The New Sudoku Players' Forum

[PDN]

Hi,

Can anyone suggest a next step or two? Thanks!

[PDN]

This is an "Inferno" puzzle (hardest level) from the Mac
program Amnesiak.

I've tried locked candidates, X-wing, XY-wing,
Swordfish, Hidden Trips and Quads, Naked Trips
and Quads, XYZ-wing, WXYZ-wing, conjugate
pair chains, and forced chains.

But -- I'm new to most of these, so I may
have missed something.

[Serg]

Hi, PDN!
You can use "Sudoku Solver by Andrew Stuart" (http://www.sudokuwiki.org/sudoku.htm), for example, to see all solution steps for your puzzle.

Serg

[StrmCkr]

YES, CURRENLY AS POSTED your puzzle is still reducible with basic techniques.

Locked Candidates Type 1 (Pointing): 3 in b1 => r1c78<>3
Locked Candidates Type 1 (Pointing): 5 in b2 => r3c79<>5
Locked Candidates Type 1 (Pointing): 7 in b5 => r4c79<>7
Skyscraper: 8 in r7c8,r8c4 (connected by r1c48) => r7c6,r8c9<>8

then some singles

Locked Candidates Type 1 (Pointing): 2 in b2 => r46c4<>2
2-String Kite: 6 in r1c2,r6c8 (connected by r5c2,r6c3) => r1c8<>6
Locked Candidates Type 2 (Claiming): 6 in c8 => r5c79<>6
XYZ-Wing: 3/4/6 in r5c18,r6c8 => r5c7<>4

Code: Select all

.--------------.--------------.----------------.
| 13  236  26  | 128  9    7  | 1256  58   4   |
| 8   7    5   | 12   6    4  | 1239  39   23  |
| 14  9    246 | 3    5    18 | 126   7    268 |
:--------------+--------------+----------------:
| 9   23   8   | 47   247  6  | 234   1    5   |
| 34  236  1   | 5    8    9  | 237   346  237 |
| 7   5    246 | 14   124  3  | 8     46   9   |
:--------------+--------------+----------------:
| 2   1    9   | 6    347  5  | 347   348  378 |
| 5   4    7   | 189  13   18 | 369   2    36  |
| 6   8    3   | 479  47   2  | 4579  459  1   |
'--------------'--------------'----------------'

once you get to here the technique required to solve the grids to singles {there is several option/paths to go}

XY-Chain: 3 3- r2c9 -2- r2c4 -1- r3c6 -8- r8c6 -1- r8c5 -3 => r8c9<>3
{single }
XY-Wing: 1/8/2 in r2c4,r3c69 => r2c79<>2
more singles

Code: Select all

.--------------.--------------.---------------.
| 13  236  26  | 18   9    7  | 256   58   4  |
| 8   7    5   | 2    6    4  | 1     9    3  |
| 14  9    246 | 3    5    18 | 26    7    28 |
:--------------+--------------+---------------:
| 9   23   8   | 47   247  6  | 234   1    5  |
| 34  236  1   | 5    8    9  | 237   346  27 |
| 7   5    246 | 14   124  3  | 8     46   9  |
:--------------+--------------+---------------:
| 2   1    9   | 6    347  5  | 347   348  78 |
| 5   4    7   | 189  13   18 | 39    2    6  |
| 6   8    3   | 479  47   2  | 4579  45   1  |
'--------------'--------------'---------------'


Almost Locked Set XZ-Rule: A=r16c4 {148}, B=r19c8 {458}, X=8, Z=4 => r6c8,r9c4<>4
singles
Locked Candidates Type 1 (Pointing): 4 in b8 => r46c5<>4
Locked Candidates Type 1 (Pointing): 4 in b8 => r46c5<>4
Naked Pair: 3,4 in r4c7,r5c8 => r5c7<>3

Code: Select all

.-------------.--------------.---------------.
| 13  23  26  | 18   9    7  | 256   58   4  |
| 8   7   5   | 2    6    4  | 1     9    3  |
| 14  9   246 | 3    5    18 | 26    7    28 |
:-------------+--------------+---------------:
| 9   23  8   | 47   27   6  | 34    1    5  |
| 34  6   1   | 5    8    9  | 27    34   27 |
| 7   5   24  | 14   12   3  | 8     6    9  |
:-------------+--------------+---------------:
| 2   1   9   | 6    347  5  | 347   348  78 |
| 5   4   7   | 189  13   18 | 39    2    6  |
| 6   8   3   | 79   47   2  | 4579  45   1  |
'-------------'--------------'---------------'

XY-Chain: 9 9- r8c7 -3- r4c7 -4- r4c4 -7- r9c4 -9 => r8c4,r9c7<>9

singles to the end.

Code: Select all

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


[PDN]

Solver = simply amazing!