The New Sudoku Players' Forum

by **JPF** » Tue Jan 16, 2007 12:05 am

m_b_metcalf wrote:A pair of flowers for the bouquet?

Two vases for these nice flowers :

Code: Select all: . . . . . . . . . . . 6 3 . 5 2 . . . . . 8 . 4 . . . . . 2 . . . 3 . . . 7 . . . . . 8 . 9 . . . . . . . 6 7 . . . . . . . 4 . 8 . . . . . 1 . . . 3 1 2 6 5 . .

SE=7.3

Code: Select all: . . 7 . . . 3 . . . . . 8 . 5 . . . . . . 9 . 2 . . . . . 2 . . . 6 . . . 4 . . . . . 5 . 9 . . . . . . . 7 8 . . . . . . . 5 . 1 . . . . . 9 . . . 3 5 6 4 2 . .

SE=7.1

JPF

by **Mauricio** » Wed Jan 17, 2007 11:13 pm

m_b_metcalf wrote:
m_b_metcalf wrote:I find the minimum number of additional clues to be 6. Are there smaller solutions?

To answer my own question, here's one with just 5 extra clues:

Code: Select all
1 4 7 . . . . . . 2 5 8 . 3 . 4 . . 3 6 9 . . . . . . . . . 1 4 7 . . . . . . 2 5 8 . . 6 . . . 3 6 9 . . . . . . . . . 1 4 7 . . 6 . . . 2 5 8 . 8 . . . . 3 6 9 SE 8.4

Regards,

Mike Metcalf

I did an extensive search looking for that kind of sudokus (it took me less than 30 minutes) with just 4 more clues and I did not find a single one, so the answer is 5.

Then I did an extensive search looking for 5 more clues and I found thousands (it took me about 2 hours). I have now coded a function that canonicalizes and only 55 are different up to isomorphism, so any other sudoku of that kind with 32 clues is isomorphic to one of this list:

Code: Select all: 123540000456000000789000000500123040000456000000789000008000123000000456000000789 123570000456000000789000000600123070000456000000789000000004123000000456000000789 123570000456000000789000000800123000000456900000789000000600123000000456000000789 123570000456000000789000000800123000000456900000789000000000123001000456000000789 123570000456000000789000000800123000000456900000789000000000123000000456000002789 123840000456000000789000000900123000000456010000789000000007123000000456000000789 123540000456000000789000000008123007000456000000789000500000123000000456000000789 123840000456000000789000000000123800900456000000789000000000123030000456000000789 123840000456000000789000000000123800900456000000789000000000123000001456000000789 123840000456000000789000000000123800300456000000789000000000123000000456000005789 123570000456000000789000000000123900070456000000789000004000123000000456000000789 123570000456000000789000000000123500000456000000789000040008123000000456000000789 123570000456000000789000000000123500000456000000789000008000123000200456000000789 123570000456000000789000000000123500000456000000789000008000123000300456000000789 123540000456000000789000000000123007200456000000789000000000123000900456000000789 123870000456000000789000000000123004008456000000789000000000123300000456000000789 123870000456000000789000000000123004008456000000789000000000123007000456000000789 123500060456070000789000000070123000000456000000789000004000123000000456000000789 123600007456030000789000000000123040000456000000789000040000123000000456000000789 123500000456010000789000600000123000900456000000789000060000123000000456000000789 123500000456010000789000300000123000200456000000789000000000123008000456000000789 123500000456070000789000300000123000090456000000789000000000123300000456000000789 123600000456010000789000300000123000008456000000789000000000123010000456000000789 123900000456030000789000500000123000000456000030789000000000123000000456600000789 123500000456010000789000000008123060000456000000789000500000123000000456000000789 123600900456000000789000000070123008000456000000789000004000123000000456000000789 123600900456000000789000000060123005000456000000789000000000123030000456000000789 123500800456000000789000000000123060070456000000789000000000123001000456000000789 123500800456000000789000000000123060070456000000789000000000123002000456000000789 123600900456000000789000000000123070008456000000789000000000123000008456000000789 123500070456000000789000000800123000000456900000789000005000123000000456000000789 123900070456000000789000000600123000000456008000789000000060123000000456000000789 123800040456000000789000000070123000000456010000789000600000123000000456000000789 123500040456000000789000000040123000000456000000789000000060123007000456000000789 123800070456000000789000000070123000000456000000789000000000123900000456000200789 123800070456000000789000000060123000000456000000789000000000123900000456000300789 123500090456000000789000000008123000000456007000789000000008123000000456000000789 123500040456000000789000000000123900800456000000789000000000123007000456000000789 123600040456000000789000000000123900800456000000789000000000123007000456000000789 123800070456000000789000000000123005900456000000789000000000123002000456000000789 123500040456000000789000000000123008007456000000789000000000123000300456000000789 123500040456000000789000000000123007000456000000789000000000123010200456000000789 123800070456000000789000000000123005000456000000789000000000123002000456000001789 123800070456000000789000000000123000010456000000789600000000123007000456000000789 123900000456000800789000000900123000000456000000789000000000123030000456000060789 123600000456000800789000000070123000000456090000789000004000123000000456000000789 123900000456000800789000000090123000000456001000789000500000123000000456000000789 123900000456000800789000000090123000000456002000789000500000123000000456000000789 123900000456000800789000000090123000000456007000789000500000123000000456000000789 123900000456000200789000000070123000000456000000789060000000123008000456000000789 123800000456000900789000000070123000000456000000789000004000123000000456000030789 123900000456000800789000000070123000000456000000789000004000123000000456000002789 123500000456000800789000000000123000200456000000789030000000123000000456000001789 123800000456000900789000000000123000070456000000789000000004123000000456002000789 123600000456000800789000000000123000000456090001789000000000123000000456000002789

by **JPF** » Thu Jan 18, 2007 7:53 am

Impressive work, Mauricio !

Congratulations to m_b_metcalf who picked the highest SE rated puzzle in the list !

JPF

by **JPF** » Sun Jan 21, 2007 1:56 am

Code: Select all: . . 5 . . . 8 . . . 6 . . . . . 1 . . 8 . . . . . 7 . . 3 . . . . . 6 . . 7 . . . . . 9 . . . 2 9 . 5 4 . . . . . . 6 . . . . . . . . 1 . . . . . . 9 3 . 4 2 . . brandy light

JPF

by **claudiarabia** » Sun Jan 21, 2007 2:34 am

JPF wrote:
Code: Select all
. . 5 . . . 8 . . . 6 . . . . . 1 . . 8 . . . . . 7 . . 3 . . . . . 6 . . 7 . . . . . 9 . . . 2 9 . 5 4 . . . . . . 6 . . . . . . . . 1 . . . . . . 9 3 . 4 2 . . brandy light

JPF

with this glass you proved once again to be the master of straight lines in sudoku. cheers!

by **m_b_metcalf** » Sun Jan 21, 2007 4:26 pm

JPF wrote:
Code: Select all
. . 5 . . . 8 . . . 6 . . . . . 1 . . 8 . . . . . 7 . . 3 . . . . . 6 . . 7 . . . . . 9 . . . 2 9 . 5 4 . . . . . . 6 . . . . . . . . 1 . . . . . . 9 3 . 4 2 . . brandy light

JPF

Beautiful. But when you invite friends for a drink, you'll need a set of six. Here are the missing five (note that r5c8 is often redundant).

À ta santé

Mike Metcalf

Code: Select all: . . 5 . . . 8 . . . 6 . . . . . 1 . . 8 . . . . . 2 . . 4 . . . . . 6 . . 1 . . . . . 5 . . . 3 9 . 5 7 . . . . . . 1 . . . . . . . . 8 . . . . . . 9 7 . 4 5 . . . . 5 . . . 8 . . . 6 . . . . . 1 . . 8 . . . . . 3 . . 4 . . . . . 6 . . 1 . . . . . 5 . . . 2 9 . 5 7 . . . . . . 1 . . . . . . . . 8 . . . . . . 9 7 . 4 5 . . . . 5 . . . 8 . . . 6 . . . . . 1 . . 3 . . . . . 4 . . 4 . . . . . 6 . . 2 . . . . . 5 . . . 3 9 . 5 7 . . . . . . 1 . . . . . . . . 6 . . . . . . 9 7 . 8 3 . . . . 5 . . . 8 . . . 6 . . . . . 1 . . 8 . . . . . 3 . . 7 . . . . . 6 . . 1 . . . . . 5 . . . 2 9 . 5 4 . . . . . . 1 . . . . . . . . 8 . . . . . . 9 7 . 4 5 . . . . 5 . . . 8 . . . 6 . . . . . 1 . . 8 . . . . . 2 . . 4 . . . . . 6 . . 1 . . . . . 5 . . . 7 9 . 5 3 . . . . . . 8 . . . . . . . . 1 . . . . . . 9 3 . 4 5 . .

by **claudiarabia** » Sun Jan 21, 2007 10:37 pm

Code: Select all: . . . . . . . . . . . . 3 9 5 2 . . 4 . . 6 . . . 3 . . . . 5 . . . 6 . . 6 . . 8 . . 5 . 7 8 . . . 9 3 1 . . . 8 . . . . . . 5 . . 4 1 . . . . 3 2 . 8 . . 5 . .

SE 4-4

by **claudiarabia** » Sun Jan 21, 2007 11:22 pm

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

Code: Select all: *-----------* |...|.2.|...| |.25|4.7|19.| |.8.|359|.2.| |---+---+---| |.13|5.4|97.| |.7.|.9.|...| |.69|273|41.| |---+---+---| |.58|932|.4.| |.47|615|38.| |...|748|...| *-----------* *-----------* |...|.2.|...| |.25|4.7|19.| |.8.|359|.2.| |---+---+---| |.13|5.4|97.| |.7.|.9.|...| |.69|273|41.| |---+---+---| |.58|932|.4.| |.47|615|38.| |...|748|...| *-----------*

Here is the pencilmark grid from which my solution originates

Code: Select all: *-----------------------------------------------------------------------------* | 134679 39 146 | 18 2 16 | 58 356 34567 | | 36 2 5 | 4 68 7 | 1 9 368 | | 1467 8 146 | 3 5 9 | 67 2 467 | |-------------------------+-------------------------+-------------------------| | 28 1 3 | 5 68 4 | 9 7 268 | | 45 7 24 | 18 9 16 | 258 356 356 | | 58 6 9 | 2 7 3 | 4 1 58 | |-------------------------+-------------------------+-------------------------| | 16 5 8 | 9 3 2 | 67 4 167 | | 29 4 7 | 6 1 5 | 3 8 29 | | 12369 39 126 | 7 4 8 | 25 56 12569 | *-----------------------------------------------------------------------------*

For this puzzle SE shows some X-Wings, a Swordfish 2 turbots, 2 forcing chains and a bi-directional y-cycle. After the Singles at the beginning I found the two X-wings in r15c47 and r59 c37. I chose another method afterwards than the Explainer. For I have problems to spot these cycles I made a contradiction-forcing chain, excluding 1 from r7c9 which solves finally the puzzle.

If r7c9 = 1 --> r7c7=7--> r3c7=6|-->r7c1=6-->r2c1=3 --> r2c9=8--> r2c5=6-->r4c5=8-->r5c4=1-->r5c6=6
If r2c9=8-->r1c7=5--> r9c7=2-->r5c7=8-->r6c9=5-->r4c9=2--> r5c89=36 ≠ r5c6=6

Then you can eliminate 1 from r7c9 --> r9c9=1 and you can make UR1 in r3c79; r7c79 upon 67--> r3c9=4

The puzzle is solved now!

by **ravel** » Mon Jan 22, 2007 9:56 am

There is a shortcut of your forcing chain, that eliminates 8 from r2c9, which leads to the same result:
r2c9=8 => r2c5=6 => r4c5=8 => r4c9=6 => r5c89=35 => r6c9=8
(or r2c9=8 => r2c5=6 => r4c5=8 => r4c9=6 => r5c7=2 => r1c7=8)

by **udosuk** » Mon Jan 22, 2007 2:02 pm

claudiarabia wrote:For this puzzle SE shows some X-Wings, a Swordfish 2 turbots, 2 forcing chains and a bi-directional y-cycle. After the Singles at the beginning I found the two X-wings in r15c47 and r59 c37. I chose another method afterwards than the Explainer. For I have problems to spot these cycles I made a contradiction-forcing chain, excluding 1 from r7c9 which solves finally the puzzle.

If r7c9 = 1 --> r7c7=7--> r3c7=6|-->r7c1=6-->r2c1=3 --> r2c9=8--> r2c5=6-->r4c5=8-->r5c4=1-->r5c6=6
If r2c9=8-->r1c7=5--> r9c7=2-->r5c7=8-->r6c9=5-->r4c9=2--> r5c89=36 ≠ r5c6=6

Then you can eliminate 1 from r7c9 --> r9c9=1 and you can make UR1 in r3c79; r7c79 upon 67--> r3c9=4

The puzzle is solved now!

Claudia, no offense but I think your chain is way too messy... There're neater ways to solve this puzzle...

For one, there is a "locked candidates"/"box-line elimination" move about the 1s in r1c13 which you didn't take... If you take the x-wings and the naked pairs I can't see why you don't take it as well... :?:

So, here is the state after the "locked candidates" move:

Code: Select all: *--------------------------------------------------------------------* | 34679 39 46 | 18 2 16 | 58 356 34567 | | 36 2 5 | 4 68 7 | 1 9 368 | | 1467 8 146 | 3 5 9 | 67 2 467 | |----------------------+----------------------+----------------------| | 28 1 3 | 5 68 4 | 9 7 268 | | 45 7 24 |@18 9 @16 |-258 #356 #356 | | 58 6 9 | 2 7 3 | 4 1 #58 | |----------------------+----------------------+----------------------| | 16 5 8 | 9 3 2 | 67 4 167 | | 29 4 7 | 6 1 5 | 3 8 29 | | 1369 39 126 | 7 4 8 | 25 56 1569 | *--------------------------------------------------------------------*

Note that there is an ALS(almost locked subsets)-xz move in r56/b56:

@: r5c46={168}
#: r5c89+r6c9={3568}
Restricted common=6 (r5c6 vs r5c89)
Eliminated common: r5c7<>8

Or to view it as chains:

r5c7=8 => r5c4=1 => r5c6=6
r5c7=8 => r6c9=5 => r5c89={36}
=> Two 6s on r5! Therefore r5c7<>8

Afterwards you can take some singles and naked pairs and reach:

Code: Select all: *--------------------------------------------------* |-379 #39 4 | 1 2 6 | 8 35 57 | | 36 2 5 | 4 8 7 | 1 9 36 | | 167 8 @16 | 3 5 9 |@67 2 4 | |----------------+----------------+----------------| | 8 1 3 | 5 6 4 | 9 7 2 | | 4 7 2 | 8 9 1 | 5 36 36 | | 5 6 9 | 2 7 3 | 4 1 8 | |----------------+----------------+----------------| |-16 5 8 | 9 3 2 |@67 4 17 | | 2 4 7 | 6 1 5 | 3 8 9 | |#39 #39 @16 | 7 4 8 | 2 -56 15 | *--------------------------------------------------*

Here you can apply a turbot fish (@) or a UR-type 1 (#) to finish it off...

:idea:

by **m_b_metcalf** » Mon Jan 22, 2007 2:23 pm

claudiarabia wrote:
Code: Select all
. . . . . . . . . . . . 3 9 5 2 . . 4 . . 6 . . . 3 . . . . 5 . . . 6 . . 6 . . 8 . . 5 . 7 8 . . . 9 3 1 . . . 8 . . . . . . 5 . . 4 1 . . . . 3 2 . 8 . . 5 . .

SE 4-4

Dear Claudia,
Another for the collection.

Code: Select all: . . . . . . . . . . . . 1 9 3 2 . . 8 . . 4 . . . 5 . . . . 9 . . . 4 . . 3 . . 5 . . 1 . 1 5 . . . 8 3 9 . . . 9 . . . . . . 6 . . 3 7 . . . . 2 1 . 6 . . 5 . . SE 8.3, minimal

Regards,

Mike Metcalf

by **claudiarabia** » Sat Jan 27, 2007 9:22 pm

udosuk wrote:....(Note that there is an ALS(almost locked subsets)-xz move in r56/b56:

@: r5c46={168}
#: r5c89+r6c9={3568}
Restricted common=6 (r5c6 vs r5c89)
Eliminated common: r5c7<>8

Or to view it as chains:

r5c7=8 => r5c4=1 => r5c6=6
r5c7=8 => r6c9=5 => r5c89={36}
=> Two 6s on r5! Therefore r5c7<>8

Afterwards you can take some singles and naked pairs and reach:
Code: Select all
*--------------------------------------------------* |-379 #39 4 | 1 2 6 | 8 35 57 | | 36 2 5 | 4 8 7 | 1 9 36 | | 167 8 @16 | 3 5 9 |@67 2 4 | |----------------+----------------+----------------| | 8 1 3 | 5 6 4 | 9 7 2 | | 4 7 2 | 8 9 1 | 5 36 36 | | 5 6 9 | 2 7 3 | 4 1 8 | |----------------+----------------+----------------| |-16 5 8 | 9 3 2 |@67 4 17 | | 2 4 7 | 6 1 5 | 3 8 9 | |#39 #39 @16 | 7 4 8 | 2 -56 15 | *--------------------------------------------------*

Here you can apply a turbot fish (@) or a UR-type 1 (#) to finish it off...

Thank you for the ALS and Turbot hints. So I'm not the only one to spot the UR-type 1.

by **claudiarabia** » Tue Jan 30, 2007 4:53 pm

Code: Select all: . . 3 . 4 . 1 . 2 . 7 5 1 . . . . . 8 . . . . . . . . . . . . . 8 . . . . . 1 . 3 . 4 . . . . . 2 . . . . . . . . . . . . . 7 . . . . . 5 8 6 . 4 . 6 . 9 . 5 . .

by **claudiarabia** » Tue Jan 30, 2007 6:30 pm

Code: Select all: 1 . . . . . . . . . . . 5 . . . 9 . 3 . 6 . 4 . . . . . . . . . 9 . 1 . 4 . . . 3 . . . 8 . 2 . 7 . . . . . . . . . 8 . 3 . 4 . 7 . . . 2 . . . . . . . . . . . 6

Bruzilla has mutable clues in r5c5 (3,6) and in
r6c2 [2 (SE 7.2), 5 (SE 4.4), 9 (SE 2.8)]. You'll have three different difficulty-levels.

by **JPF** » Sun Feb 04, 2007 7:44 pm

Here is a 18 clues puzzle with symmetry :

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

Not easy to design, but easy to solve

and

Code: Select all: . . . . . . . . 5 . 9 6 4 . . . 8 . . 7 . . . . 2 . . . 6 . 8 . 2 . . . . . . . . . . . . . . . 1 . 5 . 9 . . . 4 . . . . 3 . . 8 . . . 7 4 6 . 5 . . . . . . . .

SE=4.5

JPF

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