## Hard One

Post puzzles for others to solve here.

### Hard One

Is it possible to solve this sudoku by logical means, that is, if you don't try various digits by chance? I managed to solve this one on a website but I was punished with two fines for incorrect answers.
Code: Select all
`070896034364120089080043060705084090640000078090070400050400000400008950010050040`
AnotherLife

Posts: 4
Joined: 07 January 2021

### Re: Hard One

Locked Candidates 2 (Claiming): 1 in r4 => r5c7<>1,r6c8<>1,r6c9<>1;stte
yzfwsf

Posts: 307
Joined: 16 April 2019

### Re: Hard One

What about this one? You see, I am a self-educated person and I don't know any methods to solve this puzzle. I don't want to try to guess the digits.
Code: Select all
`007135020032798001800426370100052700240617053005040012000264007000581230020070100`
AnotherLife

Posts: 4
Joined: 07 January 2021

### Re: Hard One

Code: Select all
`*------------------------------------------------*|*469    69   7     | 1   3 5  | 4689 2    4689  ||*456    3    2     | 7   9 8  | 456  46   1     || 8      159  19    | 4   2 6  | 3    7    59    ||-------------------+----------+-----------------|| 1      689  3689  | 389 5 2  | 7    4689 4689  || 2      4    89    | 6   1 7  | 89   5    3     || 3679   6789 5     | 389 4 39 | 689  1    2     ||-------------------+----------+-----------------|| 359    1589 1389  | 2   6 4  | 589  89   7     || 679-4  679  469   | 5   8 1  | 2    3    469   || 3569-4 2    34689 | 39  7 39 | 1    4689 45689 |*------------------------------------------------*`

When you mark off the clues you get to here. Look at the two cells marked * in column 1. Since they are the only 4's in Box 1 one of them must be True, so you can remove the 4's outside of Box 1 in Column 1. That's called a pointing pair.

Code: Select all
`*---------------------------------------------------*| 469   69   7      | 1   3  5  | 4689 2     4689   || 456   3    2      | 7   9  8  | 456  46    1      || 8     159  19     | 4   2  6  | 3    7     59     ||-------------------+-----------+-------------------|| 1     689  3689   | 389 5  2  | 7    4689  4689   || 2     4    89     | 6   1  7  | 89   5     3      || 3679  6789 5      | 389 4  39 | 689  1     2      ||-------------------+-----------+-------------------|| 359   1589 1389   | 2   6  4  | 589  89    7      || 679   679  469    | 5   8  1  | 2    3     469    || 56-39 2    468-39 |*39  7 *39 | 1    468-9 4568-9 |*---------------------------------------------------*`

At the same point you'll notice two cells with 39 in Row 9. Since the 3 and 9 must be in those cells you can mark off other 3's and 9's in Row 9. That's called a naked pair.

Code: Select all
`*---------------------------------------------*| 469  69   7    | 1   3 5  |*4689 2    689-4 || 456  3    2    | 7   9 8  |*456  6-4  1     || 8    159  19   | 4   2 6  | 3    7    59    ||----------------+----------+-----------------|| 1    689  3689 | 389 5 2  | 7    4689 4689  || 2    4    89   | 6   1 7  | 89   5    3     || 3679 6789 5    | 389 4 39 | 689  1    2     ||----------------+----------+-----------------|| 359  1589 1389 | 2   6 4  | 589  89   7     || 679  679  469  | 5   8 1  | 2    3    469   || 56   2    468  | 39  7 39 | 1    468  4568  |*---------------------------------------------*`

Next notice the two cells marked * in Box 3 Column 7. Since they are the only 4's in Column 7, one of them must be True, so you can remove other 4's from Box 3. That's called a claiming pair.

Code: Select all
`*-------------------------------------------*| 469 *69    7    | 1   3 5  | 489 2   89   || 45   3     2    | 7   9 8  | 45  6   1    || 8    15-9  19   | 4   2 6  | 3   7   59   ||-----------------+----------+--------------|| 1   *689   369-8| 389 5 2  | 7   489 489  || 2    4     9-8  | 6   1 7  | 89  5   3    || 379 *789   5    | 389 4 39 | 6   1   2    ||-----------------+----------+--------------|| 359  15-89#1389 | 2   6 4  | 589 89  7    || 679 *679   469  | 5   8 1  | 2   3   469  || 56   2    #468  | 39  7 39 | 1   48  4568 |*-------------------------------------------*`

That solves a cell and gets you to here. Notice the 4 cells marked * in Column 2. They contain 4 digits 6789, which must go in those cells, so you can remove these digits from other cells in Column 2. That's a naked quad.

Also notice the pointing pair of 8's in Box 7 marked #, which removes some 8's in Column 3 outside of Box 7. That solves r5c3, which must be 9, and the puzzle solves with a series of singles from there.

So this puzzle solves with Singles, Intersections and Naked Subsets, which you can read about here .

Leren
Leren

Posts: 4006
Joined: 03 June 2012

### Re: Hard One

Hi leren,

just for fun

Leren wrote:
Code: Select all
`*-------------------------------------------*| 469 *69    7    | 1   3 5  | 489 2   89   || 45   3     2    | 7   9 8  | 45  6   1    || 8    15-9  19   | 4   2 6  | 3   7   59   ||-----------------+----------+--------------|| 1   *689   369-8| 389 5 2  | 7   489 489  || 2    4     9-8  | 6   1 7  | 89  5   3    || 379 *789   5    | 389 4 39 | 6   1   2    ||-----------------+----------+--------------|| 359  15-89#1389 | 2   6 4  | 589 89  7    || 679 *679   469  | 5   8 1  | 2   3   469  || 56   2    #468  | 39  7 39 | 1   48  4568 |*-------------------------------------------*`

That solves a cell and gets you to here. Notice the 4 cells marked * in Column 2. They contain 4 digits 6789, which must go in those cells, so you can remove these digits from other cells in Column 2. That's a naked quad.

Leren

This is a naked quad ... or a hidden pair... just a matter of taste

Sudoku Explainer would show first the hidden pair

(and both have the same eliminations for sure)
champagne
2017 Supporter

Posts: 7178
Joined: 02 August 2007
Location: France Brittany

### Re: Hard One

AnotherLife wrote:What about this one? You see, I am a self-educated person and I don't know any methods to solve this puzzle. I don't want to try to guess the digits.
Code: Select all
`007135020032798001800426370100052700240617053005040012000264007000581230020070100`

Singles and whips[1] (intersections)
Code: Select all
`whip[1]: c3n4{r9 .} ==> r9c1 ≠ 4, r8c1 ≠ 4whip[1]: r7n3{c3 .} ==> r9c3 ≠ 3, r9c1 ≠ 3whip[1]: c7n4{r2 .} ==> r2c8 ≠ 4, r1c9 ≠ 4naked-single ==> r2c8 = 6hidden-single-in-a-column ==> r6c7 = 6whip[1]: b8n9{r9c6 .} ==> r9c9 ≠ 9, r9c1 ≠ 9, r9c3 ≠ 9, r9c8 ≠ 9`

Code: Select all
`RESOLUTION STATE:   469       69        7         1         3         5         489       2         89           45        3         2         7         9         8         45        6         1            8         159       19        4         2         6         3         7         59           1         689       3689      389       5         2         7         489       489          2         4         89        6         1         7         89        5         3            379       789       5         389       4         39        6         1         2            359       1589      1389      2         6         4         589       89        7            679       679       469       5         8         1         2         3         469          56        2         468       39        7         39        1         48        4568      `

and a simple Hidden Pair finishes the job:

Code: Select all
`hidden-pairs-in-a-column: c2{n1 n5}{r3 r7} ==> r7c2 ≠ 9, r7c2 ≠ 8, r3c2 ≠ 9whip[1]: b7n8{r9c3 .} ==> r4c3 ≠ 8, r5c3 ≠ 8stte`
denis_berthier
2010 Supporter

Posts: 1983
Joined: 19 June 2007
Location: Paris

### Re: Hard One

Leren wrote:So this puzzle solves with Singles, Intersections and Naked Subsets, which you can read about here .

Leren

Thanks for your advice! It was useful in many cases, but I think these methods do not work in this one. What can you suggest here?
Code: Select all
`000041307300967004470083000090028035003705800200630071000302568530076009002050703`
AnotherLife

Posts: 4
Joined: 07 January 2021

### Re: Hard One

AnotherLife wrote:Thanks for your advice! It was useful in many cases, but I think these methods do not work in this one. What can you suggest here?
Code: Select all
`000041307300967004470083000090028035003705800200630071000302568530076009002050703`

Look at

digit 6 in row 3 x box3
digit 4 in box 7 x row 7

the path to the end is not that far after

r1c3=6
r3c3=9
r1c8=9
champagne
2017 Supporter

Posts: 7178
Joined: 02 August 2007
Location: France Brittany

### Re: Hard One

Well, they worked for me.

Code: Select all
`*------------------------------------------------*| 689   2568   5689  | 25  4  1  | 3    2589  7  || 3     1258   158   | 9   6  7  | 12   1258  4  || 4     7      159-6 | 25  8  3  |*1269 1259 *26 ||--------------------+-----------+---------------|| 167   9      1467  | 14  2  8  | 46   3     5  || 16    146    3     | 7   19 5  | 8    249   26 || 2     58-4   58-4  | 6   3 @49 |@49   7     1  ||--------------------+-----------+---------------|| 179  #14    #1479  | 3   19 2  | 5    6     8  || 5     3      18-4  | 148 7  6  | 124  124   9  || 1689  168-4  2     | 148 5  49 | 7    14    3  |*------------------------------------------------*`

1. A Pointing Pair of 6's in Box 3 => r3c3 <> 6
2. A Claiming Pair of 4's in Box 7 => r8c3, r9c2 <> 4
3. A Naked Pair (49) in r6c67 => r6c23 <> 4.

Code: Select all
`*---------------------------------------------*| 689  2568  69-58 | 25  4  1  | 3    2589 7  || 3    1258 *158   | 9   6  7  | 12   1258 4  || 4    7     9-15  | 25  8  3  | 1269 1259 26 ||------------------+-----------+--------------|| 167  9     467-1 | 14  2  8  | 46   3    5  || 16   146   3     | 7   19 5  | 8    249  26 || 2    58   *58    | 6   3  49 | 49   7    1  ||------------------+-----------+--------------|| 179  14    479-1 | 3   19 2  | 5    6    8  || 5    3    *18    | 148 7  6  | 124  124  9  || 1689 168   2     | 148 5  49 | 7    14   3  |*---------------------------------------------*`

A Naked Triple (158) in r268c3 removes 15&8 from other cells in Column 3 and solves r3c3 = 9. The puzzle should solve with singles from there.

Leren

PS you can go to a free online solver here.

Click on the blue "Import a Sudoku" button, copy and paste your puzzle into the dialog box and click OK.

When the puzzle comes up in the main box, to solve, just click on the red "Take Step" button. You may have to click on it 4 or 5 times before it executes a move, which will shown and explained in the main box.

To solve this puzzle it made the same 4 moves I did, although not in the same order.

Leren
Leren

Posts: 4006
Joined: 03 June 2012

### Re: Hard One

Leren wrote:A Naked Triple (158) in r268c3 removes 15&8 from other cells in Column 3 and solves r3c3 = 9.

Leren

Leren, thanks once again! I failed to find the Naked Triple and got stuck here. Maybe, my concentration is too low. You see, it's almost the same as you miss a combination in chess. I used to play in Russian chess tournaments before the COVID pandemic.
AnotherLife

Posts: 4
Joined: 07 January 2021

### Re: Hard One

Leren wrote:A Naked Triple (158) in r268c3 removes 15&8 from other cells in Column 3 and solves r3c3 = 9. The puzzle should solve with singles from there.

Hi leren,

once more, Sudoku Explainer select the hidden pair 47 in column 3, leading to r1c3=6, but the final result is the same
champagne
2017 Supporter

Posts: 7178
Joined: 02 August 2007
Location: France Brittany

### Re: Hard One

Hi Champagne,

Hodoku's solution was exactly the same as mine, in the same order. Andrew's solver puts Naked and Hidden Tuples before Intersections, so it's first move after singles was the Naked Pair, then the Intersections, then the Naked Triple.

Just goes to show that you can't get agreement on move ordering on anything after singles

Leren
Leren

Posts: 4006
Joined: 03 June 2012

### Re: Hard One

Leren wrote:Hi Champagne,

Hodoku's solution was exactly the same as mine, in the same order. Andrew's solver puts Naked and Hidden Tuples before Intersections, so it's first move after singles was the Naked Pair, then the Intersections, then the Naked Triple.

Just goes to show that you can't get agreement on move ordering on anything after singles

Leren

Solving without the full grid of pencil marks, singles in cells can be difficult to spot, I think that this is why long ago, surely after endless discussions, it has been rated relatively high in Sudoku Explainer

When I solve a sudoku on paper with very limited pencil marks (what I did not do for months) I mark mainly digits locked in mini rows/ mini columns, this gives somehow a priority to hidden pairs often seen first. My wife hates pencil marks and solves in a different way. This for "easy sudokus", but it is the situation here.
champagne
2017 Supporter

Posts: 7178
Joined: 02 August 2007
Location: France Brittany