x3 one... i explain this later on the post.

Most common non square Sudokus are on the form of N^M x M^N, for example 3^2 x 2^3, etc...

Note: I do not have any relation with the web i put links to... it is just one i found using Google Search... if you need maybe i can find other pages... but since just as a "poof of concept" it is valid with just one.

Here you can see a rectangular one:
http://www.sachsentext.de/en/taxonomy/term/6

But they can also be Triangular:
http://www.sachsentext.de/en/taxonomy/term/145

And also Hexagonal:
http://www.sachsentext.de/en/taxonomy/term/144

But also with more strange forms, like Spiral, etc...
http://www.sachsentext.de/en/taxonomy/term/152

That web has a lot of types... a relly huge amount of different types (that is the reason i put diret links to it, as i said i have no relation with it and till today i did not know about it... i have added to Favourites)

Etc. etc.

Till now my algorithm / program was restricted to NxM (with no limit on N and M values, from 1 up to a millon, but Integer of course).

I know most of people that create algorithms for Sudoku solvers allways think on what they know (or have seen), me not... i allways do the opposite... just try to support more than what i know... like that... for example... some time ago i had at my hands a small magazine with traditional 9x9 sudokus, but hey after some pages ther where some with an X form (well that ones that are really five sudokus, central one sharing one corner block), and some pages after there where some rectangular ones.

I hope, now such points can be a little more clear.

Can you imagine now how is a 50x50 one? I know that is not enough info... i must say how much values can go on each cell... if i say only five... you can get it very easy... ten x ten groups of 5x5, each one a "small" Sudoku of 5x5, but hey, remember that on such 50 cells rows and columns there can only be 10 times the same number... it implies more rules that "Standard" Sudokus...

But you can make a 50x50 as a just one block...

I will explain this, so it can be just more clear:

The typical Sudoku is a 3x3-3x3 (Three blocks on Horizontal x Three blocks on vertical, each block with 3x3 cells)
Well imagine a Sudoku of 1x1 - 9x9 (One block on Horizontal x One block on vertical, each block with 9x9 cells), this one is like a normal 9x9 Sudoku except if has no "block" rule, no 3x3 blocks inside the 9x9 block, much more easy to solve it

For example this will be a valid solution for a 9x9 Sudoku [1x1-9x9 to be trully specific]:

Code: Select all: 123456789 234567891 345678912 456789123 567891234 678912345 789123456 891234567 912345678

That is a "Good"/"Valid" solution for a 1x1-9x9 Sudoku, but not for a 3x3-3x3 Sudoku (the common known as "Sudoku")...

Remember that Sudokus has two Grids, one Bigger (outer one), one Smaller (Inner one)... so if you want to create a 50x50 one... you can do it as all this ways (with both grids as a square):
- 1x1-50x50 (This is very easy, numbers from 01 up to 50 or 00 up to 49, rules are only for Rows and Cols, no more rules)
- 2x2-25x25 (This one has numbers only from 01 up to 25, or 00 up to 24, normal rules, each number twice on each row and column, but just once on each inner grid of 2x2 size)
- 5x5-10x10 (This one has numbers only from 0 up to 9... same rules as previous one, each number appear five times on each row and col)
- 10x10-5x5 (This one has numbers only from 0 up to 4... same rules as previous one, each number appear ten times on each row and col)
- 25x25-2x2 (This one has numbers only from 0 or 1... same rules as previous one, each number appear twenty five times on each row and col)
- 50x50-1x1 (This is ridiculus, all cells with same exact number)

Hope now is it more clear!!!

The notation of NxN-MxM is Standard, not mine... N represents the number of blocks, each of this block havving MxM cells.

Since it is most common to simplify the notation... it is normally reduced to just (N*MxN*M) and represented as (AxB)...

Hope know your mind is more "open"... i do not only solve "normal" Sudokus, also such other ones (buy now, only Square and rectangular).

Thanks for asking for such, so i could explain it more or less, well or bad... i do my best (my native language is not English, sorry for mistakes) ...

My error was thinking it was clear for all people that not all Sudokus have the same Shape and size, i hope that now it will be more clear for at least one more person.

Thanks a lot.

by **m_b_metcalf** » Fri Mar 08, 2013 4:50 pm

Well, thanks very much for all that instruction :roll:

. Many of us will be much enlightened

. Now we just await your solution to the posted puzzle(s) and knowing where you found your 10000x10000.

Regards,

Mike Metcalf

P.S. Out of curiosity, whar is your native language?

P.P.S. With "well that ones that are really five sudokus, central one sharing one corner block" you probably mean a samurai, gattei or butterfly, like the ones m_b_metcalf posted here?

by **m_b_metcalf** » Sat Mar 09, 2013 9:24 am

I have produced the very difficult 100x100 puzzle below. However, my solver cannot solve it (after 6 hours), nor can I prove it has only one solution. Can someone else please check it (gsf, are you still there?)?

Thanks,

Mike Metcalf

P.S. The obvious question is, how can I produce a puzzle that I can't solve? The answer is that the puzzle is produced by removing a clue at a time, and each successful step helps the next. When solving the finished puzzle from scratch, no such help is available. I do, of course, have the solution (if there's only one).

. 33 21 . . 05 66 . 63 . . 83 17 58 04 . 90 . . 75 80 . . 94 . 76 97 . . 29 48 86 . . 73 45 06 59 54 15 39 01 . 14 . . 16 40 . 30 . 68 03 . .100 . 95 07 28 69 84 25 56 . 89 . . 50 . . 81 . 35 78 . . 65 12 . 36 99 79 . . . . 26 24 . 87 60 27 52 49 91 72 70 62 .
49 94 11 15 . 92 74 . 29 25 40 . 46 39 . 62 . 82 88 . 27 . . 02 . 77 . 96 28 . 07 . 13 . 87 . 19 80 38 24 . 47 76 . . 33 45 85 75 79 34 61 . . 09 83 18 78 50 . 36 58 . 20 51 66 54 68 05 86 26 17 23 93 . . 72 64 . 89 55 35 .100 . . . 97 . 91 08 57 . 81 63 . 98 65 22 .
40 73 . . 17 75 . . . 91 81 27 97 . . . . 05 35 . . 53 78 85 54 65 18 72 69 16 10 68 . . . 99 71 04 79 90 . 46 51 . 03 . 57 29 . 23 55 . . . . . 94 45 74 59 . 43 34 12 70 . . . . . 61 52 . . 33 28 . 62 . 76 22 31 . . 96 66 13 39 11 . 56 . 36 . 58 89 . . .100
56 69 60 34 44 58 42 . 03 26 13 43 12 06 02 18 . . 84 67 10 30 81 . . . . 04 11 . 88 17 . 28 . . 50 . .100 41 . . 63 . . . 71 . 09 82 79 89 62 . 65 29 72 . . 59 . . 16 85 . . 53 83 . . . . 32 . . 46 96 36 . . 93 23 48 05 80 78 08 . . 75 . 45 61 92 . 31 . . 95
55 32 95 . . 22 76 46 . 97 . . 54 10 48 14 31 34 . 61 . 73 . . 87 . . 17 . 08 09 . 91 . 66 . . 74 89 02 13 11 . . . 62 12 72 . 65 . . . . 35 . 16 . 70 . 82 . . 23100 94 . 99 96 79 30 . . . 92 . 63 . 07 . 98 . . . . 60 88 . 50 67 68 04 40 69 24 80 . . . 06
. 53 . 47 50 87 . 18 02 16 . 66 94 11 32 07 92 63 . 52 25 83 35 26 . . . . 49 95 27 . 44 98 82 . . . 39 .100 43 97 81 48 . 88 . 17 60 91 . . . 08 84 96 06 . 77 90 . . . 40 03 22 42 30 41 24 80 38 . 01 . . . . 69 . 04 59 33 . 64 71 62 61 . . 76 46 . 10 93 . . 23 05
. 36 . 90 85 . 81 77 57100 74 33 89 . . 86 37 . . 42 . 47 . 56 . 41 . 62 52 . 51 . . 21 94 58 . . 03 . 95 27 05 . . 25 19 . 44 54 . . . 93 04 99 17 . 66 12 . 76 . 80 13 39 24 . . . 88 55 31 73 97 60 53 14 22 20 72 68 34 . . . 40 46 75 . 07 78 . . 48 . 02 . 71 .
04 . . 37 19 89 31 . 35 59 64 . 56 65 . . . 78 72 85 03 93 . 12 14 . 45 75 48 . 83 97 42 08 . . . 57 . 61 80 96 . . 58 28 52 34 86 10 . . . . . . 36 33 30 . 60 26 01 63 91 71 73 27 . . 68 . . 95 . . 05 . . 99 . 94 . 92 . . 29 17 06 49 50 43 18 . . . 13 . . 39
. 06 . 79 68 . . . 28 27 55 .100 . . 95 . 53 . . . . . . 70 57 40 51 46 88 36 69 96 25 41 85 60 56 62 . 66 90 . . 08 91 84 . . 42 . 39 26 . 14 75 . . 67 24 04 . 21 . 78 . 72 87 . . 50 . 77 . 83 . 48 47 71 43 . 09 65 . . 44 32 01 . 89 34 29 97 33 12 . 59 16 73 .
65 71 . 93 70 01 . . 45 . 79 . 87 96 49 26 . . . . 05 89 82 . . 19 . 92 66 74 . 14 75 . . . 43 . . 31 . 67 83 68 36 . 59 . 98 73 10 . 38 . 80 40 02 . 48 15 97 62 . 07 . . . 17 . 09 . 03100 04 . 39 . 91 . . 18 . . . 90 16 . . 69 . 47 94 30 . 88 35 20 55 99 64
17 93 47 . 61 56 . 36 66 . 62 25 34 . 37 . 12 33 51 90 18 . . 57 . 68 69 74 . . . 58 32 64 98 73 72 35 78 . 43 97 . 04 . 92 71 67 91 22 96 . 02 95 48 08 87 44 21 45 39 . . 31 59 20 49 50 84 16 . 86 41 . . 52 70 60 38 79 10 . . . . . 65 85 03 77 . 01 53 54 . . . 42 63 .
19 24 12 87 . . 40 27 34 79 82 88 92 17 13 . 35 54 38 09 91 . 75 . 77 . . 56 . 10 25 74 . 63 . . 15 03 . 36 46 81 . 32 . 39 11 18 64 . 60 . . 16 . 61 70 01 58 . 05 . 45 99 . . 21 . . . . 69 04 51 . 48 94 . 76 84 90 . . . 73 . 30 . 02 68 83 07 . . . . 33 71 66 98
51 01 18 16 08 . 02 49 15 94 . . . . . 81 41 44 70 45 61 66 . 21 . 73 87 63 . . . . . . . . . 68 . 26 84 12 . . 23 88 83 . . . 57 28 52 29 33 . 35 . 77 03 78 48 98 14 . . 71 36 . 55 74 . . 58 99 10 17 . . . 40 07 56 . 20 . . 38 . 46 . . 65 89 . 39 . 91 59 .
53 95 . . 45 81 . 11 . 64 05 39 08 . 76 . 55 97 36 14 . 33 . . 96 67 24 94 . 43 91 20 . 04 50 . 29 46 . 52 42 79 73 51 26 . 15 30 54 17 69 59 . 85 68 47 . . 27 09 23 . . . . . . . . 07 35 65 . 77 71 93 . 92 18 . . . 86 28 57 . . 32 98 12 . 37 99 . 80 60 . 13 . .
. 35 33 59 . 85 . 42 58 . 22 57 10 95 29 32 46 28 . 69 01 . 47 30 . 36 76 06 . . 93 34 39 88 . . . 19 56 97 05 . 99 . 50 21 . . 45 55 67 . 41 86 66 74 63 92 51 40 87 . 37 27 53 24 02 . . . . . 98 81 . . . 83100 07 . . 60 44 . 18 43 . . 09 . 15 38 82 16 70 . 48 . .
. 91 . 99 . 13 48 57 52 70 . 80 18 . . 93 59 31 63 . . . 51 98 . 95 . 11 . 37 24 08 . 14 . 07 44 . 47 66 . 28 41 . . . 25 . 85 62 17 54 30 . 81 72 34 . 75 26 92 46 12 68 . 38 83 . 73 04 . 42 . 20 36 22 67 55 15 . . . . . . . 27100 . . 19 79 10 . 69 . 77 . . 87
. 55 30 . 29 90 . 67100 73 . 07 75 47 26 99 . . 66 96 . . 53 62 48 93 20 . 80 23 . 38 57 . . 77 . 05 27 . 59 16 37 98 94 87 . . . . 79 . . 97 12 11 39 89 91 . 76 . . 86 43 . 32 . . 17 . . 49 . 61 34 . . 19 88 95 21 . 64 72 . 74 . . . . 36 09 . 81 51 04 35 08 .
31 . . . . 06 . . . 75 . 52 . 79 . . . . 15 19 . . 92 83 . 12 86 . 81 25100 30 54 . 23 . . 09 33 10 53 . . . 47 89 . 14 . . . 24 71 . 94 80 46 56 . . . 42 65 . 74 85 62 13 08 95 . 21 32 . . . 44 40 57 . 35 . . 39 . 41 93 78 37 26 . 20 43 . . . . . . .
. 07 44 26 92 . . 74 22 54 . 71 98 73 77 . 94 58 . . 14 . 31 . . 08 27 03100 38 81 . 37 . . 53 67 . 28 . 02 65 . 86 34 01 78 . 61 35 04 06 83 50 64 . 19 49 99 76 . 15 56 82 93 52 63 75 47 11 . 16 . . 89 . 96 . 13 . 79 24 69 . . . 42 91 55 66 . 23 . . 45 62 41 95 30 25
. 86 . . 60 23 . . 72 39 . 89 . 53 . . 02 24 64 . . 90 26 . . . 79 . 97 . 76 . 83 . 12 65 01 71 . 45 57 19 96 06 44 . 56 38 66 75 88 36 . . 62 14 93 . . . . 81 . . 03 29 80 . . 91 11 78 . . . 43 . . . 95 . 48 . 67 33 17 . . 04 31 . . 84 46 52 05 92 73 . 40
73 . 15 . 18 70 . . . 09 51 . 76 . 64 08 43 04 81 95 22 . 80 60 66 86 01 42 13 82 . 94 . 03 . . 40 06 67 63 . . 91 . 14 57 90 79 33 92 31 02 05 . . . 71 . 44 . . 25 38 . . . 52 37 56 . 62 47 34 . 26 65 58 78 49 74 96 61 36 89 23 69 72 . . 28 . 27 21 . 97 . . 68 19 .
23 67 . 57 37 12 . 32 48 . 44 77 40 . . 36 . . . . 70 . 72 74 04 . 26 29 76 85 . 61 66 . 38 . . 87 50 . . 08100 . . . 13 49 10 82 . 46 . . . . 83 . 96 22 55 . 94 . . 33 . 07 80 . 51 60 97 64 . 73 02 88 84 09 63 06 11 62 . . 39 47 . 43 . . 69 . 28 56 25 . 14 65
26 21 . 80 58 . 49 . 84 38 . 54 32 . . . . 46 . 62 28 69 95 . . . . 57 . 50 . 19 . . 20 88 34 . 11 33 60 . . 47 . . 96 02 . 53 86 43 . . 36 . 90 25 52 . 68 83 51 75 14 67 40 63 . . . . 06 82 . . 15 . 27 71 29 . 81 65 37 . . . 16 78 74 . 55 23 09 10 . 22 13 .
76 30 . 27 63 . . . 77 31 73 . 21 12 59 . . 71 86 . 81 19 45 40 . 62 41 99 25 . . 95 . 79 29 . . 44 09 14 22 . 88 61 68 03 85 28 . . 70 60 . 72 06 89 65 . . . 84 36 . 10 49 26 96 64 . . . 35 17 . . 75 83 . . . 38 . 13 82 02 . . 55 . 53 54 39 57 90 47 . .100 51 11
. . . 17 . 65 53 . 74 . 14 93 . 61 63 05 52 . 06 37 . 09 56 . . 84 67 02 24 . . 12 47 . 39 68 35 . 15 89 98 . 36 40 . 54 07 25 58 . 51 . . .100 21 . . 03 . . 04 76 60 . 41 . 57 18 13 . 32 . . . 59 11 . . 23 . 73 . 66 30 77 83 99 . . 82 . . 94 46 79 86 . . 38
. . . . . 96 44 03 11 . . 31 . 09 27 . 60 92 . . 49 08 06 47 . 51 . 38 . 78 . . . . 45 . 82 17 . 48 72 94 . 35 77 65 . 75 . 64 39 14 . 87 99 15 97 24 76 . . . 88 61 . 05 34 . . . . 37 07 . 91 . . 46 30 86 85 71 57 04 42 . 79 80 . . 63 33 32 43 73 95 26 . . .
60 . . 54 . . . 40 43 92 . 47 . . . 13 53100 . 99 . 16 . . 44 . 46 97 68 17 74 . . 91 58 . . . 81 . 11 18 42 45 51 41 80 93 62 24 12 19 . . . 38 . . 26 . 28 35 70 22 82 21 29 02 15 . 56 08 . . 25 31 66 63 67 39 27 86 . . 09 76 94 95 07 84 48 96 71 04 . . . 05 61 85
. 62 14 91 . . . 25 47 . 24 34 96 97 33 . 48 98 29 79 . 88 . . 27 87 . 43 23 11 56 . 99 49 . . . 73 02 . 06 . . 37 38 . 31 . 71 44 13 . . . . . . . . . 53100 39 92 . . 95 09 . . . 94 03 . 05 12 . 68 . . 26 19 75 20 35 50 . 21 15 . 70 41 93 40 77 17 36 . . 52
61 . 56 19 . . . . . . 38 . 65 23 . . 67 94 . . . 20 37 . 39 . 21 . 77 . 26 . 55 96 69 . . . 57 . 15 . 66 12 01 . 43 78 34 97 63 . 82 . 92 . . 09 93 11 . 47 30 . 62 . 79 86 71 . 70 44 13 53 50 . . . 54 29 46 03 . 17 . . . . . 48 . 06 31 . . . . 07 88 60
95 90 71 . 59 79 . . . 24 84 11 . 74 18 82 72 02 . . 30 91 34 . . 64 12 . . . 31 65 . . 77 92 . 27 25 53 63 . . . 86 50 . 21 70 32 81 . 55 . 56 . 47 73 40 23 17 . . 69 87 44 08 97 99 19 80 14 45 41 . 38 42 61 01 . .100 . . 52 22 68 . 33 . . 62 . 15 89 76 66 49 . 78
14 . . 61 87 17 11 . . . . . 99 60 19 22 54 48 . 65 66 . 18 15 97 06 56 27 . 31 70 90 09 23 34 . 73 67 24 . . 21 . . 96 . . 26 63 28 . . 88 89 76 93 75 . 47 83 . 30 . 59 . 95 58 77 . 62 . 10 43 . 37 . 16 85 . . 12 72 38 74 53 36 82 79 86 52 51 . 94 45 13 07 84 . 32 .
30 10 40 50 . . . . 92 45 . 04 11 66 . 64 33 06 . 47 23 95 91 43 . 48 63 05 67 . 01 . 31 38 53 16 . 28 . . 82 74 54 . . . 03 39 52 . 62 . 27 81 20 19 . 08 78 25 . . . . 24 56 75 96 12 93 87 99 . . 72 . . . 59 22 70 . . 71 98 29 . . 44 41 73 34 . . 17 83 57 . 76 69
. 22 . . . 71 . . 16 . 10 53 95 69 67 . 44 36 59 49 . 80 85 19 01 . . . 82 30 . . 78 33 . . . 84 94 58 75 . 09 23 91 . 61 48 72 . 68 92 07 . . . . . 41100 25 28 74 . . 70 43 81 57 . 79 02 . 38 13 . . . 24 56 . . 64 93 . 88 . 65 66 62 35 . . . 08 . . 20 46 .
42 05 08 . . 26 . . 89 43 . 30 74 . 38 . . 32 . . 29 . 58 33 . . 55 . 09 . 61 25 . . 14 . . . 13 41 . 83 60 17 . 20 . 22 49 . 95 . 24 73 15 . 52 . 11 . 31 . 90 21 76 19100 . 36 . . 66 71 57 44 98 97 67 46 . 23 . . 68 40 84 28 69 34 03 62 70 06 63 82 . . . 10 .
90 . 36 86 72 29 28 38 62 19 41 . 16 . 84 . 17 12 50 76 45 68 20 92 42 26 70 . . 65 97 18 03 . . . 47 79 52 . 69 . 81 71 67 08 . . 13 . 94 04 . 99 39 . . . 53 06 48 64 . 40 . 35 . 22 63 . 58 93 . . . 09 32 21 96 78 30 85 95 73 . 49 01 59 46 33 89 74 02 31 . 61 . . 91 43
75 83 53 . 41 24 . 44 . . 35 18 62 . . . . 72 37 07 74 . . . . 90 77 . 17 . . . . 10 63 . . . 46 . 45 73 . 76 16 38 01 . . . 48 87 . 34 54 . 61 03 86 . 85 51 . 91 39 23 . 14 29 67 95 88 25 47 27 81 55 52 33 30 80 20 . 32 . 02 60 . 05 21 . 40 11 96 . . 97 79 26 93
67 77 74 98 . 31 85 34 91 35 97 08 . . . 73 . 87 71 83 21 . 57 75 . 53 52 60 . 49 17 89 93 07 . 36 95 . . . . 88 65100 . . . . . . . . . . 69 59 64 . 37 70 13 . . . 45 79 94 32 . 50 . 39 11 . . . 82 . 63 01 14 10 18 42 27 26 . 25 96 24 81 05 66 99 . 48 30 . 09 54
59 . 01 . . 69 23 . 13 49 . . . . . . 63 . . 51 . 32 76 39 . 38 96 10 . 72 . 27 . . . 04 . . . . 56 . 58 97 . . 18 . 99 47 22 . 29 14 65 . 31 60 85 30 61 73 82 71 34 15 33 . . 46 90 . . 17 . 36 92 74 91 . 07 55 08 . 87 81 57 89 45 . . 86 67 75 . 16 19 . . 28
. . 66 33 84 93 . . 39 78 90 42 09 . 52 . 77 03 85 13 . 41 59 04 69 . . 87 . 62 44 81 . 22 . . 54 82 71 86 37 . 57 . 89 46 14 . . . 23 . 96 . . . . . . 43 . 06 60 . 72 . . 65 . 08 07 . 26 28 . 83 75 . . 68 61 11 . 99 76 56 . . . 58 49 . 80 . . 18 29 21 . .
. 46 52 63 99 . . . 18 37 29 75 25 91 57 27 . . . . . 24 11 . . . . . 79 . 68 35 . 74 65 64 39 30 83 . 31 50 10 59 62 . 87 . . 34 33 32 28 58 . . . 66 38 . . . . 17 . 80 16 . 09 05 14 . .100 45 . 51 70 89 60 15 . 47 . . 43 54 92 48 06 12 . 77 44 90 . 42 . 36 .
16 15 32 . . . 06 . 97 . 53 . 59 67 . . 34 49 . . 83 . 01 . . . 30 . 19 73 . . 11 . 60 94 . . . . . . 48 . 75 23 29 09 40 . . . 45 . 07 . 26 21 92 . 43 . 27 28 57 81 . . 37 74 86 24 54 13 . 79 . . 02 77 . 88 62 31 . 90 66 63 51 64 . . 35 20 03 . 52 . 55 46
. . 37 . . 73 . . 21 . . 29 26 57 91 40 . 81 . . 94 13 . 79 11 02 . . . 71 65 76 35 39 68 . . 96 64 30 . 93 . 07 31 . 34 10 50 87 56 38 01 82 . 33 66 67 . 58 16 . 05 41 09 84 98 80 86 49 53 89 70 45 . 14 60 . 61 51 . 43 . . . 97 48 . 54 47 . . 12 72 85 42 23 . 04 .
39 . . . 27 . 33 93 . 66 42 90 85 52 05 77 . . . . . . . . 59 47 . 41 . . 32 48 . . 44 71 22 86 19 82 . 55 . 46 37 30 94 . 53 14 36 35 79 43 96 23 . 50 97 63 88 . 08 06 38 . . 10 72 . 83 73 . . 28 07 68 26 40 75 99 56 . 61 67 . 17 . 91 . 80 25 49 .100 29 . 24 92 .
25 87 81 11 . 02 . 17 14 55 98 . . 19 60 54 22 65 99 48 06 27 97 35 18 . 31 40 15 56 34 . 90 73 . 24 . 20100 . . . 26 80 . . . 64 21 04 . 47 76 83 88 71 . 75 . . 58 59 . 30 . 77 42 95 69 78 . . 85 37 29 08 49 43 . . 74 36 52 . . . . 53 . . 94 . 51 50 . 84 07 . . 32
. 72 19 . . 38 86 29 90 36 23 . . 84100 17 56 76 16 12 26 . 42 51 . . . 68 92 70 37 03 18 47 . 52 . 55 80 79 67 . 98 . 69 . 27 . . 66 44 53 . 06 . 94 10 . 04 . 11 . 87 64 . 22 . 35 07 54 . 96 21 34 15 58 78 . 93 32 . 49 . 30 . . . 83 01 95 02 . . . 74 . 61 31 43 91
91 47 35 85 77 34 98 31 67 . 08 . 71 78 . 58 . 83 80 87 53 . 61 . . 21 49 12 75 . 15 93 89 95 17 . 07 62 . . 90 41 84 43 . . 68 65 88 . . 37 69 70 . 16 55 . . 46 . 44 50 03 04 32 . . 45 92 23 63 20 . 19 76 01 . 39 . 42 26 24 14 25 10 96 27 . 18 . 38 81 56 . 30 48 99 54 09
89 48 43 94 . 54 64 26 42 08 . 01 79 38 92 88 96 . 74 32 16 07 93 . 58 . 81 37 33 55 14 87 . 45 61 . 56 41 72 91 85 49 22 20 35 17 77 60 . 51 . 11 15 18 24 95 . . . 73 . . 99 . 36 47 . 19 76 . . 46 67 44 57 04 50 . 66 97 68 84 . 23 69 . 34 40 28 . 06 82 62 59 70 65 . . . 10
92 . 45 60 10 68 50 . 30 40 . 02 61 14 66 . 64 . 11 06 48 05 . 67 91 23 89 . 43 63 53 31 88 85 . . 38 49 16 28 32 52 39 79 82 . 86 54 . 03 19 78 20 25 27 62 . 51 . 81 75 55 93 97 12 . . 56 24 18 84 59 94 72 42 . 22 80 99 65 . . . . 77 13 . 98 35100 15 17 73 37 34 . 83 . 69 76
13 80 49 23 79 88 . . 59 01 21 20 68 24 94 . . . 43 93 38 . . . . 54 . . 39 96 06 05 . 66 . 26 . 50 04 40 . . 12 11 . . 47 58 25 18 . . 65 30 29 22 60 31 . 14 33 71 . . 52 . . 15 . 82 36 91 . 62 . . . 35 . 92 . . . 07 89 55 45 87 . . . . 95 41 86 19 . 75 28 53
. 41 58 65 83 44 56 24 75 . 18 . . . 82 15 . . . 72 . . . 17100 74 99 84 . 77 63 . 98 57 59 . . 43 08 69 16 . 70 38 . 76 . . . . 09 86 54 . . . . 61 . 34 66 . 67 . . . 85 23 . 68 . 33 . 27 . 95 30 25 88 55 32 02 21 80 50 20 05 04 60 94 11 . 22 79 40 97 64 96 93 26
. 58 38 . 21 45 . 72 . 87 . . . 70 41 39 . . . 46 . 57 79 18 95 28 . 69 93 94 20100 19 34 64 11 97 33 88 . 73 . 02 56 60 . . 59 76 96 85 . 36 08 . 86 25 90 43 . . . 42 83 31 . 68 . 14 . . 27 89 . 82 77 71 . 98 15 65 05 . . 24 12 16 . 92 81 55 09 . . . 44 . . 35 13
11 66 93 . . 03 22 96 69 20 . 56 58 27 . 60 83 25 . . 51 38 52 36 . . . 08 47 . 45 70 28 . 54 41 62 48 98 . . 89 . 65 72 . . 74 94 81 15 . 99 . 10 39 . . 14 . 34 . . . 23 12 50 05 16 . 21 30 46 91 18 19 86 07 .100 04 40 90 . 80 71 67 . 79 57 . 73 . 02 . . 95 . 84 .
88 18 09 . 16 83 41 . 73 15 85 51 81 64 . 43 08 . 76 . 86 42 . 13 80 . .100 . 01 30 59 . . 46 . . . 84 06 . 33 79 57 . . . 91 . 90 29 . . . 05 31 . 71 02 32 52 11 77 . . . 93 . . 38 65 49 78 26 55 62 74 34 . 58 89 . 28 . 10 61 87 . . 36 21 97 24 68 . 50 45 53 . .
43 75 . . 64 40 54 . 60 06 47 78 69 . 88 . . . 49100 59 . . . 73 55 . 16 . 46 58 36 . 90 74 . 91 83 . 23 . . . 41 . . . . . 80 38 26 50 20 . 12 57 . 19 33 . 22 03 . . 02 28 21 82 70 31 67 . . 87 56 39 . . . 01 . 84 . 95 86 . . 94 14 71 30 48 05 96 37 34 04 . 61
77 63 31 01 30 . 27 33 76 46 . . 86 . 12 66 42 50 . . 62 . . 25 . 81 98 . . . 29 04 95 78 80 . 79 14 18 44 68 23 . 03 22 61 48 . 05 . . . 06 07 34 70 . 65 60 72 96 10 . . 32 64 84 26 49 58 75 92 93 69 52 . 24 17 35 . 82 . 53 . . 74 . 02 56 13 . 47 54100 39 . 08 . 11 51
99 81 05 . 02 . . 28 61 56 16 38 90 . 23 67 91 . 65 . 75 . . 77 37 89 . 20 32 . 69 . 24 . 26 . . 51 10 08 01 34 78 52 . 12 97 . 84 43 . 93 92 . 82 63 09 . 95 04 79 72 . 47 . . 74 . 62 30 40 . 33 50 53 . 29 13 44 36 . . . . 45 . 41 18 . 98 . 42 . 07 . 58 87 . 60 88
. . 82 08 62 25 . 51 78 14 . 24 29 33 97 48 . 79 . 98 87 43 . . 90 63 11 . . . 85 99 22 . 56 . 49 07 60 73 38 . 55 83 06 . . 16 30 31 01 64 67 54 . 13 42 58 69 . 95 . 66100 . . 53 45 46 39 12 . 68 05 76 72 57 03 . 81 . . . . . 19 15 35 59 75 93 77 70 80 . 36 17 40 52 18
. 34 50 53 97 55 17 . . 29 93 . 06 . 61 52 05 . 19 . . . . 24 . . . 09 96 . 39 . 12 35 71 . 42 89 68 . 87 58 . . . 40 . 36 26 . 21 03 . 88 78 . . 62 . 80 91 60 . 04 18 57 27 . . 76 59 90 28 . 22 . 23 . 32 11 66 77 . 08 . . 49 30 . 70 01 46 82 64 72 86 79 . 38 .
48 37 42 35 67 32 57 12 23 86 77 44 . 15 68 . . 20 . 01 71 29 . 76 . . 85 58 74 26 38 66 61 . . 50 05 . . 87 27 . 49 19 . . 82100 08 13 . 96 59 22 91 18 30 . 46 53 81 . . 90 80 . . 33 . 94 73 84 88 79 . 51 09 97 60 02 62 54 . . . . 31 34 39 11 69 28 03 . 99 25 56 92 65 14
. 59 24 36 . 04 39 . . 71 11 84 07 18 74 72 . . . 02 64 48 05 . . . 83 . 54 . . 43 65 13 31 25 37 53 . 27 86 70 . . 63 . 32 . 29 . 28 . 56 23 55 81 73 47 . 35 08 69 . 98 99 97 17 44 87 06 38 01 . . . 80 85 45 14 42 60 22 51 58 93100 . 52 68 88 20 89 16 49 62 . . . . 75
. 08 94 02 01 . . . 51 . 06 67 . 30 86 41 81 . . 44 . . 32 05 64 61 54 . 21 87 96 79 85 80 . 90 . 26 . . . . . 88 84 . . 31 . 83 . . . . . . 13 35 28 29 71 14 . 48 22 . 78 34 60 . 10 62 37 99 58 . . . 75 . . 92 46 40 . 07 . 20 53 56 . . 76 91 11 . 39 . 50 59
. . 70 48 91 57 99 . 32 65 80 50 63 40 . . 93 23 18 31 . 11 60 71 . 09 . 39 98 35 . . . 44 24 . 14 . . 94 . 85 33 . 76 82 . . 28 25 72 75 81 . . . 53 34 54 . . 68 . . . . 92 . 97 . . 15 55 36 20 . 90 . . . 84 01 96 88 . 58 89 16 27 . 10 69 19 . 79 . 06 03 87 21
72 60 39 . . 41 77 23 98 . . . 64 87 . 02 . 21 42 24 82 59 16 . . 15 07 90 70 79 12 83 51 . . . 55 45 65 71 . . . 49 57 06 75 . 19 . 14 . . 10 18 .100 93 36 . . . 91 81 . 58 . 29 03 35 . 68 . 09 08 11 95 50 78 28 67 17 . . . 48 04 33 47 . 84 52 85 73 . 92 05 46 40 .
66 . 80 14 . 36 . 56 17 47 25 62 51 37 . 12100 90 34 33 . . 40 . 29 18 19 28 57 69 98 32 . 72 11 78 64 13 . 35 . . . 92 43 04 22 . 97 71 . 21 48 . . 96 44 . 15 95 49 31 16 09 84 . 39 . . . . . 60 46 . 05 79 41 86 70 . . . . 85 82 03 81 65 76 . 55 . 42 . . 27 54 94 63
83 45 . 21 . . 25 . . . 39 05 36 76 01 55 49 . 08 . . 94 96 . 02 58 43 33 89 24 50 16 . 29 91 . 04 . 06 46 . 54 30 . 42 . . 73 79 15 47 27 68 09 84 69 82 . . 85 70 66 07 88 . 90 . 40 44100 93 . . . 77 . 03 72 65 31 28 34 12 75 32 87 98 57 63 86 99 80 . 13 . . 60 78 . 56
82 04 75 . . . 38 06 . 88 52 91 . . 79 11 16 19 . . 12 34 49 81 92 . 25 22 83 86 23 . . 87 . 33 99 10 59 09 . 69 . 89 53 48 . . . 36 80 . . 90 . . 56 . . . . 77 . . . 13 . 85 . . . . 40 . 66 01 . 32 21 44 39 . 26 35 78 . 37 61 93 05 43 . 64 . . 28 68 18 02 97
100 . 73 10 55 67 46 . 71 30 . 65 66 26 . . 99 96 . 56 . 45 48 80 53 . 23 44 62 20 . 57 38 31 92 . 41 . . 05 94 . . . 59 98 40 37 16 70 11 91 12 78 42 79 89 39 25 97 32 86 . . 33 01 76 . 43 . 34 19 02 . . . 88 . 82 . 64 83 15 . 22 . 52 . 74 . . 81 58 . 36 . . 14 . .
. 28 79 40 . 27 . . . 12 88 82 . . 17 35 . . . . . . 77 55 . . 10 . 50 . 86 . 74 15 . 95 . 36 . 03 93 . 18 . 46 32 . 52 81 . . . . 65 22 60 01 70 23 . 21 99 89 57 41 72 . 06 67 45 48 . . 14 51 97 84 . 69 94 49 . 68 90 29 08 02 73 . . . 26 83 . . 33 96 47 98 66
. . 84 20 35 . 59 85 . . 57 . 78 29 95 46 32 69 10 28 36 . 65 72 . . 04 52 30 . 75 39 34 89 93 . 88 . 61 . 50 45 13 21 . 90 . 99 77 08 74 51 66 . 41 67 . 63 73 86 . . . 79 64 54 87 . 53 37 . . 83 . . 25 . . . 26 . 18 . . 71 14 62 11 43 . 38 . 17 48 15 . . 82 49 31
. . 54 43 . . . 09 . . 71 . 60 77 73 94 85 68 98 . 08 03 88100 31 14 38 46 . 27 18 37 . 67 81 . . . 53 70 34 61 . . . 86 35 20 65 78 32 99 64 76 . 04 49 . 06 50 63 82 11 . 47 75 10 52 . 56 . 13 59 . . 33 12 . 16 . 97 51 66 . 91 . . 36 42 69 . 45 90 95 . 41 . 57 25 .
. . . 13 . 30 79 . 20 10 . 55 22 . 03 23 . 38100 53 57 51 70 46 . 99 . 98 63 40 41 . 69 . 36 62 25 93 85 . . 92 82 91 66 74 . 35 90 84 75 67 14 . 26 54 86 05 39 19 72 37 31 49 . . 04 18 78 21 94 . 47 . 02 50 43 . 11 48 45 44 . 52 . . . . 32 65 97 . 34 . 29 . 15 33 17 73
. 38 . . 33 43 . . 96 . 83 19 44 . 58 90 . . 17 08 . 31 23 . 13 80 . . 94 97 73 46 86 06 48 54 . 15 45 59 64 . 40 . . 14 30 . 01 .100 07 11 28 03 20 . . 68 98 . 56 57 84 50 88 69 89 . 25 . . 65 . 35 82 18 42 . 10 02 . 74 36 26 . . 51 . 79 27 49 . . 60 72 91 52 . 62
. 85100 81 36 77 90 . 08 67 . 74 . . 98 . 86 . 89 . . 62 50 . 09 . 59 47 . . 94 . 49 . . 03 21 65 58 18 70 44 . 25 95 . . 05 27 19 99 . 04 12 87 . 23 17 . 93 . 80 10 . . 28 . . . . 60 . 14 . . . . 31 55 53 . 38 30 . . . 75 43 40 34 . 48 07 26 . 02 82 . 79 71
. 50 16 78 53 18 47 . . 99 66 . 28 32 . 92 . 52 94 63 37 79 67 49 . 25 95 83 26 36 82 44 . 70 27 39 98 12 . . . 17 . . . . 60 97 . 88 84 31 08 77 73 . 06 96 . 13 22 65 41 74 30 . 90 . 40 75 57 . . 01 . 24 . . . 45 . . . 21 62 04 . . 71 . 46 . . 19 . . 93 51 05 .
80 . . . 73 . 24 75 40 . 27 81 35 93 50 . 47 30 97 . . . . 69 . . 16 53 85 18 95 64 68 71 . 79 . 90 99 . 03 . 29 02 . 26 . 51 . 57 . . . 59 44 . 45 . . 60 19 12 15 43 06 08 67 92 70 34 . . . 33 21 61 76 . 52 98 . . 87 22 . 31 . . . 07 . 58 56 77 83 14 89 84100 .
. . 23 12 71 52 . 01 65 72 60 79 . 49 . 25 . 29 87 57 19 . 21 . 82 05 74 . 58 44 . 75 14 43 78 . . 31 34 37 36 98 50 24 . 68 . . . 59 40 . . . 38 10 . 02 . 27 . . 09 62 95 . . 11 77 32 39 . 91 . 04 . 13100 03 08 56 16 54 . 84 . 69 90 85 63 30 88 47 55 . . 35 28 . 99
35 19 59 . . 62 37 89 04 07 09 64 . 20 65 24 21 85 56 .100 75 . 48 . . 15 93 12 45 22 42 97 . . 40 08 . . . . 86 34 . . 53 10 . 96 52 . 30 25 69 . 76 33 36 88 51 73 63 02 26 81 27 60 71 . . 66 79 . 67 . 68 . 84 87 . . 47 49 . . 94 . 70 . 82 18 54 . . 43 13 . 74 39 .
. 14 25 74 . . 15 92 . . 59 40 . 99 39 . . 70 . 82 77 96 43 . 71 27 06 01 02 60 . . . . 07 . . 24 . . 04 75 . 33 21 . 79 76 47 45 83 . 09 41 32 . 78 18 61 52 54 20 86 58 05 68 36 . . 48 44 56 . 90 . 26 89 23 . 72 . 37 . . 97 . 73 12 95 10 . . 08 . 57 98 . 81 . 22
. . 97 76 32 46 . 22 55 . 45 . 77 . . . 14 61 . 34 33 . 87 90 . . 08 73 . . . 91 . 26 09 89 81 . 05 74 . . 72 62 . . . . 11 . 58 . . 21 . . 43 . . . . . . . 96 99 . 94100 . 27 . 75 92 59 . 41 19 29 63 . . 67 . 28 15 . . . . 40 24 . 01 . 85 80 69 06 37
. 44 26 . 69 39 34 . . 60 43 13 . 02 06 . 18 67 . 73 . 04 86 . . 10 68 30 22 91 . 01 . 50 88 35 .100 . . 55 . . 94 . . . 87 07 99 . . . 64 89 82 . 29 79 . 14 . 52 38 83 53 . 98 . 33 . 36 96 70 32 54 40 15 . 46 48 80 27 76 08 93 19 . 78 . 45 . 75 . 66 . 21 61 . .
24 23 02 . 74 . 73 15 38 . . 28 . 25 . 98 . . . 88 44 21 10 31 89 43100 . 01 . 35 53 41 51 55 12 . . 29 95 40 06 17 42 65 70 . . 87 50 . 33 47 . . 45 04 . . 67 77 05 14 13 58 78 86 60 68 22 . 72 99 . 07 32 . 66 . 37 34 . 92 03 . 27 36 . . 61 79 56 . . 18 . 94 39 . 80
. 40 34 05 39 80 71 16 87 28 . 03 67 85 81 09 . 89 . 64 11 86 94 29 . . . 15 06 . 62 33 56 . 79 31100 . . 99 10 32 . . 19 55 . 08 48 . 73 12 43 . 95 35 88 07 49 . 18 54 . 45 42 . 57 . . 47 . 26 . 68 . 13 59 90 . 21 91 65 04 51 75 52 84 41 . . 14 22 . 27 50 74 . 97 . .
06 . 69 . 11 91 32 78 . 90 92 . . . . 80 68 16 05 . . . . 61 99 52 . 65 87 66 43 . . 02 72 . . 76 96 38 29 . 45 34 . 22 . . 82 98 . . 23 31 58 03 . . . 56 44 . 63 . 26 59 .100 . 73 17 53 86 . 74 42 93 79 . 04 25 62 97 . 64 30 09 . . . 33 . 41 67 84 . 55 08 83 .
46 12 . 75 . . . . 94 98 . 49 . 42 51 . 57 77 01 43 60 23 30 . . . . . . 28 . . . 20 03 . . 92 . . 25 36 90 67 . 85 38 04 95 05 52 17 37 39 19 . . . . . . 87 . 50 . 74 . 31 02 71 41 . . 84 . 55 . . . . 69 79 83 . 06 78 76 . 99 93 . . . . 21 . . . 68 82
. 43 51 62 . . . 53 . 03 15 99 . . 07 50 79 41 . 18 . . 17 14 22 35 39 49 45 . 04 . . . 05 . . . 37 . 28 80 . 77 . 16 74 61 . 33 . . 21 94 . 87 40 32 63 71 06 34 20 . 75 30 56 55 66 72 . . 57 12 . 89 25 . 09 . . 67 29 59 . 95 38 31 . 85 91 19 26 10 . . 81 76 42 .
. . 89 97 25 99 45 . . 85 72 95 . . 55 87 . 22 . 17 42 78 . . . . 33 76 38 03 . 26 80 58 19 . . . 44 . 81 56 . 13 30 73 91 53 . 49 77 . 60 79 . 05 84 . 29 74 . . 23 . 10 46 12 04 . 61 69 . 82 94 . 47 . . 43 . 16 28 . . 48 . . 88 21 40 37 02 92 . 75 . 01 36 86 07
. 42 76 . 56 . 29 66 09 77 . 26 . . 75 19 . . . 60 97 50 24 08 41 . 58 . 91 . . 23 73 48 57 17 94 32 . 39 83 . . . 71 18 21 92 14 . 30 . . . 16 25 69 11 . 36 99 95 . 85 . 43 07 62 27 80 67 . 81 . 88 02 . . 70 . 37 . 22 . 86 . . . 20 55 05 59 . 93 65 90 54 06 15 45
. . 83 95 65 60 55 10 33 .100 37 . 45 . 76 61 91 47 35 79 . 19 73 . 34 . 81 . . 89 06 . . . 74 59 25 14 78 . 31 . 58 . 84 . . 57 . 66 . 75 42 51 97 54 99 82 02 38 . 40 . . 49 . 16 90 . 18 . . . 56 92 . 22 . 27 24 63 . 50 15 39 . 94 23 . 29 87 04 85 53 71 43 88 96 70
. 31 68 67 . 47 70 14 . 04 86 . 33 34 . 65 38 . 20 . 46 55 . 37 84 56 . . 07 . 52 15 21 83 13 . 93 22 91 42 54 . . . 99 . 26 23 . 63 50 18 . 92 53 78 . 76 . . 35 29 64 24 79 51 09 25 . 36 71 . . 49 16 96 19 48 . 80 . 45 02 . 74 32 . 82 . 73 98 61 . . 44 . 11 30 . .
. 49 13 . 52 21 . 35 07 22 70 . 02 . 56 29 . . 73 11 40 . 74 . . . 32 . . . . 71 . . 28 87 . . . . . 78 . . . 64 20 94 . 72 24 55 . . 98 . . . 62 96 . 67 84 33 . 93 37 . 88 81100 . 08 10 . 15 34 76 . . . . . 05 44 89 14 66 . 19 . 31 60 09 51 . . . 48 77
.100 . 92 43 53 . 48 44 51 99 15 23 . 08 79 50 . . . . 49 . . 17 . 90 . 14 39 05 . 84 . 04 . 68 11 86 . 52 . 61 . 28 77 . 24 80 74 87 63 . 71 . 27 32 40 . . 56 . . . . 55 06 30 75 . 89 09 73 . 12 . 54 57 97 25 59 95 85 13 . 67 58 60 38 29 26 . 91 76 . 81 46 10 . .
. 74 57 73 23 . . 19 24 02 28 63 93 . . . 98 88 82 59 43 26 89 01 . . 09 21 31 . . 41 53 30 35 29 51 95 12 . 65 . 11 70 40 42 . 17 06 . . . . . 47 64 20 . 33 . 86 . 22 05 . 60 . . 58 . 32 85 66 . 75 . 37 99 72 . . . 61 34 49 96 . . . . . . . 39 56 94 . . 80 16
94 96 98 . . 08 75 86 46 61 49 32 01 51 42 57 . . 48 77 88 18 62 59 . 60 . . . 47 . 07 . 27 16 63 20 54 . 92 09 . . . 25 67 05 90 36 . 26 . . 91 37 52 22 80 . 39 15 . 71 87 . . 65 . 11 97 . . 44 . 84 41 14 . 64 . 81 78 93 69 . 79 . . 76 . 13 .100 34 35 40 . . 82 68
. . . . . . 67 47 81 68 . 86 . 62 . 38 65 66 33 40 . . 84 07 12 . 57 55 37 . . . . 93 52 91 83 42 97 . . 59 . 60 54 75 . 69100 26 . 08 53 . . 50 76 41 18 92 . . . 29 94 25 35 51 79 . 96 . . . . 71 80 . 95 19 . . . 43 . . 10 . . 02 28 . . . . 11 03 17 72 89
37 11 90 32 20 . 18 91 06 . 94 . . . 54 68 . . . 16 . . 99 . 36 85 66 . . 75 72 . 60 24 . . 02 38 01 76 . 82 . . . . 98 . 51 . 03 81 . 56 . . 28 15 13 31 89 70 73 19 48100 44 59 . 63 . 50 79 74 . . . 86 53 93 77 . 35 25 07 62 12 64 09 97 41 84 33 08 95 55 49 67 . 83
07 . 22 58 49 35 30 . . . . 70 73 56 36 04 29 11 . 39 92 . 63 95 . . . 54 . 32 28 . 71 65 90 75 18 47 . . 79 03 94 64 . 27 72 43 78 20 . . . . 86 . . 59 55 57 37 33 . 67 88 91 . 93 17 84 . . 76 23 .100 61 08 83 . 05 89 19 . 66 . 26 44 . 42 60 51 . 12 31 99 38 . 77 48
. 56 . 29 42 66 82 63 . . . 12 13 75 . . . 60 52 74 . . 41 91 24 97 51 . 08 58 . 73 23 94 40 . . . 17 . . 14 . 18 . 96 89 . 35 21 25 . 16 36 . . 11 69 10 61 07 . 80 95 . 62 99 43 28 . 02 70 01 88 . 67 87 81 31 38 47 98 . . 68 . . 86 . 22 78 . 05 06 59 54 . . 45 15
50 . 85 45 . . 97 99 . 89 95 72 . 55 90 06 . 17 24 22 96 76 68 38 83 42 03 . 27 . . 80 26 09 67 44 58 . . 34 . 15 53 73 . 13 . 62 56 91 05 29 . 74 60 . . . . . 12 08 61 39 98 04 . 46 10 23 47 43 51 65 . . 35 . 20 52 . 57 40 . 88 . . 48 18 71 92 75 37 36 02 01 63 . . .
. 39 28 71 . . . 80 36 34 03 . 53 . 85 78 09 . 67 89 . 15 . 06 94 . 93 86 29 02 . . . . 62 . . 99 31 . 19 48 . 55 10 66 46 01 . 37 . 49 95 . 43 . . 88 . 44 . 45 47 54 . 82 18 76 42 . 13 77 . 60 . . 21 30 . 59 . . 17 91 41 65 70 . 84 04 23 . . . . . 74 . 20 58
33 65 . . . 10 . . 64 83 . . . . 45 61 76 35 30 91 . . 98 20 . . 48 67 73 . . . . 59 89 14 46 78 74 25 07 57 . 84 12 58 93 86 . 41 97 82 51 02 75 66 99 54 09 . 03 52 . 32 90 . 38 . 21 . 92 28 22 56 11 . . 36 05 62 . . 72 24 94 . . 15 . 01 04 53 29 88 87 43 . 85 70 96

EDIT: I can now prove that this 'puzzle' has multiple solutions and so is invalid.

by **dobrichev** » Sat Mar 09, 2013 12:41 pm

m_b_metcalf wrote:I have produced the very difficult 100x100 puzzle below. However, my solver cannot solve it (after 6 hours), nor can I prove it has only one solution. Can someone else please check it (gsf, are you still there?)?

Try exchanging some rows and/or columns, stacks, with hope that this will take you away from the "worst case" of your solving algorithm.

Website · by **denis_berthier** » Sun Mar 10, 2013 5:37 am

One of the questions such huge puzzles suggest is, how deep one must go into T&E to solve them.

On the Programmer's Forum, Blue mentioned his tries for finding larger than usual puzzles (i.e. 16x16 and 25x25).
(I tried to find the exact reference but the forum seems to be down.)
As far as I can remember, the proportion of puzzles solvable by T&E(1) (almost 100% for the standard 9x9) decreases very fast (~30% for the 16x16 - again as far as I can remember). It is very likely to be close to 0 already for the 64x64.
Computations times also increase very fast with n when T&E(n) is required.

Now, I understand that solving with T&E(n) is more stringent than using some form of structured search (DFS) (in T&E, there's no guessing). Therefore DFS may be faster - but I strongly doubt that it is very much faster in the mean.

Unless it was generated by a very special process, a 10,000 x 10,000 puzzle should require a very large depth of search (be it by T&E or DFS). I can hardly imagine the computation power required for this purpose. And I don't want to even imagine how this could be solved by hand as z666zz666z claims he did - I fear my hands would explode just at the thought of it.

This brings us back to Mike's question: how was this 10,000 x 10,000 puzzle generated ?

(Off the record:
- 10,000x10,000 = 10^8 cells. Supposing it takes 1s. to write down a digit in a cell, this means about 27,778 hrs, or 1157 days, or 3.17 years, only for handwriting the solution, supposing it is already available;
- 666 = the symbol of the Beast. Who's online ?
)

by **Pat** » Sun Mar 10, 2013 12:30 pm

m_b_metcalf wrote:
I have produced the very difficult 100x100 puzzle below.
However, my solver cannot solve it (after 6 hours),
nor can I prove it has only one solution.
Can someone else please check it (gsf, are you still there?)?

our forum allows attaching files
(small files)

here's your new puzzle as an attached file

by **m_b_metcalf** » Fri Mar 15, 2013 10:38 am

z666zz666z wrote:So now, i am on 100x100 upto 250x250... they take me from one day up to two days per each one to solve them.

Looks as though these are taking a little bit longer?

Regards,

Mike Metcalf

The New Sudoku Players' Forum

100X100 Sudoku

Re: re: 15x15

Re: 100X100 Sudoku

Re: 100X100 Sudoku

Re: 100X100 Sudoku

Re: 100X100 Sudoku

Re: 100X100 Sudoku

T&E depth of nXn Sudoku as n increases

Re: 100X100 Sudoku