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by **ArkieTech** » Fri Apr 25, 2014 11:21 pm

Code: Select all: *-----------* |.1.|95.|.46| |...|...|98.| |7..|...|...| |---+---+---| |..4|.9.|2.5| |.57|...|.9.| |...|...|3..| |---+---+---| |6..|7.8|...| |4..|.6.|...| |..9|..3|..1| *-----------*

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by **Leren** » Sat Apr 26, 2014 1:17 am

Code: Select all: *---------------------------------------------------------------* |b38 1 a38 | 9 5 2 | 7 4 6 | |b25 4 256 | 136 137 167 | 9 8 23 | | 7 9 26 | 3468 348 46 | 15 15 23 | |--------------------+---------------------+--------------------| | 138 368 4 | 1368 9 167 | 2 167 5 | | 138-2 5 7 | 123468 12348 146 | 168 9 48 | | 9 268 a28 | 12468 12478 5 | 3 167 478 | |--------------------+---------------------+--------------------| | 6 23 1235 | 7 124 8 | 45 235 9 | | 4 2378 12358 | 125 6 9 | 58 2357 78 | |b258 278 9 | 245 24 3 | 4568 2567 1 | *---------------------------------------------------------------*

(2=3) r16c3 - (3=2) r129c1 => - 2 r5c1; lclste

Leren

by **SteveG48** » Sat Apr 26, 2014 1:27 am

Code: Select all: *-----------------------------------------------------------------------------* | 38 1 38 | 9 5 2 | 7 4 6 | | 25 4 256 | 136 137 167 | 9 8 23 | | 7 9 26 | 3468 348 46 | 15 15 23 | *-------------------------+-------------------------+-------------------------| | 138 368 4 | 1368 9 167 | 2 167 5 | | 1238 5 7 | 123468 12348 146 | 168 9 48 | | 9 268 28 | 12468 12478 5 | 3 167 478 | *-------------------------+-------------------------+-------------------------| | 6 23 d1235 | 7 124 8 |c45 c235 9 | | 4 2378 12358 | 125 6 9 |b58 2357 a78 | | 28-5 278 9 |a245 a24 3 |a4568 a2567 1 | *-----------------------------------------------------------------------------*

(5=24678)r8c9,r9c4578 - (8=5)r8c7 - r7c78 = r7c3 => -5 r9c1 ; lclste

by **Marty R.** » Sat Apr 26, 2014 1:44 am

Leren wrote:
Code: Select all
*--------------------------------------------------------------* |b38 1 a38 | 9 5 2 | 7 4 6 | |b25 4 256 | 136 137 167 | 9 8 23 | | 7 9 26 | 3468 348 46 | 15 15 23 | |--------------------+--------------------+--------------------| | 138 368 4 | 1368 9 167 | 2 167 5 | | 138-2 5 7 | 12346 12348 146 | 168 9 48 | | 9 268 a28 | 12468 12478 5 | 3 167 478 | |--------------------+--------------------+--------------------| | 6 23 1235 | 7 124 8 | 45 235 9 | | 4 2378 12358 | 125 6 9 | 58 2357 78 | |b258 278 9 | 245 24 3 | 4568 2567 1 | *--------------------------------------------------------------*

(2=3) r16c3 - (3=2) r129c1 => - 2 r5c1; lclste

Leren

Leren, how'd you get rid of the 8 in r5c4?

by **Leren** » Sat Apr 26, 2014 2:45 am

Marty R wrote : Leren, how'd you get rid of the 8 in r5c4?

Just a typo in my PM - now edited my post to correct it. Thanks for spotting the error.

Leren

by **daj95376** » Sat Apr 26, 2014 3:10 am

SteveG48 wrote:
Code: Select all
*-----------------------------------------------------------------------------* | 38 1 38 | 9 5 2 | 7 4 6 | | 25 4 256 | 136 137 167 | 9 8 23 | | 7 9 26 | 3468 348 46 | 15 15 23 | *-------------------------+-------------------------+-------------------------| | 138 368 4 | 1368 9 167 | 2 167 5 | | 1238 5 7 | 123468 12348 146 | 168 9 48 | | 9 268 28 | 12468 12478 5 | 3 167 478 | *-------------------------+-------------------------+-------------------------| | 6 23 d1235 | 7 124 8 |c45 c235 9 | | 4 2378 12358 | 125 6 9 |b58 2357 a78 | | 28-5 278 9 |a245 a24 3 |a4568 a2567 1 | *-----------------------------------------------------------------------------*

(5=24678)r8c9,r9c4578 - (8=5)r8c7 - r7c78 = r7c3 => -5 r9c1 ; lclste

Interesting. However, an ALS is limited to cells in a single house/unit. A workaround for your solution.

Code: Select all: (5=24)r9c45 - (24=5678)r9c78,r8c79 - 5r7c78 = 5r7c3 => -5 r9c1

Here's another way to get the same elimination. I reworked a SIN from my solver.

Code: Select all: +--------------------------------------------------------------------------------+ | 38 1 38 | 9 5 2 | 7 4 6 | | 25 4 256 | 136 137 167 | 9 8 23 | | 7 9 26 | 3468 348 46 | 15 15 23 | |--------------------------+--------------------------+--------------------------| | 138 368 4 | 1368 9 167 | 2 167 5 | | 1238 5 7 | 123468 12348 146 | 168 9 48 | | 9 268 28 | 12468 12478 5 | 3 167 478 | |--------------------------+--------------------------+--------------------------| | 6 23 1235 | 7 124 8 | 45 235 9 | | 4 d2378 d12358 | b125 6 9 | c58 2357 c78 | | e258 e278 9 | a245 24 3 | 4568 2567 1 | +--------------------------------------------------------------------------------+ # 101 eliminations remain 5r9c4 = r8c4 - (5=78)r8c79 - (78)r8c23 = (78)r9c12 => -5 r9c1

by **SteveG48** » Sat Apr 26, 2014 4:52 am

Code: Select all: *-------------------------------------------------------------------------------* | D38 1 C38 | 9 5 2 | 7 4 6 | | 25 4 256 | 136 137 167 | 9 8 23 | | 7 9 26 | 3468 348 46 | 15 15 23 | *--------------------------+-------------------------+--------------------------| | 138 368 4 | 1368 9 167 | 2 167 5 | | 1238 5 7 | 123468 12348 146 | 168 9 48 | | 9 268 28 | 12468 12478 5 | 3 167 478 | *--------------------------+-------------------------+--------------------------| | 6 A23 B1235 | 7 124 8 | 45 235 9 | | 4 aA2378 B12358 | 125 6 9 |cG5-8 2357 bF78 | | E258 278 9 |E245 E24 3 | F4568 F2567 1 | *-------------------------------------------------------------------------------* Kraken cell [2378]r8c2 => -8 r8c7 ; stte (8)r8c2 - (8)r8c7 || (7)r8c2 - (7=8)r8c9 - (8)r8c7 || (23)r78c2 - (3)r78c3 = r1c3 - (3=8)r1c1 - (8=245)r9c145 - (245=678)r9c78,r8c9 - (8)r8c7

Danny, thanks for your observations. I'll look at the other solution again.

(This one edited to incorporate a fix.)

by **SteveG48** » Sat Apr 26, 2014 1:59 pm

daj95376 wrote:
SteveG48 wrote:
Code: Select all
*-----------------------------------------------------------------------------* | 38 1 38 | 9 5 2 | 7 4 6 | | 25 4 256 | 136 137 167 | 9 8 23 | | 7 9 26 | 3468 348 46 | 15 15 23 | *-------------------------+-------------------------+-------------------------| | 138 368 4 | 1368 9 167 | 2 167 5 | | 1238 5 7 | 123468 12348 146 | 168 9 48 | | 9 268 28 | 12468 12478 5 | 3 167 478 | *-------------------------+-------------------------+-------------------------| | 6 23 d1235 | 7 124 8 |c45 c235 9 | | 4 2378 12358 | 125 6 9 |b58 2357 a78 | | 28-5 278 9 |a245 a24 3 |a4568 a2567 1 | *-----------------------------------------------------------------------------*

(5=24678)r8c9,r9c4578 - (8=5)r8c7 - r7c78 = r7c3 => -5 r9c1 ; lclste

Interesting. However, an ALS is limited to cells in a single house/unit. A workaround for your solution.

Code: Select all
(5=24)r9c45 - (24=5678)r9c78,r8c79 - 5r7c78 = 5r7c3 => -5 r9c1

Danny, I like your work around. It gets the job done. On the other hand, it's obvious that my original conclusion, that if neither r9c4, r9c7, nor r9c8, is a 5 then r8c7 must be a 5, is logically correct. If I needed that specific result as part of a solution, what would be the correct way to write it?

by **daj95376** » Sat Apr 26, 2014 4:26 pm

SteveG48 wrote:On the other hand, it's obvious that my original conclusion, that if r9c478 is not 5 then r8c7 must be a 5, is logically correct. If I needed that specific result as part of a solution, what would be the correct way to write it?

To get your intermediate state of (8=5)r8c7, I need to split your initial assumption into two parts -- a dynamic process.

Code: Select all: Assumption ========== Part #1: (5=24)r9c45 - (24 )r9c78 = (678)r9c78,r8c9 - (8=5)r8c7 Part #2: ( 5)r9c78 /

However, and this is a BIG however, both parts of the initial assumption must be factored into any final conclusion.

by **SteveG48** » Sat Apr 26, 2014 4:41 pm

Thanks, Danny. I was afraid it would be a complex expression like that.

Note that if we simply run my initial expression backwards we get a 2456 quad in r9c3478 and the whole problem goes away.

by **Marty R.** » Sat Apr 26, 2014 8:08 pm

I have a situation which I don't know how to interpret--hardly a shocking development.

Code: Select all: +-----------------+------------------+---------------+ | 38 1 38 | 9 5 2 | 7 4 6 | | 25 4 256 | 136 137 167 | 9 8 23 | | 7 9 26 | 3468 348 46 | 15 15 23 | +-----------------+------------------+---------------+ | 138 368 4 | 1368 9 167 | 2 167 5 | | 1238 5 7 | 123468 12348 146 | 168 9 48 | | 9 268 28 | 12468 12478 5 | 3 167 478 | +-----------------+------------------+---------------+ | 6 23 1235 | 7 124 8 | 45 235 9 | | 4 2378 12358 | 125 6 9 | 58 2357 78 | | 258 278 9 | 245 24 3 | 4568 2567 1 | +-----------------+------------------+---------------+

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Look at the potential DP on 23 in r78,c28. Working with the cells in c2 I do an external analysis; it doesn't matter whether the box or column is used. If any of the externals is 2, then r7c2=3 or if any of the externals is 3, then r7c2=2.

What conclusions can be made from this? I almost want to say that none of the external cells can contain a 2 or 3, but I don't dare.

by **SteveG48** » Sat Apr 26, 2014 8:26 pm

Marty R. wrote:I have a situation which I don't know how to interpret--hardly a shocking development.

Code: Select all
+-----------------+------------------+---------------+ | 38 1 38 | 9 5 2 | 7 4 6 | | 25 4 256 | 136 137 167 | 9 8 23 | | 7 9 26 | 3468 348 46 | 15 15 23 | +-----------------+------------------+---------------+ | 138 368 4 | 1368 9 167 | 2 167 5 | | 1238 5 7 | 123468 12348 146 | 168 9 48 | | 9 268 28 | 12468 12478 5 | 3 167 478 | +-----------------+------------------+---------------+ | 6 23 1235 | 7 124 8 | 45 235 9 | | 4 2378 12358 | 125 6 9 | 58 2357 78 | | 258 278 9 | 245 24 3 | 4568 2567 1 | +-----------------+------------------+---------------+

Play this puzzle online at the Daily Sudoku site

Look at the potential DP on 23 in r78,c28. Working with the cells in c2 I do an external analysis; it doesn't matter whether the box or column is used. If any of the externals is 2, then r7c2=3 or if any of the externals is 3, then r7c2=2.

What conclusions can be made from this? I almost want to say that none of the external cells can contain a 2 or 3, but I don't dare.

Marty, your observation with respect to externals is correct, but I don't see any useful conclusion from it. It's manifest at the outset that r7c2 is either 2 or 3. I don't know why you would conclude that none of the externals is 2 or 3. You can certainly conclude that either none of the externals is 2 or none of the externals is 3, but you don't know which conclusion is correct.

by **SteveG48** » Sat Apr 26, 2014 8:49 pm

Code: Select all: *------------------------------------------------------------------------------* |ad38 1 b38 | 9 5 2 | 7 4 6 | | 25 4 256 | 136 137 167 | 9 8 23 | | 7 9 26 | 3468 348 46 | 15 15 23 | *--------------------------+-------------------------+-------------------------| | 138 368 4 | 1368 9 167 | 2 167 5 | | d1238 5 7 | 123468 12348 146 | 168 9 48 | | 9 268 c28 | 12468 12478 5 | 3 167 478 | *--------------------------+-------------------------+-------------------------| | 6 23 1235 | 7 124 8 | 45 235 9 | | 4 2378 12358 | 125 6 9 | 58 2357 78 | | 25-8 278 9 | 245 24 3 | 4568 2567 1 | *------------------------------------------------------------------------------*

(8)r1c1 = r1c3 - (8=2)r6c3 - (2=138)r145c1 => -8 r9c1 ; lclste

by **Marty R.** » Sat Apr 26, 2014 9:33 pm

Marty, your observation with respect to externals is correct, but I don't see any useful conclusion from it. It's manifest at the outset that r7c2 is either 2 or 3. I don't know why you would conclude that none of the externals is 2 or 3. You can certainly conclude that either none of the externals is 2 or none of the externals is 3, but you don't know which conclusion is correct.

Thanks Steve. It just looked odd to me and I thought it might be a contradiction. I just never saw that kind of result from a UR.

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