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by **ArkieTech** » Sun May 31, 2015 11:26 pm

Code: Select all: *-----------* |..4|...|...| |...|7..|...| |.1.|.68|.37| |---+---+---| |2.6|...|..1| |...|821|...| |3..|...|9.8| |---+---+---| |86.|29.|.5.| |...|..6|...| |...|...|4..| *-----------*

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by **Leren** » Mon Jun 01, 2015 12:28 am

Code: Select all: *---------------------------------------------------------------* | 567 2357 4 | 1359 135 2359 | 268-5 189 29-5 | |b56 235 8 | 7 135 2359 | c256 149 249-5 | |b59 1 b259 | 4 6 8 |ca25 3 7 | |--------------------+--------------------+---------------------| | 2 8 6 | 359 3457 3579 | 7-5 47 1 | | 4579 4579 59 | 8 2 1 | 3 467 456 | | 3 457 1 | 6 457 57 | 9 2 8 | |--------------------+--------------------+---------------------| | 8 6 7 | 2 9 4 | 1 5 3 | | 1459 2459 2359 | 135 13578 6 | 278 789 29 | | 159 259 2359 | 135 13578 357 | 4 6789 269 | *---------------------------------------------------------------*

ALS XY Wing: (5=2) r3c7 - (2=6) r2c1, r3c13 - (6=5) r23c7 => - 5 r1c79, r2c9, r4c7; lclste

or

Code: Select all: *---------------------------------------------------------------* | 567 2357 4 | 1359 135 2359 | 2568 189 259 | |b56 235 8 | 7 135 2359 | c256 149 2459 | |b59 1 b259 | 4 6 8 |ca25 3 7 | |--------------------+--------------------+---------------------| | 2 8 6 | 359 345-7 359-7 |ca57 4-7 1 | | 4579 4579 59 | 8 2 1 | 3 46-7 456 | | 3 457 1 | 6 457 57 | 9 2 8 | |--------------------+--------------------+---------------------| | 8 6 7 | 2 9 4 | 1 5 3 | | 1459 2459 2359 | 135 13578 6 | 28-7 789 29 | | 159 259 2359 | 135 13578 357 | 4 6789 269 | *---------------------------------------------------------------*

ALS XY Wing: (7=2) r34c7 - (2=6) r2c1, r3c13 - (6=7) r234c7 => - 7 r4c568, r5c8, r8c7; lclste

Leren

by **Marty R.** » Mon Jun 01, 2015 1:37 am

Code: Select all: +----------------+-----------------+----------------+ | 567 2357 4 | 1359 135 2359 | 2568 189 259 | | 56 235 8 | 7 135 2359 | 256 149 2459 | | 59 1 259 | 4 6 8 | 25 3 7 | +----------------+-----------------+----------------+ | 2 8 6 | 359 3457 3579 | 57 47 1 | | 4579 4579 59 | 8 2 1 | 3 467 456 | | 3 457 1 | 6 457 57 | 9 2 8 | +----------------+-----------------+----------------+ | 8 6 7 | 2 9 4 | 1 5 3 | | 1459 2459 2359 | 135 13578 6 | 278 789 29 | | 159 259 2359 | 135 13578 357 | 4 6789 269 | +----------------+-----------------+----------------+

Play this puzzle online at the Daily Sudoku site

DP (59) r35c13. Venturing into uncharted waters with internals, 2 in r3c3 and externals, 5 in r5c9: 5r5c9=2r3c3-(2=5) r3c7=>r12c9,r4c7<>5

by **pjb** » Mon Jun 01, 2015 3:23 am

Code: Select all: 567 2357 4 | 1359 135 2359 | 2568 189 259 c56 235 8 | 7 135 2359 |d256 149 2459 c59 1 c259 | 4 6 8 |bd25 3 7 ------------------------+----------------------+--------------------- 2 8 6 | 359 3457 3579 |a57 47 1 4579 4579 59 | 8 2 1 | 3 467 456 3 457 1 | 6 457 57 | 9 2 8 ------------------------+----------------------+--------------------- 8 6 7 | 2 9 4 | 1 5 3 1459 2459 2359 | 135 13578 6 | 278 789 29 159 259 2359 | 135 13578 357 | 4 6789 269

I could only come up with a slight variation on Leren's:

(7=5)r4c7 - (5=2)r3c7 - (2=6)r2c1,r3c13 - (6=5)r23c7 => -5 r4c7; lclste

Phil

PS Marty: Apologies if I'm missing something obvious, but any chance you could give more detail on this move: 5r5c9=2r3c3?

by **SteveG48** » Mon Jun 01, 2015 3:30 am

Code: Select all: *---------------------------------------------------------------------* | 67-5 2357 4 | 1359 135 2359 | 2568 189 259 | | 6-5 235 8 | 7 135 2359 | 256 149 2459 | |ai59 1 a259 | 4 6 8 |b25 3 7 | *-----------------------+----------------------+----------------------| | 2 8 6 | 359 3457 3579 |c57 47 1 | | e4579 e4579 e59 | 8 2 1 | 3 467 d456 | | 3 f457 1 | 6 457 g57 | 9 2 8 | *-----------------------+----------------------+----------------------| | 8 6 7 | 2 9 4 | 1 5 3 | | 1459 2459 2359 | 135 13578 6 | 278 789 29 | | i159 259 h2359 |h135 13578 h357 | 4 6789 269 | *---------------------------------------------------------------------* (5=92*)r3c13 - (2=5)r3c7 - r4c7 = r5c9 - (5)r5c123 = r6c2 - (5=7)r6c6 - (7*2*9=351)r9c346 - (1=59)r39c1 => -5 r12c1 ; stte = (9*)r5c3

by **Marty R.** » Mon Jun 01, 2015 3:50 am

pjb wrote:
Code: Select all
567 2357 4 | 1359 135 2359 | 2568 189 259 c56 235 8 | 7 135 2359 |d256 149 2459 c59 1 c259 | 4 6 8 |bd25 3 7 ------------------------+----------------------+--------------------- 2 8 6 | 359 3457 3579 |a57 47 1 4579 4579 59 | 8 2 1 | 3 467 456 3 457 1 | 6 457 57 | 9 2 8 ------------------------+----------------------+--------------------- 8 6 7 | 2 9 4 | 1 5 3 1459 2459 2359 | 135 13578 6 | 278 789 29 159 259 2359 | 135 13578 357 | 4 6789 269

I could only come up with a slight variation on Leren's:

(7=5)r4c7 - (5=2)r3c7 - (2=6)r2c1,r3c13 - (6=5)r23c7 => -5 r4c7; lclste

Phil

PS Marty: Apologies if I'm missing something obvious, but any chance you could give more detail on this move: 5r5c9=2r3c3?

Phil,

Anything I try can always go wrong. As the internal, the 2 in r3c3 kills the DP. As an external, the 5 in r5c9 kills it as well, thus 5=2 is the way I saw it. In the meantime, anticipating a question or challenge, I asked the resident expert on externals.

by **sultan vinegar** » Mon Jun 01, 2015 11:11 am

Hi Marty,

For DP (59) r35c13, there are three ways to prevent it:

Code: Select all: 567 2357 4 | 1359 135 2359 | 2568 189 259 56 235 8 | 7 135 2359 | 256 149 2459 (59) 1 2(59) | 4 6 8 | 25 3 7 ------------------------+----------------------+--------------------- 2 8 6 | 359 3457 3579 | 57 47 1 47(59) 4579 (59) | 8 2 1 | 3 467 456 3 457 1 | 6 457 57 | 9 2 8 ------------------------+----------------------+--------------------- 8 6 7 | 2 9 4 | 1 5 3 1459 2459 2359 | 135 13578 6 | 278 789 29 159 259 2359 | 135 13578 357 | 4 6789 269

One of (2)r3c3, (4)r5c1, (7)r5c1 must be true. No internals/externals are necessary! I can't find any eliminations with this DP.

by **JC Van Hay** » Mon Jun 01, 2015 2:22 pm

DP(53)r35c13 or r35c13 -> +7r4c7; lclste or ...

Code: Select all: +-----------------------+-------------------+---------------------+ | 5(67) 5(237) 4 | 1359 135 2359 | 2-5(68) 189 259 | | 56 5(23) 8 | 7 135 2359 | 256 149 2459 | | 59 1 59(2) | 4 6 8 | (25) 3 7 | +-----------------------+-------------------+---------------------+ | 2 8 6 | 359 3457 3579 | -5(7) 47 1 | | 459(7) 459(7) 59 | 8 2 1 | 3 46-7 456 | | 3 45(7) 1 | 6 457 57 | 9 2 8 | +-----------------------+-------------------+---------------------+ | 8 6 7 | 2 9 4 | 1 5 3 | | 1459 2459 2359 | 135 13578 6 | 2(78) 789 29 | | 159 259 2359 | 135 13578 357 | 4 6789 269 | +-----------------------+-------------------+---------------------+

7r4c7=(7-8)r8c7=(8-6)r1c7=(6-7)r1c1=7r5c1-7r56c2=HP(73-2)r12c2=2r3c3-(2=5)r3c7 :=> -7r5c8, -5r14c7; 11 Singles; HP(78)r9c58; stte

by **daj95376** » Mon Jun 01, 2015 4:15 pm

Marty, my solver finds only one elimination associated with your UR.

Code: Select all: +-----------------------------------------------------------------------+ | 567 2357 4 | 1359 135 2359 | 2568 189 259 | | 56 235 8 | 7 135 2359 | 256 149 2459 | | *59 1 *59+2 | 4 6 8 | 25 3 7 | |-----------------------+-----------------------+-----------------------| | 2 8 6 | 359 3457 3579 | 57 47 1 | | *59+47 4579 *59 | 8 2 1 | 3 467 456 | | 3 457 1 | 6 457 57 | 9 2 8 | |-----------------------+-----------------------+-----------------------| | 8 6 7 | 2 9 4 | 1 5 3 | | 1459 2459 2359 | 135 13578 6 | 278 789 29 | | 159 259 2359 | 135 13578 357 | 4 6789 269 | +-----------------------------------------------------------------------+ # 105 eliminations remain 9r5c1, 5r5c3 + 5r3c1, 9r3c3; DP => -9 r5c1

However, while trying to decipher JC's DP deduction, I ran across some logic that my solver doesn't use.

Code: Select all: (4+7=59)r5c13 - 5r5c9 = 5r4c7 - (5=2)r3c7 - (2=59)r3c13; DP => -59 r5c1

_

by **Marty R.** » Mon Jun 01, 2015 4:23 pm

sultan vinegar wrote:Hi Marty,

For DP (59) r35c13, there are three ways to prevent it:

Code: Select all
567 2357 4 | 1359 135 2359 | 2568 189 259 56 235 8 | 7 135 2359 | 256 149 2459 (59) 1 2(59) | 4 6 8 | 25 3 7 ------------------------+----------------------+--------------------- 2 8 6 | 359 3457 3579 | 57 47 1 47(59) 4579 (59) | 8 2 1 | 3 467 456 3 457 1 | 6 457 57 | 9 2 8 ------------------------+----------------------+--------------------- 8 6 7 | 2 9 4 | 1 5 3 1459 2459 2359 | 135 13578 6 | 278 789 29 159 259 2359 | 135 13578 357 | 4 6789 269

One of (2)r3c3, (4)r5c1, (7)r5c1 must be true. No internals/externals are necessary! I can't find any eliminations with this DP.

SV,

Thanks, your comments are always appreciated and respected. Obviously your first statement is inarguable, that a 2, 4 or 7 kill the DP. However, that is strictly using internals. To the best of my knowledge, a mix of internals and externals can be used, which I decided to do with this puzzle. Using the external 5 obviates the need for the 4 and 7 and combined with the internal 2 results in an extremely simple solution of the type that I see only seldomly.
When it comes to sudoku theory, I usually leave those discussions to the experts. After thinking about this one, I can't see anything wrong, and if there is, I'd like to see the details, even if if I can't say my confidence factor is 100%.

Marty

by **daj95376** » Mon Jun 01, 2015 4:39 pm

Marty R. wrote:
Code: Select all
+----------------+-----------------+----------------+ | 567 2357 4 | 1359 135 2359 | 2568 189 259 | | 56 235 8 | 7 135 2359 | 256 149 2459 | | 59 1 259 | 4 6 8 | 25 3 7 | +----------------+-----------------+----------------+ | 2 8 6 | 359 3457 3579 | 57 47 1 | | 4579 4579 59 | 8 2 1 | 3 467 456 | | 3 457 1 | 6 457 57 | 9 2 8 | +----------------+-----------------+----------------+ | 8 6 7 | 2 9 4 | 1 5 3 | | 1459 2459 2359 | 135 13578 6 | 278 789 29 | | 159 259 2359 | 135 13578 357 | 4 6789 269 | +----------------+-----------------+----------------+

DP (59) r35c13. Venturing into uncharted waters with internals, 2 in r3c3 and externals, 5 in r5c9: 5r5c9=2r3c3-(2=5) r3c7=>r12c9,r4c7<>5

Okay, tackling your logic. 2r3c3 is an internal that blocks the DP. However, 5r5c9 is not the only external <5> in [r5] that blocks the DP. There's also 5r5c2. Thus, you can't form the SL 5r5c9=2r3c3.

_

by **David P Bird** » Mon Jun 01, 2015 7:17 pm

Code: Select all: +----------------+-----------------+----------------+ | 567 2357 4 | 1359 135 2359 | 2568 189 259 | | 56 235 8 | 7 135 2359 | 256 149 2459 | | 59 1 259 | 4 6 8 | 25 3 7 | +----------------+-----------------+----------------+ | 2 8 6 | 359 3457 3579 | 57 47 1 | | 4579 4579 59 | 8 2 1 | 3 467 456 | | 3 457 1 | 6 457 57 | 9 2 8 | +----------------+-----------------+----------------+ | 8 6 7 | 2 9 4 | 1 5 3 | | 1459 2459 2359 | 135 13578 6 | 278 789 29 | | 159 259 2359 | 135 13578 357 | 4 6789 269 | +----------------+-----------------+----------------+

Marty, using only AICs
(4|7)r5c1 = (59)r5c13 -[UR]- (59)r3c13 = (5)r3c7 - (5)r4c7 = (5)r5c9 => r5c1 <> 5

(4|7)r5c1 (either 4 or 7) (internal) prevents (59)r5c13 and (5)r3c7 (external) prevents (59)r3c13 and leads to (5)r5c9
either way r5c1 <> 5

The chain can be extended to
(4|7a)r5c1 = (59)r5c13 -[UR]- (59)r3c13 = (5)r3c7 - (5)r4c7 = (5b)r5c9 - (5=9c)r5c3 => [ab] r5c1 <>5, [ac] r5c1 <> 9
This doesn't crack the puzzle though!

(59)r5c13 -[UR]- (59)r3c13 is a way to notate that two different pairs of cells in a UR pattern can't hold the same pair of digits. I find that writing it like that makes checking my work easier.

In your original notation you were trying to use (5)r5c9 as an external disruptor but you must use all the (5)'s and (9)'s in the same house which includes (5) & (9) in r5c2 as well (just one of these three would have to be true).
So your link should have been (59)r5c13 = (5|9)r5c29 which isn't very useful.

DPB

by **Marty R.** » Mon Jun 01, 2015 8:09 pm

Danny and David,

Thank you, mea culpa. I never noticed the extra internals in r5. I thought my solution was a little too easy. :oops:

I'll look a little more carefully before I try my next external.

by **sultan vinegar** » Tue Jun 02, 2015 10:43 am

Hi Marty,

Sorry, I see what you were trying to do now. I don't tend to consider 'externals' as most of the time there will be more of them than 'internals' and hence more work to add to the chain. The same information is always available in the 'internals' anyway, so I suggest if you are more comfortable with the 'internal' logic then just stick to that.

I.e. using 'internals' for DPBs chain you get:

(47)r5c1 = (2)r3c3[AUR59:r35c13] - (2=5)r3c7 - (5)r4c7 = (NP57)r5c39 => r5c1 <> 5,9.

David P Bird wrote:So your link should have been (59)r5c13 = (5|9)r5c29 which isn't very useful.

DPB, given that I haven't wound you up in a while I can't resist pointing out the following chain

Hidden Text: Show

Too bad it doesn't crack the puzzle.

by **David P Bird** » Tue Jun 02, 2015 11:11 am

sultan vinegar wrote:DPB, given that I haven't wound you up in a while I can't resist pointing out the following chain
Hidden Text: Show
(NP59)r5c39 = (5)r4c7 - (5=2)r3c7 - (2)r3c3 = (QNP59)r5c239[AUR59:r35c13] => r5c1 <> 5,9.

SV I refuse to rise to that dig, except to say that I prefer to call a spade a spade not a MEMD (Manual Earth Moving Device). 8-)

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