7*1*2*3**
*4*5**7**
*6*7**8**
1***6***4
2*6*4*1*5
8*4*9*6*7
6*7453*1*
41*97256*
**9*8*47*
What's the next logical move?
Can't figure this one out.
7 posts
• Page 1 of 1
Can't figure this one out.
by gkrosner » Sun Jan 15, 2006 8:10 pm
- gkrosner
- Posts: 3
- Joined: 08 August 2005
by tso » Sun Jan 15, 2006 8:53 pm
This is one of many ways to solve this. There is no one "next logical move".
After three naked pairs and a naked quad, the candidate grid looks like this:
The six cells in [brackets] form a forcing loop, excluding the candidates marked with 'x'.
Exactly one of r1c24 must be 8, eliminating 8s from the rest of the row.
Exactly one of r1c49 must be 6, eliminating 6s from the rest of the row, etc.
A single and a couple more naked pairs, then:
The [bracket cells] form a forcing chain. Either value in r2c3 excludes the 8 from r1c2.
After this, the puzzle solves with singles.
- Code: Select all
7 . 1 | . 2 . | 3 . .
. 4 . | 5 . . | 7 . .
. 6 . | 7 . . | 8 . .
-------+-------+------
1 . . | . 6 . | . . 4
2 . 6 | . 4 . | 1 . 5
8 . 4 | . 9 . | 6 . 7
-------+-------+------
6 . 7 | 4 5 3 | . 1 .
4 1 . | 9 7 2 | 5 6 .
. . 9 | . 8 . | 4 7 .
After three naked pairs and a naked quad, the candidate grid looks like this:
- Code: Select all
7 [58] 1 |[68] 2 4x6x89| 3 45 [69]
39 4 238 | 5 13 689 | 7 [29] 126x9
359 6 235 | 7 13 49 | 8 45 12x9
-------------------+-------------------+-------------------
1 79 35 | 238 6 578 | 29 x2389 4
2 79 6 | 38 4 78 | 1 389 5
8 [35] 4 | 12x3 9 15 | 6 [23] 7
-------------------+-------------------+-------------------
6 28 7 | 4 5 3 | 29 1 289
4 1 38 | 9 7 2 | 5 6 38
35 23x5 9 | 16 8 16 | 4 7 23
The six cells in [brackets] form a forcing loop, excluding the candidates marked with 'x'.
Exactly one of r1c24 must be 8, eliminating 8s from the rest of the row.
Exactly one of r1c49 must be 6, eliminating 6s from the rest of the row, etc.
A single and a couple more naked pairs, then:
- Code: Select all
7 [5x8] 1 |[68] 2 49 | 3 45 [69]
39 4 [28] | 5 13 68 | 7 [29] 126
39 6 25 | 7 13 49 | 8 45 12
----------------+----------------+----------------
1 79 35 | 238 6 578 | 29 389 4
2 79 6 | 38 4 78 | 1 389 5
8 35 4 | 12 9 15 | 6 23 7
----------------+----------------+----------------
6 28 7 | 4 5 3 | 29 1 289
4 1 38 | 9 7 2 | 5 6 38
5 23 9 | 16 8 16 | 4 7 23
The [bracket cells] form a forcing chain. Either value in r2c3 excludes the 8 from r1c2.
After this, the puzzle solves with singles.
- tso
- Posts: 798
- Joined: 22 June 2005
by bennys » Sun Jan 15, 2006 9:09 pm
- Code: Select all
Use the Almost locked sets xz rule
+----------------+----------------+----------------+
| 7 58 1 | 68 2 4689 | 3 45 69 |
| 39 4 *238 | 5 13 689 | 7 29 1269 |
| 359 6 235 | 7 13 49 | 8 45 129 |
+----------------+----------------+----------------+
| 1 79 *35 | 238 6 578 | 29 2389 4 |
| 2 79 6 | 38 4 78 | 1 389 5 |
| 8 ^35 4 | 123 9 15 | 6 ^23 7 |
+----------------+----------------+----------------+
| 6 28 7 | 4 5 3 | 29 1 289 |
| 4 1 *38 | 9 7 2 | 5 6 38 |
| 35 235 9 | 16 8 16 | 4 7 23 |
+----------------+----------------+----------------+
a=*
b=^
x=5
z=2
we get r2c8<>2
Last edited by bennys on Sun Jan 15, 2006 8:19 pm, edited 1 time in total.
- bennys
- Posts: 156
- Joined: 28 September 2005
by tarek » Sun Jan 15, 2006 11:16 pm
Try this one,
Following 2 seperate box-line eliminations:
Following 2 seperate box-line eliminations:
- Code: Select all
*--------------------------------------------------------*
| 7 58 1 | 68 2 4689 | 3 459 69 |
| 39 4 238 | 5 13 689 | 7 29 1269 |
| 359 6 235 | 7 13 49 | 8 2459 129 |
|------------------+------------------+------------------|
| 1 3579 35 | 238 6 578 | 29 2389 4 |
| 2 379 6 | 38 4 78 | 1 389 5 |
| 8 35 4 | 123 9 15 | 6 23 7 |
|------------------+------------------+------------------|
| 6 28 7 | 4 5 3 | 29 1 289 |
| 4 1 38 | 9 7 2 | 5 6 38 |
| 35 235 9 | 16 8 16 | 4 7 23 |
*--------------------------------------------------------*
r4c2 Must only have 79 as valid Candidates (79 is a Hidden Double in Column 2)
r5c2 Must only have 79 as valid Candidates (79 is a Hidden Double in Column 2)
*--------------------------------------------------------*
| 7 58 1 | 68 2 4689 | 3 459 69 |
| 39 4 238 | 5 13 689 | 7 29 1269 |
| 359 6 235 | 7 13 49 | 8 2459 129 |
|------------------+------------------+------------------|
| 1 79 35 | 238 6 578 | 29 2389 4 |
| 2 79 6 | 38 4 78 | 1 389 5 |
| 8 35 4 | 123 9 15 | 6 23 7 |
|------------------+------------------+------------------|
| 6 28 7 | 4 5 3 | 29 1 289 |
| 4 1 38 | 9 7 2 | 5 6 38 |
| 35 235 9 | 16 8 16 | 4 7 23 |
*--------------------------------------------------------*
r1c8 Must only have 45 as valid Candidates (45 is a Hidden Double in Column 8)
r3c8 Must only have 45 as valid Candidates (45 is a Hidden Double in Column 8)
*--------------------------------------------------------*
| 7 58 1 | 68 2 4689 | 3 45 69 |
| 39 4 238 | 5 13 689 | 7 29 1269 |
| 359 6 235 | 7 13 49 | 8 45 129 |
|------------------+------------------+------------------|
| 1 79 35 | 238 6 578 | 29 2389 4 |
| 2 79 6 | 38 4 78 | 1 389 5 |
| 8 35 4 | 123 9 15 | 6 23 7 |
|------------------+------------------+------------------|
| 6 28 7 | 4 5 3 | 29 1 289 |
| 4 1 38 | 9 7 2 | 5 6 38 |
| 35 235 9 | 16 8 16 | 4 7 23 |
*--------------------------------------------------------*
Candidates in r2c3 will force r1c9 to have only 6 as valid Candidates
r2c3=2: r2c3=2 => r2c8=9 => r1c9=6
r2c3=3: r2c3=3 => r4c3=5 => r6c2=3 => r6c8=2 => r2c8=9 => r1c9=6
r2c3=8: r2c3=8 => r1c2=5 => r6c2=3 => r6c8=2 => r2c8=9 => r1c9=6
Threfore r1c9=6
-
tarek - Posts: 3762
- Joined: 05 January 2006
by QBasicMac » Mon Jan 16, 2006 4:02 am
tso wrote:This is one of many ways to solve this. There is no one "next logical move".
True, for example this gets to the same point without "Naked quad"
Locked candidate 9 in box 4
Locked candidate 1 in col 5
Naked pair 35 in box 4
Hidden pair 45 in col 8
Mac
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7 posts
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