The New Sudoku Players' Forum

by **daj95376** » Mon Jun 30, 2014 3:25 pm

Code: Select all: +-----------------------+ | . 3 . | 5 . 4 | . 7 . | | 6 . 4 | 7 8 2 | . . . | | . 2 . | . 1 . | . . 5 | |-------+-------+-------| | 7 8 . | 1 . . | . . . | | . 1 6 | . . 5 | . . 4 | | 5 4 . | . 3 . | 8 . . | |-------+-------+-------| | . . . | . . 3 | 5 . . | | 3 . . | . . . | . 4 . | | . . 5 | . 7 . | . . 3 | +-----------------------+ +--------------------------------------------------------------+ | 189 3 189 | 5 69 4 | 26 7 268 | | 6 5 4 | 7 8 2 | 3 19 19 | | 89 2 7 | 3 1 69 | 4 68 5 | |--------------------+--------------------+--------------------| | 7 8 3 | 1 4 69 | 269 5 269 | | 29 1 6 | 8 29 5 | 7 3 4 | | 5 4 29 | 269 3 7 | 8 169 169 | |--------------------+--------------------+--------------------| | 1248 679 128 | 2469 269 3 | 5 2689 6789 | | 3 679 28 | 269 5 18 | 169 4 6789 | | 248 69 5 | 2469 7 18 | 169 2689 3 | +--------------------------------------------------------------+ # 68 eliminations remain

Play this puzzle online at the Daily Sudoku site

_

by **ArkieTech** » Mon Jun 30, 2014 6:47 pm

I am sure it can be simplified: :roll:

Code: Select all: *-----------------------------------------------------------* | 189 3 189 | 5 69 4 | 26 7 268 | | 6 5 4 | 7 8 2 | 3 19 19 | | 89 2 7 | 3 1 69 | 4 68 5 | |-------------------+-------------------+-------------------| | 7 8 3 | 1 4 69 | 269 5 269 | | 29 1 6 | 8 29 5 | 7 3 4 | | 5 4 29 | 269 3 7 | 8 169 169 | |-------------------+-------------------+-------------------| | 1248 679 128 | 2469 269 3 | 5 2689 6789 | | 3 679 28 | 269 5 18 | 169 4 6789 | | 248 69 5 | 2469 7 18 | 169 2689 3 | *-----------------------------------------------------------* ------------------(69=28)r79c8 (6)ur19r26c89=6r4c6-6r3c6=6r3c8-r6c8=6r6c9-6r78c9 -(6=8)r3c16-r1c13=r1c9--8r78c9 =79r78c9 (2=8)r8c3-r7c3================================================8r7c8-(8=2)r9c8 => -2r9c1; ste

by **JC Van Hay** » Mon Jun 30, 2014 8:11 pm

Even though the puzzle can be solved by using ~SSTS [XW(2) + XW(9) + WW(28)], here is a one-stepper, a 7-SIS AAIC, after Subsets and Locked Candidates :!:

Code: Select all: +------------------+---------------------+----------------------+ | 189 3 19(8) | 5 9(6) 4 | 26 7 26(8) | | 6 5 4 | 7 8 2 | 3 19 19 | | 89 2 7 | 3 1 9(6) | 4 (68) 5 | +------------------+---------------------+----------------------+ | 7 8 3 | 1 4 69 | 269 5 269 | | 29 1 6 | 8 29 5 | 7 3 4 | | 5 4 29 | 269 3 7 | 8 169 169 | +------------------+---------------------+----------------------+ | 1248 679 12(8) | 2469 9-2(6) 3 | 5 9-6(28) 679(8) | | 3 679 (28) | 69(2) 5 18 | 169 4 679(8) | | 248 69 5 | 2469 7 18 | 169 69(28) 3 | +------------------+---------------------+----------------------+

Kite(6r7c5=6r1c5-6r3c6=6r3c8)-8r3c8=8r1c9-[8r1c3=8r78c9]=*[2r7c8=(2-8)r9c8=*8r7c8-8r7c3=*(8-2)r8c2=2r8c4]

:=> [6r7c5==6r3c8]-6r7c8, [6r7c5==2r7c8==2r8c4]-2r7c5; ste

by **blue** » Mon Jun 30, 2014 10:18 pm

Code: Select all: +------------------+-------------------+---------------------+ | 189 3 19(8) | 5 9(6) 4 | (26) 7 (268) | | 6 5 4 | 7 8 2 | 3 19 19 | | 89 2 7 | 3 1 69 | 4 6(8) 5 | +------------------+-------------------+---------------------+ | 7 8 3 | 1 4 69 | 269 5 269 | | 29 1 6 | 8 29 5 | 7 3 4 | | 5 4 29 | 269 3 7 | 8 169 169 | +------------------+-------------------+---------------------+ | 1248 679 12(8) | 2469 9-2(6) 3 | 5 69(28) 6789 | | 3 679 (28) | 69(2) 5 18 | 169 4 6789 | | 248 69 5 | 2469 7 18 | 169 69(28) 3 | +------------------+-------------------+---------------------+

Dual Kraken column 8c38 => -2r7c5; stte

Code: Select all: 8r8c3 - 2r8c3 = 2r8c4 ------------------- || \ 8r1c3 ------- \ || \ \ || 8r3c8 - (8=26)r1c79 - 6r1c5 = 6r7c5 - 2r7c5 || || / 8r7c3 - 8r7c8 / || / 8r9c8 - 2r9c8 = 2r7c8 -----------

Similar:

[ There's a Kite elimination for 9r3c1, leading to r3c1=8,r1c3<>8,r3c8<>8, that would make the center chain unnecessary ]

Code: Select all: 8r8c3 - 2r8c3 = 2r8c4 --------------------------- || \ 8r1c3 --------- \ || \ \ || 8r3c8 - (8=9)r3c1 - r3c6 = r4c6 - (9=2)r5c5 - 2r7c5 || || / 8r7c3 - 8r7c8 / || / 8r9c8 - 2r9c8 = 2r7c8 -------------------

by **daj95376** » Tue Jul 01, 2014 4:15 am

_

My solver didn't find a short network. However, I find rewriting it produced an unexpected cascade effect.

Code: Select all: Kraken Cell r7c8: 8r7c8 - r7c3 = (8-2)r8c3 || || || = 8 r1c3 - r1c9 = (8-6)r3c8 \ || \ 9r7c8 - (19=6)r26c8 _____________ \ \ || \ \ 6r7c8 - r3c8 = r3c6 - r1c5 = (6-2)r7c5 \ || \ 2r7c8 - r7c5 = r5c5 - r5c1 = r6c3 - 2r8c3

_

by **pjb** » Tue Jul 01, 2014 6:52 am

Code: Select all: 189 3 189 | 5 69 4 | 26 7 268 6 5 4 | 7 8 2 | 3 19 19 b89 2 7 | 3 1 a69 | 4 68 5 ---------------------+----------------------+--------------------- 7 8 3 | 1 4 69 | 269 5 269 c29 1 6 | 8 d29 5 | 7 3 4 5 4 29 | 269 3 7 | 8 169 169 ---------------------+----------------------+--------------------- 1248 679 128 | 2469 269 3 | 5 2689 6789 3 679 28 | 269 5 18 | 169 4 6789 248 69 5 | 2469 7 18 | 169 2689 3

I'm afraid I had to resort to a two stepper:

1. skyscraper (9)r3c6 = r3c1 - r5c1 = r5c5 => -9 r1c5, r4c6
or
1. Type 2 UR(19)r26c89 => -6 r4c79, r6c4
either leading to

Code: Select all: 19 3 19 | 5 6 4 | 2 7 8 6 5 4 | 7 8 2 | 3 9 1 8 2 7 | 3 1 9 | 4 6 5 ---------------------+----------------------+--------------------- 7 8 3 | 1 4 6 | 9 5 2 29 1 6 | 8 29 5 | 7 3 4 5 4 29 | 29 3 7 | 8 1 6 ---------------------+----------------------+--------------------- 124 679 b128 | 469-2 9-2 3 | 5 a28 79 3 679 c28 |d269 5 18 | 16 4 79 24 69 5 | 2469 7 18 | 16 28 3

Then:
2. (2=8)r7c8-r7c3=(8-2)r8c3=r8c4, -2 r7c45; stte

Phil

by **Leren** » Tue Jul 01, 2014 8:01 am

Code: Select all: *--------------------------------------------------------------------------------* | 189 3 a189 | 5 Ee69 4 | 26 7 b268 | | 6 5 4 | 7 8 2 | 3 19 19 | | 89 2 7 | 3 1 Dd69 | 4 Cc68 5 | |--------------------------+--------------------------+--------------------------| | 7 8 3 | 1 4 69 | 269 5 269 | | 29 1 6 | 8 29 5 | 7 3 4 | | 5 4 29 | 269 3 7 | 8 169 169 | |--------------------------+--------------------------+--------------------------| | 1248 679 A128 | 2469 EFf69-2c 3 | 5 DB2689 6789 | | 3 679 28a | 269b 5 18 | 169 4 6789 | | 248 69 5 | 2469 7 18 | 169 C2689 3 | *--------------------------------------------------------------------------------* Kraken Column 3 Digit 8: 8 r1c3 - r1c9 = (8-6) r3c8 = r3c6 - r1c5 = r7c5 - 2 r7c5; 8 r7c3 - r7c8 = (8-6) r3c8 = r3c6 - r1c5 = r7c5 - 2 r7c5; (8-2) r9c8 = r7c8 - 2 r7c5; 8 r8c3 - 2 r8c3 = r8c4 - 2 r7c5; => - 2 r7c5; stte

Leren

by **daj95376** » Tue Jul 01, 2014 8:55 am

_

Interestingly enough:

1) The original puzzle doesn't contain any 9s as a clue/given.

2) No 9s are solved before reaching the single-stepper grid.

3) No one posted a single-stepper solution using an elimination for any value other than <2>.

_

by **JC Van Hay** » Tue Jul 01, 2014 10:42 am

daj95376 wrote:
Code: Select all
Kraken Cell r7c8: 8r7c8 - r7c3 = (8-2)r8c3 || || || = 8 r1c3 - r1c9 = (8-6)r3c8 \ || \ 9r7c8 - (19=6)r26c8 _____________ \ \ || \ \ 6r7c8 - r3c8 = r3c6 - r1c5 = (6-2)r7c5 \ || \ 2r7c8 - r7c5 = r5c5 - r5c1 = r6c3 - 2r8c3

Danny's 9-SIS network :

Code: Select all: +-------------------+-------------------+---------------------+ | 189 3 19(8) | 5 9(6) 4 | 26 7 26(8) | | 6 5 4 | 7 8 2 | 3 (19) 19 | | 89 2 7 | 3 1 9(6) | 4 (68) 5 | +-------------------+-------------------+---------------------+ | 7 8 3 | 1 4 69 | 269 5 269 | | 9(2) 1 6 | 8 9(2) 5 | 7 3 4 | | 5 4 9(2) | 269 3 7 | 8 (169) 169 | +-------------------+-------------------+---------------------+ | 1248 679 1-2(8) | 2469 9(26) 3 | 5 (289-6) 6789 | | 3 679 -2(8) | 269 5 18 | 169 4 6789 | | 248 69 5 | 2469 7 18 | 169 2689 3 | +-------------------+-------------------+---------------------+

The exclusion matrix :

Hidden Text: Show

with more details ...

Hidden Text: Show

The kraken cell (2689)r7c8 :

Hidden Text: Show

fully documented ...

Hidden Text: Show

by **Leren** » Tue Jul 01, 2014 11:19 am

Code: Select all: *--------------------------------------------------------------* | 189 3 189 | 5 69 4 | 26 7 268 | | 6 5 4 | 7 8 2 | 3 19 19 | | 89 2 7 | 3 1 69 | 4 68 5 | |--------------------+--------------------+--------------------| | 7 8 3 | 1 4 69 | 269 5 269 | | 29 1 6 | 8 29 5 | 7 3 4 | | 5 4 2-9 | 269 3 7 | 8 169 169 | |--------------------+--------------------+--------------------| | 1248 679 128 | 2469 269 3 | 5 2689 6789 | | 3 679 28 | 269 5 18 | 169 4 6789 | | 248 69 5 | 2469 7 18 | 169 2689 3 | *--------------------------------------------------------------* Forcing Chain Contradiction in Row 8 Digit 8: 9 r6c3 - 2 r6c3 = r6c4 - r8c4 = 2 r8c3 - 8 r8c3; 9 r6c3 - 2 r6c3 = r78c3 - 2 r9c1; 9 r6c3 - 2 r6c3 = r6c4 - 2 r9c4 = (2-8) r9c8; 9 r6c3 - r5c1 = r5c5 - r1c5 = r3c6 - (9=8) r3c1 - r9c1 = r9c6 - 8 r8c6; 9 r6c3 - r5c1 = r5c5 - r1c5 = r3c6 - (9=8) r3c1 - r3c8 = r1c9 - 8 r8c9; => - 9 r6c3; stte

Leren

by **blue** » Tue Jul 01, 2014 4:24 pm

Code: Select all: +-------------------+-------------------+---------------------+ | 8(19) 3 89(1) | 5 (69) 4 | 2(6) 7 28(6) | | 6 5 4 | 7 8 2 | 3 (19) 19 | | 8(9) 2 7 | 3 1 6(9) | 4 8(6) 5 | +-------------------+-------------------+---------------------+ | 7 8 3 | 1 4 6(9) | 269 5 269 | | 2(9) 1 6 | 8 -9(2) 5 | 7 3 4 | | 5 4 29 | 269 3 7 | 8 (169) 169 | +-------------------+-------------------+---------------------+ | 1248 679 (128) | 2469 69(2) 3 | 5 (2689) 6789 | | 3 679 28 | 269 5 18 | 169 4 6789 | | 248 69 5 | 2469 7 18 | 169 2689 3 | +-------------------+-------------------+---------------------+

What would this be called ?
AAALS or AAANS ?
Kraken something ?

Code: Select all: 28r7c38 - 2r7c5 = 2r5c5 ------------------------ || \ 1r7c3 - r1c3 = (1-9)r1c1 = [Skyscraper: 9c16\r3] - 9r5c5 => r5c5<>9; stte || / 69r7c8 -(NT 169r267c8)- 6r3c8 = r1c79 - (6=9)r1c5

by **ArkieTech** » Tue Jul 01, 2014 4:56 pm

blue wrote:
Code: Select all
+-------------------+-------------------+---------------------+ | 8(19) 3 89(1) | 5 (69) 4 | 2(6) 7 28(6) | | 6 5 4 | 7 8 2 | 3 (19) 19 | | 8(9) 2 7 | 3 1 6(9) | 4 8(6) 5 | +-------------------+-------------------+---------------------+ | 7 8 3 | 1 4 6(9) | 269 5 269 | | 2(9) 1 6 | 8 -9(2) 5 | 7 3 4 | | 5 4 29 | 269 3 7 | 8 (169) 169 | +-------------------+-------------------+---------------------+ | 1248 679 (128) | 2469 69(2) 3 | 5 (2689) 6789 | | 3 679 28 | 269 5 18 | 169 4 6789 | | 248 69 5 | 2469 7 18 | 169 2689 3 | +-------------------+-------------------+---------------------+

What would this be called ?
AAALS or AAANS ?
Kraken something ?

Code: Select all
28r7c38 - 2r7c5 = 2r5c5 - 9r5c5 ---------------- || \ 1r7c3 - r1c3 = (1-9)r1c1 = [Skyscraper: 9c16\r3] - 9r5c5 => r5c5<>9; stte || / 69r7c8 -(NT 169r267c8)- 6r3c8 = r1c79 - (6=9)r1c5

I would call it "nice find"

by **blue** » Tue Jul 01, 2014 5:05 pm

ArkieTech wrote:I would call it "nice find"

Thanks Dan.
I see I had an extra 9r5c5 in the top chain -- fixed now.

by **DonM** » Tue Jul 01, 2014 6:18 pm

blue wrote:
Code: Select all
+-------------------+-------------------+---------------------+ | 8(19) 3 89(1) | 5 (69) 4 | 2(6) 7 28(6) | | 6 5 4 | 7 8 2 | 3 (19) 19 | | 8(9) 2 7 | 3 1 6(9) | 4 8(6) 5 | +-------------------+-------------------+---------------------+ | 7 8 3 | 1 4 6(9) | 269 5 269 | | 2(9) 1 6 | 8 -9(2) 5 | 7 3 4 | | 5 4 29 | 269 3 7 | 8 (169) 169 | +-------------------+-------------------+---------------------+ | 1248 679 (128) | 2469 69(2) 3 | 5 (2689) 6789 | | 3 679 28 | 269 5 18 | 169 4 6789 | | 248 69 5 | 2469 7 18 | 169 2689 3 | +-------------------+-------------------+---------------------+

What would this be called ?
AAALS or AAANS ?
Kraken something ?

Code: Select all
28r7c38 - 2r7c5 = 2r5c5 ------------------------ || \ 1r7c3 - r1c3 = (1-9)r1c1 = [Skyscraper: 9c16\r3] - 9r5c5 => r5c5<>9; stte || / 69r7c8 -(NT 169r267c8)- 6r3c8 = r1c79 - (6=9)r1c5

Regardless of the suggestions below, this is some very clever solving (I like the almost-Skyscraper). The overall logic is valid.

My main concern is the notation in the 3rd chain which has two weak inferences in a row, but that can be fixed by separating the 6 and the 9 (as below) or I suppose by showing some sort of 'quantum' NT.

I'm also concerned about the use of the 8 in chain one- I know that with the 2, it forms a NP28, but still, the 8 is not doing anything. I could be wrong there, but it doesn't matter because I don't think you need the 8 anyway: All that is necessary is accounting for 4 digits in the 2 cells to get a valid AAALS. (More a question of notation taste: I prefer keeping with the purity of AIC notation where the final weak inference is not shown.)

So, here's a suggested workaround:

Code: Select all: 2r7c38 - 2r7c5 = 2r5c5 || 1r7c3 - r1c3 = (1-9)r1c1 = [Skyscraper: 9c16\r3] || 6r7c8 - r3c8 = (6-9)r3c6 = r4c6 || 9r7c8 - als(9=16)r26c8 - r3c8 = (6-9)r3c6 = r4c6 => r5c5<>9 stte

by **blue** » Tue Jul 01, 2014 7:24 pm

Thanks for the critique, Don.

DonM wrote:My main concern is the notation in the 3rd chain which has two weak inferences in a row, but that can be fixed by separating the 6 and the 9 (as below) or I suppose by showing some sort of 'quantum' NT.

"Quantum NT" ... I like that !

I struggled with what to write in the bottom row.
The notation was meant to indicate a (single) "labeled" weak link.
In English, it was meant to read "... or there's a (6 or 9) in r7c8, which with r26c8, would make a naked triple eliminating 6r3c8".

I thought this would be going too far:

Code: Select all: 28r7c38 - || 1r7c3 - || 169r267c8 - 6r3c8

DonM wrote:I'm also concerned about the use of the 8 in chain one- I know that with the 2, it forms a NP28, but still, the 8 is not doing anything.

{...)

So, here's a suggested workaround:

Code: Select all
2r7c38 - 2r7c5 = 2r5c5 || 1r7c3 - r1c3 = (1-9)r1c1 = [Skyscraper: 9c16\r3] || 6r7c8 - r3c8 = (6-9)r3c6 = r4c6 || 9r7c8 - als(9=16)r26c8 - r3c8 = (6-9)r3c6 = r4c6

=> r5c5<>9 stte[/code]

This is correct, technically, but it leaves it to the reader wondering about the "missing 8's", to divine that if none of the items in the '||' column were true, there would be a conflict with an 8 in each cell.

To me, r7c38 first seemed like a "finned naked pair", where if the naked pair wasn't "true", then one of the "fin" candidates would need to be true. That's why I thought "AAANS, maybe ?".

BTW: I saw the " - r3c8 = (6-9)r3c6 = r4c6" route, too.
Since it got mixed in with the skyscraper 9's, I went the other way -- hoping it would make the PM easier to follow.

The New Sudoku Players' Forum

Network 6/30/2014

Network 6/30/2014

Re: Network 6/30/2014

Re: Network 6/30/2014

Re: Network 6/30/2014

Re: Network 6/30/2014

Re: Network 6/30/2014

Re: Network 6/30/2014

Re: Network 6/30/2014

Re: Network 6/30/2014

Re: Network 6/30/2014

Re: Network 6/30/2014

Re: Network 6/30/2014

Re: Network 6/30/2014

Re: Network 6/30/2014

Re: Network 6/30/2014