## Difficult Games

Everything about Sudoku that doesn't fit in one of the other sections
hahahahahaha... The SS (Simple Sudoku) cant solve it lol i tried to see if there were a better way to pass that step but it didnt find anything at all... I tried again from start to solve it with it but it couldnt either ... Any1 knows about a better program? (I am interested in finding and the best way to solve it maybe (less steps but that will make it take more time).
Maybe i need a program that shows what techiques it used to solving it and i can modify it a bit but i guess i just have to program it my own
Claw_gr

Posts: 9
Joined: 13 December 2005

This Sudoku is like The One Ring,

to destroy it, bring it back to where it was made...

Ruud.
Ruud

Posts: 664
Joined: 28 October 2005

If you don't mind, I'd like to submit one more from my collection.

I particulary like this one. It requires a wide array of solving techniques, but no T&E. It even has a rare uniqueness test 3.

And it looks cool!

Introducing: The Galaxy.

Code: Select all
`. . .|. . 3|6 7 .. . .|6 . .|. . 9. . 8|. 7 .|. . .-----+-----+-----. 5 .|. . 1|. 8 .. 7 6|. 2 .|5 3 .. 2 .|5 . .|. 9 .-----+-----+-----. . .|. 4 .|2 . .1 . .|. . 5|. . .. 6 4|2 . .|. . .`

Ruud.
Ruud

Posts: 664
Joined: 28 October 2005

Code: Select all
`+----------------+----------------+----------------+| 2   *149  59   | 149  159  3    | 6    7    8    | | 357 *134  357  | 6    158  248  | 13   24   9    | | 6   *1349 8    | 149  7    249  | 13   24   5    | +----------------+----------------+----------------+| 349  5    39   | 349  6    1    | 7    8    2    | | 489  7    6    | 489  2    489  | 5    3    1    | | 38   2    1    | 5    38   7    | 4    9    6    | +----------------+----------------+----------------+| 3579 389  3579 | 1389 4    6    | 2    15   37   | | 1    389  2    | 7    389  5    | 89   6    4    | | 357  6    4    | 2    13   89   | 89   15   37   | +----------------+----------------+----------------+we will show that R2C5<>8B={R1C2,R2C2,R3C2}R8C2=3 or R8C5 = 3R8C5=3 =>R6C5=8=>R2C5<>8R8C2=3 =>B locked on 149 =>R1C3=5=>R2C5=5and that solve the puzzle`
bennys

Posts: 156
Joined: 28 September 2005

bennys – how do you do it?? That’s figurative, not literal!

Thanks Ruud for the puzzles and the solver.

Ruud wrote:This Sudoku is like The One Ring,
to destroy it, bring it back to where it was made...

then is Sudo Cue like Mt Doom and you are ... Sauron??

bennys could be Frodo.

So who will be Aragorn? (sigh)
emm

Posts: 987
Joined: 02 July 2005

Ruud,

As you probably know, I try to keep my solver up-to-date with the smartest human solvers such as bennys and, seemingly, elf. Here are its thoughts on your latest puzzles. (You'll notice that I now allow table results to appear in the output, as human solvers have adopted these techniques).

Of course, as I've used a solver, I won't qualify for the big cigar!

Code: Select all
`    3   1   7 |     4   58   258 |   6   9   28     4   6  89 |   189    7  1289 |  23   5  238     5   2  89 |     3    6    89 |   1   7    4 --------------+------------------+-------------     6  39   5 |     7   39     4 |   8   2    1     8   4   1 |    59    2   359 |   7   6   39     7  39   2 |     6   18    18 |  39   4    5 --------------+------------------+-------------   129   7   4 |  1289  138     6 |   5  38   29   129   5   6 |   128    4   138 |  29  38    7    29   8   3 |   259   59     7 |   4   1    6 Consider the chain r2c4-1-r2c6=<2|9>=r2c4.When the cell r2c4 contains the value 9, it likewise contains the value 1 - a contradiction.Therefore, the cell r2c4 cannot contain the value 9.- The move r2c4:=9 has been eliminated.The value 9 in Column 6 must lie in Box 2.- The move r5c6:=9 has been eliminated.Consider the chains r5c6-3-r5c9-<3|2>-r7c9 and r1c9-2-r1c6-5-r5c6.When the cell r5c6 contains the value 3, one chain states that the value 2 in Column 9 belongs in the cell r7c9 while the other says it doesn't - a contradiction.Therefore, the cell r5c6 cannot contain the value 3.- The move r5c6:=3 has been eliminated.The value 5 is the only candidate for the cell r5c6.`

The chain chain r2c4-1-r2c6=<2|9>=r2c4 basically says that when r2c4 contains a 9, the set {r2c6,r3c6,r6c6} is locked, which forces a 2 into r2c6. Since there is now no candidate position for the value 1 in Box 2 or Row 2, we have a contradiction.

Code: Select all
`    2   149    59 |   149  159    3 |   6   7   8   357   134   357 |     6  158  248 |  13  24   9     6  1349     8 |   149    7  249 |  13  24   5 ------------------+-----------------+------------   349     5    39 |   349    6    1 |   7   8   2   489     7     6 |   489    2  489 |   5   3   1    38     2     1 |     5   38    7 |   4   9   6 ------------------+-----------------+------------   579   389  3579 |  1389    4    6 |   2  15  37     1   389     2 |     7  389    5 |  89   6   4    57     6     4 |     2   13   89 |  89  15  37 Consider the chains r6c5-<8|1>-r9c5-1-r7c4 and r5c4-8-r7c4.Since it is certain that Box 5 will not contain the value 8 in at least one of the cells r6c5 and r5c4, the cell r7c4 does not contain the value 1.- The move r7c4:=1 has been eliminated.The cell r9c5 is the only candidate for the value 1 in Box 8.Later ...    2    14   59 |   14   59    3 |   6   7  8    35   134    7 |    6   58  248 |  13  24  9     6  1349    8 |  149    7  249 |  13  24  5 -----------------+----------------+-----------    49     5   39 |  349    6    1 |   7   8  2   489     7    6 |  489    2  489 |   5   3  1    38     2    1 |    5   38    7 |   4   9  6 -----------------+----------------+-----------    59    89  359 |   38    4    6 |   2   1  7     1    38    2 |    7  389    5 |  89   6  4     7     6    4 |    2    1   89 |  89   5  3 Consider the chains r2c2-<4|5>-r2c1-3-r6c1 and r2c2-<4|8>-r2c5-<5|3>-r6c5.When the cell r2c2 doesn't contain the value 4, one chain states that the value 3 in Row 6 belongs in the cell r6c1 while the other says it doesn't - a contradiction.Therefore, the cell r2c2 must contain the value 4.`

The link r2c2-<4|5>-r2c1 uses the set {r2c1,r2c2,r2c7} while the link r2c2-<4|8>-r2c5 uses the set {r2c1,r2c2,r2c5,r2c7}.

As ever, one more link type is necessary in order to match bennys ...
rubylips

Posts: 149
Joined: 01 November 2005

I’m not sure what you mean by T&E - it covers a lot of things, I hope you don't mean guessing! I agree with you about Ruud’s puzzle – it’s not easy. If you're still there elf I’d be interested to know how you got past this point?

Code: Select all
`*-----------------------------------------------------------* | 3     1     7     | 4     58    258   | 6     9     28    | | 4     6     89    | 189   7     1289  | 23    5     238   | | 5     2     89    | 3     6     89    | 1     7     4     | |-------------------+-------------------+-------------------| | 6     39    5     | 7     39    4     | 8     2     1     | | 8     4     1     | 59    2     359   | 7     6     39    | | 7     39    2     | 6     18    18    | 39    4     5     | |-------------------+-------------------+-------------------| | 129   7     4     | 1289  138   6     | 5     38    29    | | 129   5     6     | 128   4     138   | 29    38    7     | | 29    8     3     | 259   59    7     | 4     1     6     | *-----------------------------------------------------------*`
[/quote]

Hi! I am not familiar with that sudoko slang, hence I don't know that you're talking about. I just developed a habit to solve the daily puzzle from sudokumad.com when I have my coffee. For ruud's puzzle I started with filling in the 1, 6, 7 and 4. afterwards, it was very simple.
cheers
elf

Posts: 3
Joined: 15 December 2005

em - I figure put what your question was about. I never got to that solution because it is simple to figure out the "9" - the key is the last vertical line of the big square - after that you work out around the small squares and "8" is sorted out too.
cheers
elf

Posts: 3
Joined: 15 December 2005

rubylips wrote:Of course, as I've used a solver, I won't qualify for the big cigar!

No, that would be bennys. I'd suggest bennys should now submit a puzzle that he cannot solve with his advanced techniques. That would be a real challenge for others...

Too bad elf, that you're not familiar with sudokulingo yet. You seem to be a very capable sudoku solver, able to learn us old hands a few new tricks. To get aquainted, I'd suggest this site: http://vanhegan.net/sudoku/dictionary.php.

Ruud.
Ruud

Posts: 664
Joined: 28 October 2005

Lets try this one
Code: Select all
`+-------+-------+-------+| . . 2 | . 9 . | 1 . 7 | | . 3 8 | 6 . . | . . . | | 4 . . | . . . | . . . | +-------+-------+-------+| . . . | . . 5 | . . . | | . . 9 | . 1 . | 3 . . | | . . . | 4 . . | . . . | +-------+-------+-------+| . . . | . . . | . . 4 | | . . . | . . 7 | 9 2 . | | 8 . 6 | . 3 . | 7 . . | +-------+-------+-------+`
bennys

Posts: 156
Joined: 28 September 2005

My solver is only able to solve the puzzle with the assistance of multiple forced chains though when I've implemented all of the results associated with Almost Locked Sets I might be able to present a shorter solution.

Code: Select all
`      56      56     2 |      38     9    348 |     1     348       7      179       3     8 |       6  2457     12 |   245      59     259        4     179    17 |  123578  2578   1238 |  2568   35689  235689 -----------------------+----------------------+----------------------    12367   12678  1347 |      39  2678      5 |  2468   16789   12689      256  245678     9 |     278     1    268 |     3   45678     258   123567  125678  1357 |       4  2678     39 |  2568  156789  125689 -----------------------+----------------------+----------------------   123579   12579  1357 |   12589  2568  12689 |    68     368       4      135      15  1345 |     158  4568      7 |     9       2     368        8     249     6 |      29     3    249 |     7      15      15 Consider the chain r3c3~7~r2c1-7-r2c5-4-r8c5-4-r8c3-<4|7>-r7c3.When the cell r3c3 contains the value 7, so does the cell r7c3 - a contradiction.Therefore, the cell r3c3 cannot contain the value 7.- The move r3c3:=7 has been eliminated.The value 1 is the only candidate for the cell r3c3.-- Easy bit --      56      56    2 |     38     9   348 |     1     348       7       79       3    8 |      6  2457     1 |   245      59     259        4      79    1 |  23578  2578   238 |  2568   35689  235689 ----------------------+--------------------+----------------------    12367   12678  347 |     39  2678     5 |  2468   16789   12689      256  245678    9 |    278     1   268 |     3   45678     258   123567  125678  357 |      4  2678    39 |  2568  156789  125689 ----------------------+--------------------+----------------------   123579   12579  357 |  12589  2568  2689 |    68     368       4      135      15  345 |    158  4568     7 |     9       2     368        8     249    6 |     29     3   249 |     7      15      15 Consider the chain r1c8=<3|4>=r1c6-4-r9c6-4-r8c5-6-r8c9=<6|3>=r7c8.When the cell r1c8 contains the value 3, so does the cell r7c8 - a contradiction.Therefore, the cell r1c8 cannot contain the value 3.- The move r1c8:=3 has been eliminated.The value 3 in Box 2 must lie in Row 1.- The moves r3c4:=3 and r3c6:=3 have been eliminated.Consider the chain r9c6~2~r9c4=<9|4>=r9c6.When the cell r9c6 contains the value 2, it likewise contains the value 4 - a contradiction.Therefore, the cell r9c6 cannot contain the value 2.- The move r9c6:=2 has been eliminated.Consider the chain r7c6~2~r3c6=<2|8>=r1c4-<8|2>-r9c4.When the cell r7c6 contains the value 2, so does the cell r9c4 - a contradiction.Therefore, the cell r7c6 cannot contain the value 2.- The move r7c6:=2 has been eliminated.Consider the chain r1c8=<8|9>=r2c1-9-r7c1~9~r7c6-<9|3>-r7c8.When the cell r7c8 contains the value 8, some other value must occupy the cell r1c8, which means that the value 3 must occupy the cell r7c8 - a contradiction.Therefore, the cell r7c8 cannot contain the value 8.- The move r7c8:=8 has been eliminated.Consider the chain r4c4-<9|8>-r1c4=<8|9>=r3c2=9=r7c1~9~r7c4.When the cell r7c4 contains the value 9, so does the cell r4c4 - a contradiction.Therefore, the cell r7c4 cannot contain the value 9.- The move r7c4:=9 has been eliminated.Consider the chain r7c1-9-r2c1-7-r2c5-4-r8c5-6-r8c9=<6|3>=r7c8.When the cell r7c1 contains the value 3, so does the cell r7c8 - a contradiction.Therefore, the cell r7c1 cannot contain the value 3.- The move r7c1:=3 has been eliminated.Consider the chain r7c1=<1|4>=r8c3-4-r8c5-4-r2c5-7-r2c1-9-r7c1.When the cell r7c1 contains the value 1, it likewise contains the value 9 - a contradiction.Therefore, the cell r7c1 cannot contain the value 1.- The move r7c1:=1 has been eliminated.Consider the chain r6c1~3~r6c6-3-r4c4-<9|8>-r1c4~8~r8c4-<8|3>-r8c1.When the cell r6c1 contains the value 3, so does the cell r8c1 - a contradiction.Therefore, the cell r6c1 cannot contain the value 3.- The move r6c1:=3 has been eliminated.Consider the chain r7c1-9-r2c1=<9|8>=r1c8=<8|4>=r1c6-4-r9c6=<4|9>=r7c6.When the cell r7c6 contains the value 9, so does the cell r7c1 - a contradiction.Therefore, the cell r7c6 cannot contain the value 9.- The move r7c6:=9 has been eliminated.The value 9 in Box 7 must lie in Row 7.- The move r9c2:=9 has been eliminated.The values 1, 2, 3, 5, 7 and 9 occupy the cells r7c1, r7c2, r7c3, r7c4, r7c5 and r7c8 in some order.- The moves r7c4:=8, r7c5:=6, r7c5:=8 and r7c8:=6 have been eliminated.The value 3 is the only candidate for the cell r7c8.-- Easy bit --      56      56    2 |     38     9   348 |     1      48       7       79       3    8 |      6  2457     1 |   245      59     259        4      79    1 |   2578  2578    28 |  2568    5689       3 ----------------------+--------------------+----------------------    12367   12678  347 |     39  2678     5 |  2468   16789   12689      256  245678    9 |    278     1   268 |     3   45678     258   123567  125678  357 |      4  2678    39 |  2568  156789  125689 ----------------------+--------------------+----------------------    12579   12579   57 |  12589  2568  2689 |    68       3       4      135      15  345 |    158  4568     7 |     9       2      68        8     249    6 |     29     3   249 |     7      15      15 Consider the chain r9c6~2~r9c4=<9|4>=r9c6.When the cell r9c6 contains the value 2, it likewise contains the value 4 - a contradiction.Therefore, the cell r9c6 cannot contain the value 2.- The move r9c6:=2 has been eliminated.Consider the chain r7c6~2~r3c6=<2|8>=r1c4-<8|2>-r9c4.When the cell r7c6 contains the value 2, so does the cell r9c4 - a contradiction.Therefore, the cell r7c6 cannot contain the value 2.- The move r7c6:=2 has been eliminated.Consider the chain r4c4-<9|8>-r1c4=<8|9>=r3c2=9=r7c1~9~r7c4.When the cell r7c4 contains the value 9, so does the cell r4c4 - a contradiction.Therefore, the cell r7c4 cannot contain the value 9.- The move r7c4:=9 has been eliminated.Consider the chain r7c1=<1|4>=r8c3-4-r8c5-4-r2c5-7-r2c1-9-r7c1.When the cell r7c1 contains the value 1, it likewise contains the value 9 - a contradiction.Therefore, the cell r7c1 cannot contain the value 1.- The move r7c1:=1 has been eliminated.Consider the chain r6c1~3~r6c6-3-r4c4-<9|8>-r1c4~8~r8c4-<8|3>-r8c1.When the cell r6c1 contains the value 3, so does the cell r8c1 - a contradiction.Therefore, the cell r6c1 cannot contain the value 3.- The move r6c1:=3 has been eliminated.Consider the chain r7c1-9-r2c1=<9|8>=r1c8=<8|4>=r1c6-4-r9c6=<4|9>=r7c6.When the cell r7c6 contains the value 9, so does the cell r7c1 - a contradiction.Therefore, the cell r7c6 cannot contain the value 9.- The move r7c6:=9 has been eliminated.The value 9 in Box 7 must lie in Row 7.- The move r9c2:=9 has been eliminated.The values 1, 2, 5, 7 and 9 occupy the cells r7c1, r7c2, r7c3, r7c4 and r7c5 in some order.- The moves r7c4:=8, r7c5:=6 and r7c5:=8 have been eliminated.The values 3, 4 and 9 occupy the cells r1c6, r6c6 and r9c6 in some order.- The move r1c6:=8 has been eliminated.Consider the chain r1c4-<8|2>-r9c4-<9|8>-r8c4.The cell r8c4 must contain the value 8 if the cell r1c4 doesn't.Therefore, these two cells are the only candidates for the value 8 in Column 4.- The moves r3c4:=8 and r5c4:=8 have been eliminated.Consider the chain r3c4-<5|8>-r1c4-<3|2>-r3c6.When the cell r3c4 contains the value 2, so does the cell r3c6 - a contradiction.Therefore, the cell r3c4 cannot contain the value 2.- The move r3c4:=2 has been eliminated.Consider the chain r6c3=3=r4c4-<3|2>-r9c4=<2|7>=r7c3.When the cell r6c3 contains the value 7, so does the cell r7c3 - a contradiction.Therefore, the cell r6c3 cannot contain the value 7.- The move r6c3:=7 has been eliminated.Consider the chain r2c5=<5|8>=r1c8-<4|3>-r1c4-<8|5>-r3c4.When the cell r2c5 contains the value 5, so does the cell r3c4 - a contradiction.Therefore, the cell r2c5 cannot contain the value 5.- The move r2c5:=5 has been eliminated.The value 5 in Box 3 must lie in Row 2.- The moves r3c7:=5 and r3c8:=5 have been eliminated.Consider the chain r1c8-<4|3>-r1c4-<8|9>-r4c4=3=r6c3~5~r6c7-5-r2c7.When the cell r2c7 contains the value 4, some other value must occupy the cell r1c8, which means that the value 5 must occupy the cell r2c7 - a contradiction.Therefore, the cell r2c7 cannot contain the value 4.- The move r2c7:=4 has been eliminated.The cell r2c5 is the only candidate for the value 4 in Row 2.`
rubylips

Posts: 149
Joined: 01 November 2005

I couldn't find a simpler argument I found short argument that will show that R1C6<>8 and then very long argument that show that R1C4<>3 and that solve the puzzle but its not very elegant.
bennys

Posts: 156
Joined: 28 September 2005

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