## Help (suggestion) needed

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### Help (suggestion) needed

This is a common point for my wife and I to get stumped on a Sudoku puzzle. Simple Sudoku only tells us what we already know--that there is a naked pair in r1c8 and r2c7. We've done all the excludes we can spot and it looks like we're down to guessing whether r1c8 and r2c7 should be a 2 or a 4. Clearly, there must be another logic step that would preclude taking a guess--perhaps a wrong one that would be difficult to undo on paper. Simple Sudoku, of course, will very nicely and quickly tell us if a 2 is correct in either cell, but we would much prefer to be able to logic it out ourselves. What's the next logical step here?

Original puzzle:
Code: Select all
`1 . . | . 8 . | 9 . .. . 6 | . . 5 | . 7 .. 9 . | . . 4 | . 1 .------+-------+------. 4 . | 7 . . | 8 5 .. . . | . . . | . . .. 6 5 | . . 2 | . 3 .------+-------+------. 7 . | 8 . . | . 6 .. 2 . | 5 . . | 3 . .. . 1 | . 2 . | . . 4`

Partially solved puzzle:

Code: Select all
`1     35     2347 | 236   8      367   | 9     24     356  234   38     6    | 19    19     5     | 24    7      38   2357  9      2378 | 236   367    4     | 56    1      3568 ------------------+--------------------+-------------------239   4      239  | 7     1369   1369  | 8     5      1269 2379  1      2379 | 3469  5      8     | 246   249    269  8     6      5    | 149   19     2     | 147   3      179  ------------------+--------------------+-------------------3459  7      349  | 8     1349   139   | 125   6      1259 469   2      489  | 5     14679  1679  | 3     89     179  3569  358    1    | 369   2      3679  | 57    89     4    `
Guest

### Help (suggestion) needed

I think I just found a next step after posting the previous question. The 2 and the 4 must either be in r1c8 or r5c8, therefore, 9 can be eliminated as a candidate from r5c8 and 9 can only be in box 6 in c9. I am continuing to try to solve this one.
Guest

Ralph&Cynthia,

Keep looking for those naked pairs. Those are the key to this puzzle.
re'born

Posts: 551
Joined: 31 May 2007

There is an uniqueness rectangle in cells r2c4, r2c5, r6c4, r6c5 with 1 and 9 which forces r6c4 to be a 4.

Code: Select all
`1     35     2347 | 236   8      367   | 9     24     356  234   38     6    |*19   *19     5     | 24    7      38    2357  9      2378 | 236   367    4     | 56    1      3568 ------------------+--------------------+------------------- 239   4      239  | 7     1369   1369  | 8     5      1269 2379  1      2379 | 3469  5      8     | 246   249    269  8     6      5    |*149  *19     2     | 147   3      179  ------------------+--------------------+------------------- 3459  7      349  | 8     1349   139   | 125   6      1259 469   2      489  | 5     14679  1679  | 3     89     179  3569  358    1    | 369   2      3679  | 57    89     4    `

MCC
MCC

Posts: 1275
Joined: 08 June 2005

### Help (suggestion) needed

MMC - thanks for your response. I placed the 4 in r6c4 and was able to solve the rest of the puzzle. After that I looked at my original post and wondered why r6c4 had to be a 4? r2c4 and c5 could have been 1 and 9, making it possible for r6c4 and c5 to be 9 and 1 or vice versa for both rows. The 4 in box 5 could have been in r5c4. What logic makes the 4 in r6c4 a lock? I realize what you told me is correct, but how do you lock the 4 in r6c4 and not in r5c4?
Guest

There is absolutely no need to apply MCC's uniqueless technique, unless you want to do it for educational purposes...

This puzzle can be easily solved by singles/doubles/locked candidates...
For example there are naked pairs of [89] in n9+c8 and [38] on r2...
udosuk

Posts: 2698
Joined: 17 July 2005

I only pointed out the uniqueness rectangle for educational purposes.

I didn't have time to work on the puzzle and the UR stood out, I thought that since Ralph&Cynthia were already working on the puzzle it would advance the techniques they were using.

MCC
MCC

Posts: 1275
Joined: 08 June 2005

Fair enough MCC...

Sorry for the interruption... Now you can resume your educational lecture by explaining the whole UR mechanism to our couple here...
udosuk

Posts: 2698
Joined: 17 July 2005

Followup to udosuk--we can see the naked pairs you mention and have eliminated other candidates based on their occurrances, however, the step that eludes us, is without guessing (and potentially choosing the wrong number), what other logic is there to eliminate the 8 or the 9 (or the 3 or the 8). We haven't been doing these puzzles for too long, so the next step on these locked pairs escapes us. Of course, some locked or naked pairs just fall into place nicely for us.
Guest

Ralph&Cynthia,

The naked pair logic allows you to exclude those 2 digits from all other cells that share a group with the two cells that make up the naked pair. It doesn't allow you to also eliminate from those two cells one of the digits that make up the naked pair.

Tracy
TKiel

Posts: 209
Joined: 05 January 2006

Okay, Tracy. We had excluded the numbers in the naked pairs in other cells before we got stumped. It's that next leap of logic that eludes us. In the partially solved puzzle above, we have eliminated all of the candidates that we can identify, using all the techniques we have learned so far. Are there more candidates that can be eliminated using other more sophisticated sudoku techniques that we haven't learned yet? Eager to learn.
Guest

This is your current progress:
Code: Select all
`1     35     2347 | 236   8      367   | 9     24     356  234   38     6    | 19    19     5     | 24    7      38   2357  9      2378 | 236   367    4     | 56    1      3568 ------------------+--------------------+-------------------239   4      239  | 7     1369   1369  | 8     5      1269 2379  1      2379 | 3469  5      8     | 246   249    269  8     6      5    | 149   19     2     | 147   3      179  ------------------+--------------------+-------------------3459  7      349  | 8     1349   139   | 125   6      1259 469   2      489  | 5     14679  1679  | 3     89     179  3569  358    1    | 369   2      3679  | 57    89     4    `

I've marked the next few eliminations:
Code: Select all
`1     35     2347 | 236   8       367   | 9     24     356  2'34  38     6    | 19    19      5     | 24    7      38   2357  9      2378 | 236   367     4     | 56    1      3568 ------------------+---------------------+-------------------239   4      239  | 7     ~136~9  #1369 | 8     5      1269 2379  1      2379 | 3469  5       8     | 246   24-9   269  8     6      5    | 149   19      2     | 147   3      179  ------------------+---------------------+-------------------3459  7      349  | 8     ~134~9  139   | 125   6      125-9469   2      489  | 5     ~1467~9 1679  | 3     89     17-9 3569  358    1    | 369   2       3679  | 57    89     4    `

': Naked pair of [38] in r2c29
-: Naked pair of [89] in r89c8
~: Naked pair of [19] in r26c5
#: Locked candidates: r4c6 cannot be 1 since the 1 on c6 is locked in n8

Afterwards it's all singles...
udosuk

Posts: 2698
Joined: 17 July 2005

Ralph & Cynthia

You can solve the puzzle using just the techniques you have used so far or…

if you're looking for something a little different … you could employ the Xwing.

There is another naked pair (19) in column 5 that allows you to eliminate those candidates from the rest of c5 …

Code: Select all
`1     35     2347 | 236   8      367   | 9     24     356  234   38     6    | 19    19     5     | 24    7      38    2357  9      2378 | 236   367    4     | 56    1      3568 ------------------+--------------------+------------------- 239   4      239  | 7     36     1369  | 8     5      1269 2379  1      2379 | 3469  5      8     | 246   249    269  8     6      5    | 149   19     2     | 147   3      179  ------------------+--------------------+------------------- 3459  7      349  | 8     34     139   | 125   6      1259 469   2      489  | 5     467    1679  | 3     89     179  3569  358    1    | 369   2      3679  | 57    89     4   `

now you have an Xwing.

XWING : If there are only two candidates of a number in any 2 rows (or columns) and they are also in exactly the same 2 columns (or rows) then they form an Xwing and you can eliminate that candidate elsewhere in those columns (or rows).

An Xwing is in r47
Code: Select all
` . . . | . . . | . . .  . . . | 1 1 . | . . .  . . . | . . . | . . . -------+-------+------  . . . | . . 1#| . . 1# . . . | . . . | . . .  . . . | 1 1 . | 1 . 1^ -------+-------+------  . . . | . . 1^| 1 . 1^ . . . | . . 1#| . . 1# . . . | . . . | . . .`

The 1# form the xwing which eliminates all the 1^. There’s another Xwing there that will eliminate yet another 1.

For a better explanation of this and other techniques click Simple Sudoku. That should keep you out of mischief for a while!
emm

Posts: 987
Joined: 02 July 2005

First, to udosuk, thank you for pointing out exclusions that we should have seen. We should have been more thorough. They are now glaringly obvious.

Second, to emm, the x-wing is something we haven't progressed to yet, but are trying to understand for this and future puzzles. Thank you for explaining how the x-wing fits this puzzle. I've looked at Angus' x-wing explanation and sample and the sample is a bit more simplistic in that there are no other candidates other than in the cells of the x-wing. In this puzzle, there are extra candidates--some to be eliminated due to the x-wing logic and others that can't be eliminated as they are outside the scope of the x-wing.

We note that you did not eliminate 1 candidates in r4c5 and r8c5. Wouldn't they be eligible for exclusion based on the same logic as the r6c9, r7c6 and r7c9 exclusions?

Also, we note that the 1s in r7c6 and r7c9 look like they could have been the base of the x-wing as well as the r8c6 and r8c9 cells. Is there a piece of logic that dictates that r8 has to be the base of the x-wing and r7 cannot be?

We really appreciate the time everyone is spending on us and this puzzle. We are eager to move beyond our current level of skills.
Guest

### re: X-wing

Ralph&Cynthia wrote:We note that you did not eliminate 1 candidates in r48c5. Wouldn't they be eligible for exclusion based on the same logic as the r7c6 and r67c9 exclusions?

Also, we note that the 1s in r7c69 look like they could have been the base of the X-wing as well as the r8c69 cells.

no (to both your questions):
A. eliminate only in c69 (1s supplied by r48)
B. r7 has 3 1s

Pat

Posts: 3732
Joined: 18 July 2005

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