## Difficult sudoku partly solved

Post the puzzle or solving technique that's causing you trouble and someone will help

### Difficult sudoku partly solved

Hi all,
I am totally stuck with this one. Can someone explain how to crack the next step, please?
Cheers.

. . . | . 6 5 | . . 8
4 . 8 | . 3 7 | 2 . .
. 1 . | 8 2 4| . 9 .
. . 5 | 6 8 1| . . .
. . . | 7 4 3 | . . .
. . . | 5 9 2 | 3 . .
. 2 . | 4 1 . | . 7 .
. . 4 | 3 7 . | 6 2 1
7 . 1 | 2 5 . | . . .
shamath

Posts: 5
Joined: 31 July 2018

### Re: Difficult sudoku partly solved

shamath wrote:Hi all,
I am totally stuck with this one. Can someone explain how to crack the next step, please?

Your puzzle requires only hidden and naked singles. Hidden singles are the easier technique for casual manual solvers but they've been exhausted for now. The next step is a naked single, which is trivial if candidate markers are added, but a bit tricky to find if pencil marks are not used.

Here's your puzzle with pencil marks:

Code: Select all
`.-------------------.------------.------------------.| 239    379   2379 | 19  6  5   | 147   134   8    || 4      569   8    | 19  3  7   | 2     156   56   || 356    1     367  | 8   2  4   | 57    9     3567 |:-------------------+------------+------------------:| 239    3479  5    | 6   8  1   | 479   (4)   2479 || 12689  689   269  | 7   4  3   | 1589  1568  2569 || 168    4678  67   | 5   9  2   | 3     1468  467  |:-------------------+------------+------------------:| 35689  2     369  | 4   1  689 | 589   7     359  || 589    589   4    | 3   7  89  | 6     2     1    || 7      3689  1    | 2   5  689 | 489   348   349  |'-------------------'------------'------------------'`

Notice the (4) in r4c8. It's the only possibility left for that cell, i.e. a naked single. It's not obvious without pencil marks, though, but you can learn to spot them if you look for cells that are at a crossroads of lots of different solved digits. In this case the cell r4c8 sees a 3 in its box, 1568 in its row, and 279 in its column, which adds up to eight digits (12356789) that can't be placed in that cell. The digit 4 is the only possibility left, so it must be the answer.

In general, naked singles and naked subsets are much more difficult to find without pencil marks than their hidden counterparts (which don't really benefit from pencil marks at all; edit: unless filters are used). They can often be found more easily indirectly by spotting their hidden partner (especially hidden pairs are much easier to spot than naked singles). In this case that's not very easy either because the corresponding hidden subsets are large. The easiest way to find this and other naked singles is to add pencil marks for all candidates, or using a software solver that does it for you.
Last edited by SpAce on Thu Aug 02, 2018 9:51 pm, edited 1 time in total.
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2574
Joined: 22 May 2017

### Re: Difficult sudoku partly solved

Naked singles are visible with out pms

The difference is you are viewing what digits are visible to the cell
for r4c8 it sees the following 12356789 directly the only one not seen is 4.
A counting method looking from starting cell checking box row col for each digit is how I find them remembering What digits are missing
From a programmers point of view naked are easiest to find, as it we do a summation of r, c, b for all digits showing PMs for that cell as, 1 left.

Hidden. Singles are easiest for a player as it's a 1 digit looking for what cells are left available for a digit. (using cross hatching on givens to remove cells)
which is slightly harder to program, as its uses what's off to find them vrs what's still on.

StrmCkr

Posts: 1177
Joined: 05 September 2006

### Re: Difficult sudoku partly solved

StrmCkr wrote:Naked singles are visible with out pms

Yes, but finding them can take time, as you have to look at one cell at a time (although some are more potential than others, of course). Until quite recently I didn't really bother to look for them at all without pms, as it was usually faster to just mark the candidates and let the naked singles reveal themselves. Lately I've been honing my no-pm skills a bit and can find almost all naked singles now but might still miss some. I still don't bother to look for them if I know I will be needing pms anyway.

I start all puzzles without pencil marks (if understood as a synonym for cell candidates -- otherwise it's not literally true as I almost always use some other helper markings) and only add them if need be. First I exhaust all box-based hidden singles (using pointing pairs/triples if needed), and I also note obvious locked pairs/triples. Then I look for line-based hidden singles and pairs, as well as claiming opportunities and conjugate pairs, starting with the least empty rows and columns. While doing that I also look for naked singles (and pairs), and make note of any bivalue cells I find too. (When all of that is exhausted, I typically use any obvious URs, X-Wings, Skyscrapers, Kites, Remote Pairs, etc. before resorting to pms; it's much more unlikely that I would see things like naked triples and quads without pms, though.)

For example, in this particular puzzle I would have found the first naked single when looking at the row 4 which has five empty cells and thus five remaining candidates (23479). When scanning each empty cell on that row I would have checked how many of those candidates were seen by that cell in its box and column, and the cell r4c8 saw four of them (3+279) -> thus a naked single. My manual solution to this puzzle used two more naked singles, one of which I found as a by-product of a hidden pair (which is by far the easiest way for me to spot them). I think there were also three line-based hidden singles. Otherwise I just used box-based hidden singles (possibly with the help of pointing pairs -- it's automatic for me, so I don't really register using them) and full-houses. No need for pms.
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2574
Joined: 22 May 2017

### Re: Difficult sudoku partly solved

just pointing out its possible to find basic steps without pm generation by using whats given and whats removed {naked | hidden } respectfully.

20 peer cells for starting cell counting 1-9. {naked}

or

checking 1 sector{row} for 9 cols { 54 spots} and 3 boxes with 24 cells for intersection removals. = 3 cells leaving a box line reduction in the sector which also finds the single}
on the same digit .... technically the hidden has more work...{yes boxes can make this work seem quicker as it reduces the number of checks down by 3 cols/rows} the search space is bigger 78 cells total.

but looking for 1 digit is easier then looking for 1 of each of the 9.

Some do, some teach, the rest look it up.

StrmCkr

Posts: 1177
Joined: 05 September 2006

### Re: Difficult sudoku partly solved

SpAce wrote:
shamath wrote:Hi all,
I am totally stuck with this one. Can someone explain how to crack the next step, please?

Your puzzle requires only hidden and naked singles. Hidden singles are the easier technique for casual manual solvers but they've been exhausted for now. The next step is a naked single, which is trivial if candidate markers are added, but a bit tricky to find if pencil marks are not used.

Here's your puzzle with pencil marks:

Code: Select all
`.-------------------.------------.------------------.| 239    379   2379 | 19  6  5   | 147   134   8    || 4      569   8    | 19  3  7   | 2     156   56   || 356    1     367  | 8   2  4   | 57    9     3567 |:-------------------+------------+------------------:| 239    3479  5    | 6   8  1   | 479   (4)   2479 || 12689  689   269  | 7   4  3   | 1589  1568  2569 || 168    4678  67   | 5   9  2   | 3     1468  467  |:-------------------+------------+------------------:| 35689  2     369  | 4   1  689 | 589   7     359  || 589    589   4    | 3   7  89  | 6     2     1    || 7      3689  1    | 2   5  689 | 489   348   349  |'-------------------'------------'------------------'`

Notice the (4) in r4c8. It's the only possibility left for that cell, i.e. a naked single. It's not obvious without pencil marks, though, but you can learn to spot them if you look for cells that are at a crossroads of lots of different solved digits. In this case the cell r4c8 sees a 3 in its box, 1568 in its row, and 279 in its column, which adds up to eight digits (12356789) that can't be placed in that cell. The digit 4 is the only possibility left, so it must be the answer.

In general, naked singles and naked subsets are much more difficult to find without pencil marks than their hidden counterparts (which don't really benefit from pencil marks at all; edit: unless filters are used). They can often be found more easily indirectly by spotting their hidden partner (especially hidden pairs are much easier to spot than naked singles). In this case that's not very easy either because the corresponding hidden subsets are large. The easiest way to find this and other naked singles is to add pencil marks for all candidates, or using a software solver that does it for you.

Thanks for the reply, I see the pencil marking can help a lot. But in the following case I found only 4 without pencil and after write all possibilities can not find the next step. I am not sure it is that difficult or just confused how to use properly this technique.

Code: Select all
`.-------------------------.--------------------------.-----------------------------.| 149          1248       12489 | 1567     3     4678    | 1589     1468    1589    || 1349           5              7    | 16        2        46    | 1489     1468    1389    || 6              134             14  | 8        15         9     | 7          134           2    |:----------------------------------+--------------------------+---------------------------:| 8               6              14    | 137        179       5   | 2         1347      1379 || 147          9              2124  | 1237         6     2378 | 148          5      1378 || 5             127                3   | 4           179     278 | 189       178           6  |:----------------------------------+--------------------------+--------------------------:| 2               378             6  |  9           57          1 | 58           78          4  || 17             178          158  | 2567       4       267  | 3             9       1578  || 13479      1347       1459   | 357        8           37 | 6             2        157  |'----------------------------------'----------------------------'---------------------------'`

shamath

Posts: 5
Joined: 31 July 2018

### Re: Difficult sudoku partly solved

shamath wrote:Thanks for the reply, I see the pencil marking can help a lot. But in the following case I found only 4 without pencil and after write all possibilities can not find the next step. I am not sure it is that difficult or just confused how to use properly this technique.

Again, this puzzle requires only singles. Now that you're using pencil marks, naked singles have become as trivial as full-house singles, and I guess you could already find box-based hidden singles using cross-hatching as well. There's one more type left and that's line-based (i.e. row- and column-based) hidden singles. Normal pencil marks don't really help with them. If you're solving with pencil and paper, you basically have to go over every row and column for every digit and see if there's only one cell into which that digit can go (easiest if you start with those rows and columns that have the fewest non-solved cells). Dedicated pencil&paper solvers (like myself) usually have their own mark-up systems to make that process more efficient, but I won't go into that now. If you're using a software helper, they usually have filters with which you can easily see all candidates of a single digit at a time, and that makes spotting hidden singles (and later more advanced single digit techniques) a lot easier. I might recommend that option to begin with so you'll learn what to look for.

Anyway, let's get to your puzzle. First of all, a little tip for presenting your pencil-mark-grid: use an external editor with a fixed-width font and then paste it into your post (within a code-section as you correctly did). Otherwise your grid will be messy. Also use the "Preview" button to see what your post will actually look like. Here's what a properly formatted grid should look like (note that it does look messy within the message editor, because it doesn't use a fixed-width font -- but it will look good when posted because the code-section has a fixed-width font):

Code: Select all
`.---------------------.--------------------.------------------.| 149    1248   12489 | 1567   3    x467-8 | 1589  1468  1589 || 1349   5      7     | 16     2     46    | 1489  1468  1389 || 6      134    14    | 8      15    9     | 7     134   2    |:---------------------+--------------------+------------------:| 8      6      14    | 137    179   5     | 2     1347  1379 || 147    9      2124  | 1237   6     2378  | 148   5     1378 || 5      127    3     | 4      179   278   | 189   178   6    |:---------------------+--------------------+------------------:| 2      378    6     |  9     57    1     | 58    78    4    || 17     178    158   | 2567   4     267   | 3     9     1578 || 13479  1347   1459  | 357    8     37    | 6     2     157  |'---------------------'--------------------'------------------'`

So, what can we see there? First, there seems to be a placed 8 in r3c4 but still a candidate 8 in the same box (r1c6). That needs to be removed, but it doesn't get us any further. What else can we learn? Look at rows 3 and 7. Both of them have a hidden single. Can you find them? The answer is below if you click open the hidden section.

Hidden Text: Show
Code: Select all
`.---------------------.--------------------.------------------.| 149    1248   12489 | 1567   3     467   | 1589  1468  1589 || 1349   5      7     | 16     2     46    | 1489  1468  1389 || 6      134    14    | 8     *1(5)  9     | 7     134   2    |:---------------------+--------------------+------------------:| 8      6      14    | 137    179   5     | 2     1347  1379 || 147    9      2124  | 1237   6     2378  | 148   5     1378 || 5      127    3     | 4      179   278   | 189   178   6    |:---------------------+--------------------+------------------:| 2     *(3)78  6     |  9     57    1     | 58    78    4    || 17     178    158   | 2567   4     267   | 3     9     1578 || 13479  1347   1459  | 357    8     37    | 6     2     157  |'---------------------'--------------------'------------------'`

Row 3 has only one available place for digit 5 (r3c5), and row 7 has only one place for digit 3 (r7c2).

PS. Once you learn about subsets you can also use those to find hidden singles indirectly (and vice versa: hidden subsets can be used to find naked singles, but that's only useful if pencil marks aren't used). For example, in the above puzzle you might notice there's a naked triple of (134) in row 3 (r3c238), which means those digits can be removed from the candidates of the other cells of that row. In this case we can remove digit 1 from r3c5, which leaves the 5 as a naked single. Similarly there's a naked triple of (578) in row 7, which removes the candidates 7 and 8 from r7c2 and leaves only the 3 there as a naked single.
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2574
Joined: 22 May 2017

### Re: Difficult sudoku partly solved

SpAce wrote:
shamath wrote:Thanks for the reply, I see the pencil marking can help a lot. But in the following case I found only 4 without pencil and after write all possibilities can not find the next step. I am not sure it is that difficult or just confused how to use properly this technique.

Again, this puzzle requires only singles. Now that you're using pencil marks, naked singles have become as trivial as full-house singles, and I guess you could already find box-based hidden singles using cross-hatching as well. There's one more type left and that's line-based (i.e. row- and column-based) hidden singles. Normal pencil marks don't really help with them. If you're solving with pencil and paper, you basically have to go over every row and column for every digit and see if there's only one cell into which that digit can go (easiest if you start with those rows and columns that have the fewest non-solved cells). Dedicated pencil&paper solvers (like myself) usually have their own mark-up systems to make that process more efficient, but I won't go into that now. If you're using a software helper, they usually have filters with which you can easily see all candidates of a single digit at a time, and that makes spotting hidden singles (and later more advanced single digit techniques) a lot easier. I might recommend that option to begin with so you'll learn what to look for.

Anyway, let's get to your puzzle. First of all, a little tip for presenting your pencil-mark-grid: use an external editor with a fixed-width font and then paste it into your post (within a code-section as you correctly did). Otherwise your grid will be messy. Also use the "Preview" button to see what your post will actually look like. Here's what a properly formatted grid should look like (note that it does look messy within the message editor, because it doesn't use a fixed-width font -- but it will look good when posted because the code-section has a fixed-width font):

Code: Select all
`.---------------------.--------------------.------------------.| 149    1248   12489 | 1567   3    x467-8 | 1589  1468  1589 || 1349   5      7     | 16     2     46    | 1489  1468  1389 || 6      134    14    | 8      15    9     | 7     134   2    |:---------------------+--------------------+------------------:| 8      6      14    | 137    179   5     | 2     1347  1379 || 147    9      2124  | 1237   6     2378  | 148   5     1378 || 5      127    3     | 4      179   278   | 189   178   6    |:---------------------+--------------------+------------------:| 2      378    6     |  9     57    1     | 58    78    4    || 17     178    158   | 2567   4     267   | 3     9     1578 || 13479  1347   1459  | 357    8     37    | 6     2     157  |'---------------------'--------------------'------------------'`

So, what can we see there? First, there seems to be a placed 8 in r3c4 but still a candidate 8 in the same box (r1c6). That needs to be removed, but it doesn't get us any further. What else can we learn? Look at rows 3 and 7. Both of them have a hidden single. Can you find them? The answer is below if you click open the hidden section.

Hidden Text: Show
Code: Select all
`.---------------------.--------------------.------------------.| 149    1248   12489 | 1567   3     467   | 1589  1468  1589 || 1349   5      7     | 16     2     46    | 1489  1468  1389 || 6      134    14    | 8     *1(5)  9     | 7     134   2    |:---------------------+--------------------+------------------:| 8      6      14    | 137    179   5     | 2     1347  1379 || 147    9      2124  | 1237   6     2378  | 148   5     1378 || 5      127    3     | 4      179   278   | 189   178   6    |:---------------------+--------------------+------------------:| 2     *(3)78  6     |  9     57    1     | 58    78    4    || 17     178    158   | 2567   4     267   | 3     9     1578 || 13479  1347   1459  | 357    8     37    | 6     2     157  |'---------------------'--------------------'------------------'`

Row 3 has only one available place for digit 5 (r3c5), and row 7 has only one place for digit 3 (r7c2).

PS. Once you learn about subsets you can also use those to find hidden singles indirectly (and vice versa: hidden subsets can be used to find naked singles, but that's only useful if pencil marks aren't used). For example, in the above puzzle you might notice there's a naked triple of (134) in row 3 (r3c238), which means those digits can be removed from the candidates of the other cells of that row. In this case we can remove digit 1 from r3c5, which leaves the 5 as a naked single. Similarly there's a naked triple of (578) in row 7, which removes the candidates 7 and 8 from r7c2 and leaves only the 3 there as a naked single.

Oh yeah sorry for the messy formatting. Now I see the logic. I am solving sudoku since only couple of months, I guess need time to get familiar with those techniques. Thank you very much, apprecite it.
shamath

Posts: 5
Joined: 31 July 2018