The New Sudoku Players' Forum

[AnotherLife]

This example shows another strange estimate by the current rating system. The puzzle is rated Extreme 8.3, and its solution should require Cell/Region Forcing Chains according to the difficulty ratings, but it can be easily solved without them. Who wants to try?

Code: Select all

|..2|7.3|6..|
|...|.1.|...|
|3..|5.4|..8|
|---+---+---|
|6.1|...|8.3|
|.4.|...|.7.|
|9.7|...|4.6|
|---+---+---|
|7..|3.5|..1|
|...|.9.|...|
|..5|1.6|7..|

..27.36......1....3..5.4..86.1...8.3.4.....7.9.7...4.67..3.5..1....9......51.67..


[eleven]

Code: Select all

 *-----------------------------------------------------------*
 |  145   1-5    2     |  7  8    3    |  6     49    a459   |
 |  458   568    468   |  9  1    2    | b35    34     7     |
 |  3     7      9     |  5  6    4    |  12    12     8     |
 |---------------------+---------------+---------------------|
 |  6    d25     1     |  4  7    9    |  8     25     3     |
 | c258   4     *38    |  6 #35   18   |  129   7      29    |
 |  9    d358    7     |  2  35   18   |  4     15     6     |
 |---------------------+---------------+---------------------|
 |  7     2689   468   |  3  24   5    |  29    4689   1     |
 |  124   1236  *346   |  8  9    7    | #35    346    245   |
 |  248   2389   5     |  1  24   6    |  7     3489   249   |
 *-----------------------------------------------------------*

Extended w-wing 35, SL 3r58c3, 35 r5c5,r8c7
5r1c9 = r2c7 - (5=3)r8c7 - r8c3 = 35r5c35 - r5c1 = r46c2 => -5r1c2

Code: Select all

+-------------------+-------------------+-------------------+
| 45    1     2     | 7     8     3     | 6     49    459   |
| 458   568   468   | 9     1     2     | 35    34    7     |
| 3     7     9     | 5     6     4     | 12    12    8     |
+-------------------+-------------------+-------------------+
| 6    #25    1     | 4     7     9     | 8    #25    3     |
| 258   4     38    | 6     35    18    | 129   7     9-2   |
| 9     358   7     | 2     35    18    | 4     15    6     |
+-------------------+-------------------+-------------------+
| 7     2689  468   | 3     24    5     | 29    4689  1     |
| 1    #236   346   | 8     9     7     | 35    346  #245   |
| 248   2389  5     | 1     24    6     | 7     3489  249   |
+-------------------+-------------------+-------------------+

Skyscraper 2r48 => -5r5c9, stte

[shye]

edit: my "nice start" was flawed (double )

found a rly nice starting move, couldnt find a clean finish

Code: Select all

.----------------.-----------.------------------.
|y145 y15    2   | 7  8   3  | 6     9-45  x459 |
|x458  68-5  68-4| 9  1   2  |y35   y345    7   |
| 3    7     9   | 5  6   4  | 12    12     8   |
:----------------+-----------+------------------:
| 6    25    1   | 4  7   9  | 8     25     3   |
| 258  4     38  | 6  35  18 | 1259  7      259 |
| 9    358   7   | 2  35  18 | 4     15     6   |
:----------------+-----------+------------------:
| 7    2689  468 | 3  24  5  | 29    24689  1   |
| 124  1236  346 | 8  9   7  | 235   23456  245 |
|#248  2389  5   | 1 #24  6  | 7     23489 #249 |
'----------------'-----------'------------------'

set [45] to x and y (orientation unknown)
r2c1 and r1c9 cannot be x and y, else r1c12 or r2c78 ALS loses too many candidates
from this:
(x=8)r2c1 - (8=249)r9c159 - (9=x)r1c9
x removed from the ALS's in r1c12 & r2c78, so y must be placed within them. gives pairs of x and y in b13
=>-45b1p56, -45b3p2, some basics to follow

from here, a less pretty path

Code: Select all

.----------------.-----------.------------------.
| 145  15    2   | 7  8   3  | 6     9      45  |
| 45   68    68  | 9  1   2  | 35    345    7   |
| 3    7     9   | 5  6   4  | 12    12     8   |
:----------------+-----------+------------------:
| 6    25    1   | 4  7   9  | 8     25     3   |
| 258  4     38  | 6  35  18 | 1259  7      259 |
| 9    358   7   | 2  35  18 | 4     15     6   |
:----------------+-----------+------------------:
| 7    2689  468 | 3  24  5  |#29    2468   1   |
|*12  *1236  346 | 8  9   7  |*235  *23456 *245 |
| 8-2  389-2 5   | 1 #24  6  | 7     2348  #249 |
'----------------'-----------'------------------'

ALS h-wing
2r8c12 = 2r8c789 - (2=94)b9p19 - (4=2)r9c5
=> -2r9c12, some singles

Code: Select all

.--------------.-----------.----------------.
| 145  15   2  | 7  8   3  | 6     9    45  |
| 45   68   68 | 9  1   2  | 35    345  7   |
| 3    7    9  | 5  6   4  | 12    12   8   |
:--------------+-----------+----------------:
| 6    25   1  | 4  7   9  | 8     25   3   |
|#25   4   *38 | 6 #35  18 | 1259  7   #259 |
| 9   *358  7  | 2  35  18 | 4     15   6   |
:--------------+-----------+----------------:
| 7    269  46 | 3  24  5  | 29    8    1   |
| 12   123  34 | 8  9   7  | 235   6    245 |
| 8   #39   5  | 1  24  6  | 7     234  24-9|
'--------------'-----------'----------------'

ALS w-wing
(9=3)r9c2 - 3b4p8 = 3b4p6 - (3=259)r5c159
=> -9r9c9 stte

[AnotherLife]

Extended w-wing 35, SL 3r58c3, 35 r5c5,r8c7...

This is a nice pattern, thanks.

This puzzle needs only two chains to be solved, one of them being an AIC with a group. I cannot find such a method in the list of methods used to determine the sudoku ratings, so there are some Extreme 8.2+ puzzles that are solvable via only AICs with groups, and it seems rather strange for me. One of my previous puzzles was rated Extreme 8.8, but its solution required only one AIC with an ALS and AICs with groups (I have not posted my solution because it was a bit long). I have some more examples showing that the current rating system should be revised.

[eleven]

shye,
i can't see the eliminations, if 8r2c1 or 9r1c9. Do i miss something ?

[shye]

shye,
i can't see the eliminations, if 8r2c1 or 9r1c9. Do i miss something ?

i just had a look at it, and yeah, i think its invalid. the pairs i claimed existed were not true because x is not set in each of r1c9 and r2c1, only at least one is true D:
so i got lucky then on the first bit... well now the whole solve just seems bad lol. thanks for being observant!

[RSW]

This puzzle needs only two chains to be solved, one of them being an AIC with a group.

This is what I got:

Code: Select all

 +-----------------+----------+--------------+
 |*45-1 a15    2   | 7  8  3  | 6   49   459 |
 |j458   568  j468 | 9  1  2  |h35 i34   7   |
 | 3     7     9   | 5  6  4  | 12  12   8   |
 +-----------------+----------+--------------+
 | 6    b25    1   | 4  7  9  | 8   25   3   |
 |c258   4    e38  | 6 d35 18 | 129 7    29  |
 | 9    b358   7   | 2  35 18 | 4   15   6   |
 +-----------------+----------+--------------+
 | 7     2689  468 | 3  24 5  | 29  4689 1   |
 | 124   1236 f346 | 8  9  7  |g35  346  245 |
 | 248   2389  5   | 1  24 6  | 7   3489 249 |
 +-----------------+----------+--------------+


I couldn't find a chain any shorter than this to give a 2 step solution:

(1=5)r1c2 - (5)r46c2 = (5)r5c1 - (5=3)r5c5 - (3)r5c3 = (3)r8c3 - (3=5)r8c7 - (5=3)r2c7 - (3=4)r2c8 - (4)r2c13 = (4)r1c1 => -1r1c1

Singles: 1r1c2 -1r8c2 1r8c1

(2)r8c9 = r8c2 - r4c2 = r4c8 => -2r5c9; stte

[denis_berthier]

.

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 145   15    2     ! 7     8     3     ! 6     459   459   !
   ! 458   568   468   ! 9     1     2     ! 35    345   7     !
   ! 3     7     9     ! 5     6     4     ! 12    12    8     !
   +-------------------+-------------------+-------------------+
   ! 6     25    1     ! 4     7     9     ! 8     25    3     !
   ! 258   4     38    ! 6     35    18    ! 1259  7     259   !
   ! 9     358   7     ! 2     35    18    ! 4     15    6     !
   +-------------------+-------------------+-------------------+
   ! 7     2689  468   ! 3     24    5     ! 29    24689 1     !
   ! 124   1236  346   ! 8     9     7     ! 235   23456 245   !
   ! 248   2389  5     ! 1     24    6     ! 7     23489 249   !
   +-------------------+-------------------+-------------------+
112 candidates.

There's a very easy solution in S+Z4:

Code: Select all

naked-triplets-in-a-column: c8{r3 r4 r6}{n1 n2 n5} ==> r9c8≠2, r8c8≠5, r8c8≠2, r7c8≠2, r2c8≠5, r1c8≠5
whip[1]: c8n5{r6 .} ==> r5c7≠5, r5c9≠5
hidden-pairs-in-a-column: c7{n3 n5}{r2 r8} ==> r8c7≠2
biv-chain[3]: c2n9{r7 r9} - r9n3{c2 c8} - b9n8{r9c8 r7c8} ==> r7c8≠9, r7c2≠8
biv-chain[3]: c2n9{r9 r7} - r7c7{n9 n2} - b8n2{r7c5 r9c5} ==> r9c2≠2
z-chain[4]: r8n2{c2 c9} - r5c9{n2 n9} - r9c9{n9 n4} - r9c5{n4 .} ==> r9c1≠2
biv-chain[3]: c5n4{r7 r9} - r9c1{n4 n8} - b9n8{r9c8 r7c8} ==> r7c8≠4
biv-chain[4]: r1c2{n5 n1} - b7n1{r8c2 r8c1} - c1n2{r8 r5} - r4c2{n2 n5} ==> r2c2≠5, r6c2≠5
naked-pairs-in-a-block: b4{r5c3 r6c2}{n3 n8} ==> r5c1≠8
biv-chain[4]: r8n1{c1 c2} - r1c2{n1 n5} - b4n5{r4c2 r5c1} - c1n2{r5 r8} ==> r8c1≠4
biv-chain[4]: r5n3{c3 c5} - r5n5{c5 c1} - r2n5{c1 c7} - c7n3{r2 r8} ==> r8c3≠3
stte

For a 2-step path, longer chains are necessary, but not necessarily involving any g-candidate. Here are two, using only reversible chains (and a fish):

Code: Select all

z-chain[4]: c5n2{r9 r7} - r7c7{n2 n9} - r9c9{n9 n4} - r9c5{n4 .} ==> r9c1≠2, r9c8≠2, r9c2≠2
     with z-candidates = n2r9c9 n2r9c5
z-chain[6]: r4n5{c2 c8} - r2n5{c8 c7} - c7n3{r2 r8} - c3n3{r8 r5} - r5c5{n3 n5} - c1n5{r5 .} ==> r1c2≠5
     with z-candidates = n5r2c2 n5r2c1 n5r1c1
stte

Code: Select all

z-chain[6]: r4n5{c2 c8} - r2n5{c8 c7} - c7n3{r2 r8} - c3n3{r8 r5} - r5c5{n3 n5} - c1n5{r5 .} ==> r1c2≠5
     with z-candidates = n5r2c2 n5r2c1 n5r1c1
singles ==> r1c2=1, r8c1=1
finned-swordfish-in-columns: n2{c1 c5 c9}{r5 r9 r7} ==> r7c7≠2, r9c8≠2, r7c8≠2
stte

[AnotherLife]

Hello, RSW,

Code: Select all

 +-----------------+----------+--------------+
 |*45-1 a15    2   | 7  8  3  | 6   49   459 |
 |j458   568  j468 | 9  1  2  |h35 i34   7   |
 | 3     7     9   | 5  6  4  | 12  12   8   |
 +-----------------+----------+--------------+
 | 6    b25    1   | 4  7  9  | 8   25   3   |
 |c258   4    e38  | 6 d35 18 | 129 7    29  |
 | 9    b358   7   | 2  35 18 | 4   15   6   |
 +-----------------+----------+--------------+
 | 7     2689  468 | 3  24 5  | 29  4689 1   |
 | 124   1236 f346 | 8  9  7  |g35  346  245 |
 | 248   2389  5   | 1  24 6  | 7   3489 249 |
 +-----------------+----------+--------------+


I couldn't find a chain any shorter than this to give a 2 step solution:

(1=5)r1c2 - (5)r46c2 = (5)r5c1 - (5=3)r5c5 - (3)r5c3 = (3)r8c3 - (3=5)r8c7 - (5=3)r2c7 - (3=4)r2c8 - (4)r2c13 = (4)r1c1 => -1r1c1

Eleven's chain leading to the same placements is definitely shorter, and it contains only five strong links:
Extended w-wing 35, SL 3r58c3, 35 r5c5, r8c7
5r1c9 = r2c7 - (5=3)r8c7 - r8c3 = r5c3 - (3=5)r5c5 - r5c1 = r46c2 => -5r1c2

Anyway, I am glad that I have urged you to solve this puzzle by yourself.