The New Sudoku Players' Forum

by **esawall** » Mon Jun 12, 2006 2:44 pm

2 1 9 | . . . | . . .
. . . | . 5 2 | 9 3 .
. . . | . . . | . . 8
------+-------+------
. 3 . | 6 . . | . . 5
. 4 . | . 8 . | . 1 .
5 . . | . . 7 | . 4 .
------+-------+------
1 . . | . . . | . . .
. 8 2 | 3 4 . | . . .
. . . | . . . | 4 9 7

by **Hud** » Mon Jun 12, 2006 3:04 pm

I'm glad you posted that one. Here's as far as I've gotten so far, and probably as far as I can get:

Code: Select all: +----------+------------+-----------+ |2 1 9 |87 763 863|5 76 4 | |864 76 86|74 5 2 |9 3 1 | |43 75 53|974 9761 16 |72 762 8 | +----------+------------+-----------+ |98 3 1 |6 92 4 |872 872 5 | |96 4 7 |952 8 53 |632 1 932| |5 2 86|1 93 7 |86 4 93 | +----------+------------+-----------+ |1 9 4 |75 76 65 |832 82 32 | |7 8 2 |3 4 9 |1 5 6 | |63 65 53|82 21 81 |4 9 7 | +----------+------------+-----------+

by **Sped** » Mon Jun 12, 2006 3:14 pm

Code: Select all: *-----------* |219|...|...| |...|.52|93.| |...|...|..8| |---+---+---| |.3.|6..|..5| |.4.|.8.|.1.| |5..|..7|.4.| |---+---+---| |1..|...|...| |.82|34.|...| |...|...|497| *-----------*

After basic steps.. pairs and triples, etc. we have:

Code: Select all: *-----------------------------------------------------------* | 2 1 9 | 478 367 368 | 57 567 46 | | 468 67 68 | 147 5 2 | 9 3 146 | | 346 567 35 | 1479 1679 16 | 127 267 8 | |-------------------+-------------------+-------------------| | 89 3 1 | 6 29* 4 | 278 278 5 | | 69 4 7 | 259 8 35 | 236 1 239 | | 5 2 68 | 19* (1)39 7 | 68 4 39 | |-------------------+-------------------+-------------------| | 1 9 4 | 57 67 56 | 238 28 23 | | 7 8 2 | 3 4 9 | 15 56 16 | | 36 56 35 | (1)28 12* 18 | 4 9 7 | *-----------------------------------------------------------*

The xy wing 1-(r6c4)-9-(r4c5)-2-(r9c5)-1 eliminates the 1s in r6c5 and r9c4
The cells forming the wing are marked with asterisks above, and the 1s that get excluded have parentheses around them.

A few simple steps later:

Code: Select all: *-----------------------------------------------------------* | 2 1 9 | 78* 367 36(8) | 5 67 4 | | 468 67 68 | 47 5 2 | 9 3 1 | | 34 57 35 | 479 1679 16* | 27 267 8 | |-------------------+-------------------+-------------------| | 89 3 1 | 6 29 4 | 278 278 5 | | 69 4 7 | 259 8 35 | 236 1 239 | | 5 2 68 | 1 39 7 | 68 4 39 | |-------------------+-------------------+-------------------| | 1 9 4 | 57* 67 56* | 238 28 23 | | 7 8 2 | 3 4 9 | 1 5 6 | | 36 56 35 | 2(8) 12 18* | 4 9 7 | *-----------------------------------------------------------*

The xy chain:

8-(r1c4)-7-(r7c4)-5-(r7c6)-6-(r3c6)-1-(r9c6)-8 eliminates the 8s in r1c6 and r9c4.

In nice loop notation:

[r1c6]-8-[r1c4]-7-[r7c4]-5-[r7c6]-6-[r3c6]-1-[r9c6]-8-[r1c6] => r1c6<>8
[r9c4]-8-[r1c4]-7-[r7c4]-5-[r7c6]-6-[r3c6]-1-[r9c6]-8-[r9c4] => r9c4<>8

asterisks and parentheses mark the chain above.

A bunch of singles later:

Code: Select all: *--------------------------------------------------* | 2 1 9 | 8 367* 36* | 5 67 4 | | 8 7 6 | 4 5 2 | 9 3 1 | | 4 5 3 | 79 (6)79 1 | 27 267 8 | |----------------+----------------+----------------| | 9 3 1 | 6 2 4 | 78 78 5 | | 6 4 7 | 59 8 35 | 23 1 239 | | 5 2 8 | 1 39 7 | 6 4 39 | |----------------+----------------+----------------| | 1 9 4 | 57 67* 56 | 238 28 23 | | 7 8 2 | 3 4 9 | 1 5 6 | | 3 6 5 | 2 1 8 | 4 9 7 | *--------------------------------------------------*

The XYZ wing in r7c5, r1c5, and r1c6 eliminates the 6 in r3c5.

It's all singles from there.

by **Carcul** » Tue Jun 13, 2006 8:07 am

Code: Select all: *-----------------------------------------------------------* | 2 1 9 | 478 367 368 | 57 567 46 | | 468 67 68 | 147 5 2 | 9 3 146 | | 346 567 35 | 1479 1679 16 | 127 267 8 | |-------------------+-------------------+-------------------| | 89 3 1 | 6 29 4 | 278 278 5 | | 69 4 7 | 259 8 35 | 236 1 239 | | 5 2 68 | 19 139 7 | 68 4 39 | |-------------------+-------------------+-------------------| | 1 9 4 | 57 67 56 | 238 28 23 | | 7 8 2 | 3 4 9 | 15 56 16 | | 36 56 35 | 128 12 18 | 4 9 7 | *-----------------------------------------------------------*

1. [r6c3]=8=[r4c1]=9=[r4c5](-9-[r3c5])=2=[r5c4]=5=[r7c4]=7=[r7c5]-
-7-[r3c56]-1,6-[r3c78]=(AUR: r34c78)=1,6|8=[r4c78]-8-[r6c7]=8=[r6c3],
=> r6c3=8.

2. [r7c7]=(AUR: r57c79)=8|9=[r5c9]-9-[r5c4]-5-[r5c6]-3-[r1c6]-6-[r1c8]-
-7-[r3c7]-2-[r5c7]-3-[r7c7], => r7c7<>3 and it solve the puzzle.

Carcul

by **Carcul** » Tue Jun 13, 2006 8:55 am

Code: Select all: *-----------------------------------------------------------* | 2 1 9 | 478 367 368 | 57 567 46 | | 468 67 68 | 147 5 2 | 9 3 146 | | 346 567 35 | 1479 1679 16 | 127 267 8 | |-------------------+-------------------+-------------------| | 89 3 1 | 6 29 4 | 278 278 5 | | 69 4 7 | 259 8 35 | 236 1 239 | | 5 2 68 | 19 139 7 | 68 4 39 | |-------------------+-------------------+-------------------| | 1 9 4 | 57 67 56 | 238 28 23 | | 7 8 2 | 3 4 9 | 15 56 16 | | 36 56 35 | 128 12 18 | 4 9 7 | *-----------------------------------------------------------*

[r7c7](=8=[r7c8]-8-[r4c8])=(AUR: r5c1|r57c79)=8|6,9=[r5c79]-9-[r5c4]=
{TILA (r5c4 not "9" and r2c4 not "4"): [r6c4]=1=[r6c5]-1-[r9c5]-2-[r4c5]-
-9-[r6c4], => r6c4<>9; [r6c4]=9=[r3c4]=4=[r3c1]-4-[r2c1]=4=[r2c9]=
=1=[r2c4]-1-[r6c4], => r6c4<>1 => r6c4=9}=9|4=[r2c4](-4-[r13c4])=
=1=[r2c9](-1-[r3c7])-1-[r8c9]-6-[r8c8]-5-[r1c8]-{TILA: [r1c8]-6-[r3c78](-
-7-[r3c45])=(AUR: r34c78)=6|8=[r4c7]-8-[r4c1]-9-[r4c5]-2-[r5c4]-
-5-[r7c4]-7-[r7c5]-6-[r3c5]=(AUR: r36c45)=6|3=[r6c5]-3-[r5c6]-5-
[r5c4], => r1c8<>6; [r1c8]-7-[r4c8]-2-[r4c5](=2=[r5c4]-2-[r9c4])-9-
-[r6c4]-1-[r9c4]-8-[r1c4]-7-[r1c8], => r1c8<>7 => r1c8=6}

So, r7c7 must be "8" and that solve the puzzle.

Carcul

by **QBasicMac** » Tue Jun 13, 2006 5:07 pm

Hud wrote:I'm glad you posted that one. Here's as far as I've gotten so far, and probably as far as I can get:

I couldn't even get that far. You have a few eliminations I couldn't find.

Mac

Code: Select all: +--------------+-----------------+---------------+ | 2 1 9 | 478 367 368 | 57 567 46 | | 468 67 68 | 147 5 2 | 9 3 146 | | 346 567 35 | 1479 1679 16 | 127 267 8 | +--------------+-----------------+---------------+ | 89 3 1 | 6 29 4 | 278 278 5 | | 69 4 7 | 259 8 35 | 236 1 239 | | 5 2 68 | 19 139 7 | 68 4 39 | +--------------+-----------------+---------------+ | 1 9 4 | 57 67 56 | 238 28 23 | | 7 8 2 | 3 4 9 | 15 56 16 | | 36 56 35 | 128 12 18 | 4 9 7 | +--------------+-----------------+---------------+

by **ronk** » Tue Jun 13, 2006 5:59 pm

Starting with the same grid as others, the puzzle is solved with an xy-wing, an xy-chain (of cycle length 6), an xyz-wing, and singles.

Code: Select all: 2 1 9 | 478 367 368 | 57 567 46 468 67 68 | 147 5 2 | 9 3 146 346 567 35 | 1479 1679 16 | 127 267 8 ----------------+----------------+--------------- 89 3 1 | 6 *29 4 | 278 278 5 69 4 7 | 259 8 35 | 236 1 239 5 2 68 |*19 -139 7 | 68 4 39 ----------------+----------------+--------------- 1 9 4 | 57 67 56 | 238 28 23 7 8 2 | 3 4 9 | 15 56 16 36 56 35 |-128 *12 18 | 4 9 7

1. xy-wing: (r6c5,r9c4)-1-r9c5-2-r4c5-9-r6c4-1-(r6c5,r9c4), implies r6c4<>1 and r9c4<>1

Code: Select all: 2 1 9 |*78 367 -836 | 5 67 4 468 67 68 | 47 5 2 | 9 3 1 34 57 35 | 479 1679 *16 | 27 267 8 ----------------+-----------------+--------------- 89 3 1 | 6 29 4 | 278 278 5 69 4 7 | 259 8 35 | 236 1 239 5 2 68 | 1 39 7 | 68 4 39 ----------------+-----------------+--------------- 1 9 4 |*57 67 *56 | 238 28 23 7 8 2 | 3 4 9 | 1 5 6 36 56 35 | 28 12 *18 | 4 9 7

2. xy chain: r1c6-8-r9c6-1-r3c6-6-r7c6-5-r7c4-7-r1c4-8-r1c6, implies r1c6<>8

Code: Select all: 2 1 9 | 8 *367*36 | 5 67 4 8 7 6 | 4 5 2 | 9 3 1 4 5 3 | 79 -679 1 | 27 267 8 -------------+-------------+------------ 9 3 1 | 6 2 4 | 78 78 5 6 4 7 | 59 8 35 | 23 1 239 5 2 8 | 1 39 7 | 6 4 39 -------------+-------------+------------ 1 9 4 | 57 *67 56 | 238 28 23 7 8 2 | 3 4 9 | 1 5 6 3 6 5 | 2 1 8 | 4 9 7

3. xyz-wing: r3c5-6-r7c5-7-(Naked Pair 36 in r1c56)-6-r3c5, implies r3c5<>6

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