The New Sudoku Players' Forum

by **1chester1** » Tue Jan 29, 2013 4:53 pm

This was a six-star Sudoku in the Toronto Globe and Mail. I am stumped; that hasn't happened in a while, so I think there is something here that I can learn, if you can guide me to an answer with a clue or a technique. Here's the puzzle as far as I can go:

Code: Select all: 2 7 5 | 4 3 6 | 8 9 1 1 8 6 | 9 5 2 | 3 7 4 4 9 3 | 8 7 1 | 5 6 2 -----------------+---------------------+----------------- 7 5 4 | 236 128 39 | 12 38 69 89 36 12 | 7 48 5 | 12 348 69 89 36 12 | 236 1248 349 | 7 348 5 -----------------+---------------------+----------------- 6 1 7 | 23 24 34 | 9 5 8 5 4 8 | 1 9 7 | 6 2 3 3 2 9 | 5 6 8 | 4 1 7

by **JasonLion** » Tue Jan 29, 2013 8:34 pm

That is a rather complex puzzle for a newspaper. The simplest next step I can see is a 5 link XY-Chain.

by **1chester1** » Tue Jan 29, 2013 10:30 pm

I understand the xy chain. Identifying one that can eliminate a candidate is another matter. I can't find one that does me any good. Example: there's one at c6r4, c9r4, c9r5, c1r5, c1r6. But I can't get that to eliminate the 9 in c6r6. How do you identify a chain that works?

by **ArkieTech** » Tue Jan 29, 2013 11:56 pm

Code: Select all: *-----------------------------------------------------------* | 2 7 5 | 4 3 6 | 8 9 1 | | 1 8 6 | 9 5 2 | 3 7 4 | | 4 9 3 | 8 7 1 | 5 6 2 | |-------------------+-------------------+-------------------| | 7 5 4 | 236 128 39 | 12 38 69 | | 89 36 12 | 7 48 5 | 12 348 69 | | 89 36 12 | 236 1248 349 | 7 348 5 | |-------------------+-------------------+-------------------| | 6 1 7 | 23 24 34 | 9 5 8 | | 5 4 8 | 1 9 7 | 6 2 3 | | 3 2 9 | 5 6 8 | 4 1 7 | *-----------------------------------------------------------* (4=8)r5c5-(8=9)r5c1-r6c1=r6c6 => -4r6c6 *--------------------------------------------------* | 2 7 5 | 4 3 6 | 8 9 1 | | 1 8 6 | 9 5 2 | 3 7 4 | | 4 9 3 | 8 7 1 | 5 6 2 | |----------------+----------------+----------------| | 7 5 4 | 26 18 39 | 12 38 69 | | 89 36 12 | 7 48 5 | 12 348 69 | | 89 36 12 | 26 148 39 | 7 348 5 | |----------------+----------------+----------------| | 6 1 7 | 3 2 4 | 9 5 8 | | 5 4 8 | 1 9 7 | 6 2 3 | | 3 2 9 | 5 6 8 | 4 1 7 | *--------------------------------------------------* (9=6)r4c9-(6=2)r4c4-(2=9)r6c246 => -9r4c6; stte

by **JC Van Hay** » Tue Jan 29, 2013 11:59 pm

Step 1 : r7c5=2; r7c4=3, r7c6=4
If r7c5<>2, then the 3 resulting Pairs (12) in columns 357 are unresolvable (Technical name : Unique Loop).

Or
If r7c5=4, then the puzzle has no solution : r6c6=4,r6c1=9,r5c1=8; cell r5c5 is empty.

Code: Select all: +--------------+-------------------+-------------+ | 2 7 5 | 4 3 6 | 8 9 1 | | 1 8 6 | 9 5 2 | 3 7 4 | | 4 9 3 | 8 7 1 | 5 6 2 | +--------------+-------------------+-------------+ | 7 5 4 | 236 128 39 | 12 38 69 | | 9(8) 36 12 | 7 (48) 5 | 12 348 69 | | (89) 36 12 | 236 1248 3-4(9) | 7 348 5 | +--------------+-------------------+-------------+ | 6 1 7 | 23 24 34 | 9 5 8 | | 5 4 8 | 1 9 7 | 6 2 3 | | 3 2 9 | 5 6 8 | 4 1 7 | +--------------+-------------------+-------------+

Simplest interpretation : (4=8)r5c5-8r5c1=(8-9)r6c1=9r6c6 :=> -4r6c6

Step 2 : row 5 has 2 solutions; the puzzle has no solution if r4c4=2 while r4c4=6 solves it.

Code: Select all: +--------------+-----------------+---------------+ | 2 7 5 | 4 3 6 | 8 9 1 | | 1 8 6 | 9 5 2 | 3 7 4 | | 4 9 3 | 8 7 1 | 5 6 2 | +--------------+-----------------+---------------+ | 7 5 4 | 2(6) 18 3(9) | 12 38 (69) | | 89 36 12 | 7 48 5 | 12 348 69 | | 89 (36) 12 | 2-6 148 (39) | 7 348 5 | +--------------+-----------------+---------------+ | 6 1 7 | 3 2 4 | 9 5 8 | | 5 4 8 | 1 9 7 | 6 2 3 | | 3 2 9 | 5 6 8 | 4 1 7 | +--------------+-----------------+---------------+

Simplest interpretation : 6r4c4=(6-9)r4c9=9r4c6-(9=3)r6c6-(3=6)r6c2 :=> -6r6c4

by **JasonLion** » Wed Jan 30, 2013 12:18 am

I was thinking of this, though it isn't nearly as neat:

Code: Select all: 2 7 5 | 4 3 6 | 8 9 1 1 8 6 | 9 5 2 | 3 7 4 4 9 3 | 8 7 1 | 5 6 2 ---------------+----------------+--------------- 7 5 4 | 236 128 39 | 12 38 69 89 36 12 | 7 48 5 | 12 348 69 89 36 12 | 236 1248 349 | 7 348 5 ---------------+----------------+--------------- 6 1 7 | 23 24 34 | 9 5 8 5 4 8 | 1 9 7 | 6 2 3 3 2 9 | 5 6 8 | 4 1 7 XY-Chain: (8=9)r5c1-(9=6)r5c9-(6=9)r4c9-(9=3)r4c6-(3=8)r4c8 => -8r5c8 and two XY-Wings and some minor stuff to the end

by **daj95376** » Wed Jan 30, 2013 12:29 am

Reasonable:

Code: Select all: +--------------------------------------------------------------+ | 2 7 5 | 4 3 6 | 8 9 1 | | 1 8 6 | 9 5 2 | 3 7 4 | | 4 9 3 | 8 7 1 | 5 6 2 | |--------------------+--------------------+--------------------| | 7 5 4 | 236 128 39 | 12 38 69 | | 89 36 12 | 7 48 5 | 12 348 69 | | 89 36 12 | 236 1248 349 | 7 348 5 | |--------------------+--------------------+--------------------| | 6 1 7 | 23 24 34 | 9 5 8 | | 5 4 8 | 1 9 7 | 6 2 3 | | 3 2 9 | 5 6 8 | 4 1 7 | +--------------------------------------------------------------+ (4=8)r5c5 - (8=9)r5c1 - (9=6)r5c9 - (6=9)r4c9 - (9=3)r4c6 - (3=4)r7c6 => r6c6,r7c5<>4 +--------------------------------------------------------------+ | 2 7 5 | 4 3 6 | 8 9 1 | | 1 8 6 | 9 5 2 | 3 7 4 | | 4 9 3 | 8 7 1 | 5 6 2 | |--------------------+--------------------+--------------------| | 7 5 4 | 26 18 39 | 12 38 69 | | 89 36 12 | 7 48 5 | 12 34+8 69 | | 89 6-3 12 | 26 14+8 39 | 7 48+3 5 | |--------------------+--------------------+--------------------| | 6 1 7 | 3 2 4 | 9 5 8 | | 5 4 8 | 1 9 7 | 6 2 3 | | 3 2 9 | 5 6 8 | 4 1 7 | +--------------------------------------------------------------+ BUG+3: (8-3)r5c8 = (3)r5c2 - (3)r6c2 (8 )r6c5 - (8=9)r6c1 - (9=3)r6c6 - (3)r6c2 (3 )r6c8 - (3)r6c2

Single-stepper:

Code: Select all: +--------------------------------------------------------------+ | 2 7 5 | 4 3 6 | 8 9 1 | | 1 8 6 | 9 5 2 | 3 7 4 | | 4 9 3 | 8 7 1 | 5 6 2 | |--------------------+--------------------+--------------------| | 7 5 4 | 236 128 39 | 12 38 69 | | 89 36 12 | 7 48 5 | 12 348 69 | | 89 36 12 | 236 1248 349 | 7 348 5 | |--------------------+--------------------+--------------------| | 6 1 7 | 23 24 34 | 9 5 8 | | 5 4 8 | 1 9 7 | 6 2 3 | | 3 2 9 | 5 6 8 | 4 1 7 | +--------------------------------------------------------------+ # 31 eliminations remain Kraken Cell r6c6 using AHS: (3)r6c6 - (3)r6c2 (4)r6c6 - r5c4 = (4-3)r5c8 = r5c2 - (3)r6c2 (9)r9c9 - (9=8)r6c1 - r5c1 = (48-3)r5c58 = r5c2 - (3)r6c2

by **Leren** » Wed Jan 30, 2013 12:38 am

Step 1

Code: Select all: *--------------------------------------------------------------------------------* | 2 7 5 | 4 3 6 | 8 9 1 | | 1 8 6 | 9 5 2 | 3 7 4 | | 4 9 3 | 8 7 1 | 5 6 2 | |--------------------------+--------------------------+--------------------------| | 7 5 4 | 236 128 a39 | 12 38 b69 | | 89 d36 12 | 7 48 5 | 12 348 c69 | | 89 e36 12 | 26-3 1248 49-3 | 7 348 5 | |--------------------------+--------------------------+--------------------------| | 6 1 7 | 23 24 34 | 9 5 8 | | 5 4 8 | 1 9 7 | 6 2 3 | | 3 2 9 | 5 6 8 | 4 1 7 | *--------------------------------------------------------------------------------*

(3=9) r4c6 - r4c9 = (9-6) r5c9 = r5c2 - (6=3) r6c2 = > r6c46 <> 3

Step 2

Code: Select all: *--------------------------------------------------------------------------------* | 2 7 5 | 4 3 6 | 8 9 1 | | 1 8 6 | 9 5 2 | 3 7 4 | | 4 9 3 | 8 7 1 | 5 6 2 | |--------------------------+--------------------------+--------------------------| | 7 5 4 | 36 12 39 | 12 8 69 | |C89 36 12 | 7 A48 5 | 12 34 69 | | 8-9 36 12 | 26 1248 B49 | 7 34 5 | |--------------------------+--------------------------+--------------------------| | 6 1 7 | 23 24 34 | 9 5 8 | | 5 4 8 | 1 9 7 | 6 2 3 | | 3 2 9 | 5 6 8 | 4 1 7 | *--------------------------------------------------------------------------------*

xy-wing cells A,B,C => r6c1 <> 9; stte

Leren

by **Marty R.** » Wed Jan 30, 2013 1:21 am

Code: Select all: +--------------------------------------------------------------+ | 2 7 5 | 4 3 6 | 8 9 1 | | 1 8 6 | 9 5 2 | 3 7 4 | | 4 9 3 | 8 7 1 | 5 6 2 | |--------------------+--------------------+--------------------| | 7 5 4 | 236 128 39 | 12 38 69 | | 89 36 12 | 7 48 5 | 12 348 69 | | 89 36 12 | 236 1248 349 | 7 348 5 | |--------------------+--------------------+--------------------| | 6 1 7 | 23 24 34 | 9 5 8 | | 5 4 8 | 1 9 7 | 6 2 3 | | 3 2 9 | 5 6 8 | 4 1 7 | +--------------------------------------------------------------+

An alternate first step is the the Deadly Pattern on 12 in boxes 456. R46c5 must be 4 or 8; combining this with the 48 pair in r5c5=>r7c5<>4.

by **pjb** » Wed Jan 30, 2013 3:17 am

I found the BUG-lite of 12's at r4c57, r5c37, and r6c35 attractive, giving r46c5 <> 2.

Then the XY chain: (3=9)r4c6 - (9=6)r4c9 - (6=2)r4c4 - (2=6)r6c4 - (6=3)r6c2; => r6c6 <> 3; stte

Phil

by **7b53** » Wed Jan 30, 2013 3:23 am

Marty R. wrote:An alternate first step is the the Deadly Pattern on 12 in boxes 456. R46c5 must be 4 or 8;

this is like an UR extension.
Andrew Stuart once said; "not many people realized this".
very nice, Marty R.

by **1chester1** » Wed Jan 30, 2013 3:31 pm

Thank you for these amazing solutions. They are very helpful, although still hard to recognize in a puzzle. I could use some help with notation (sometimes "=" means "or" and sometimes it means "equal", not sure what "-" means, when placed between two cell references, like "r2c3 - r6c3"). Is there a standard set of notation symbols I can refer to, or a brief tutorial on notation?

Again, thanks for your creative help.

by **JasonLion** » Thu Jan 31, 2013 3:18 am

"a=b" is a strong link, it means at least one of a and b must be true.
"a-b" is a weak link, it means at least one of a and b must be false.

For more detail see for example here.

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