The New Sudoku Players' Forum

[hobiwan]

This is the only other 17 with 62 unresolved cells (in the PM) that might take more than one advanced step.

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2.......6.....1.3..5..4.....7...54..3...........6.....6..23....8..9...........1.. #26677

Depends on what qualifies as "advanced":

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Discontinuous Nice Loop [r1c6]-3-[r3c4]=3=[r3c3]=6=[r3c6]-6-[r9c6]=6=[r9c5]=5=[r1c5]=9=[r1c6] => [r1c6]<>3
Singles, Locked Candidates lead to
.------------------.------------------.------------------.
| 2     38    4    | 37    5     9    | 78    1     6    |
| 7     6     9    | 8     2     1    | 5     3     4    |
| 1     5     38   | 37    4     6    | 2     789   789  |
:------------------+------------------+------------------:
| 9     7     6    | 1     8     5    | 4     2     3    |
| 3     18    18   | 4     79    2    | 6     5     79   |
| 5     4     2    | 6     79    3    | 789   789   1    |
:------------------+------------------+------------------:
| 6     19    157  | 2     3     78   | 789   4     5789 |
| 8     2     57   | 9     1     4    | 3     6     57   |
| 4     39    37   | 5     6     78   | 1     789   2    |
'------------------'------------------'------------------'
W-Wing: 7 in [r1c7],[r7c6] connected through 8 in [r37c9] => [r7c7]<>7
Uniqueness Test 3: 5/7 in [r7c39],[r8c39] => [r7c6]<>8
Naked Single: [r7c6]=7
Full House: [r9c6]=8
W-Wing: 7 in [r5c9],[r9c8] connected through 9 in [r3c89] => [r6c8],[r8c9]<>7
Singles

While testing I found this really impressing nice loop, that eliminates 14 candidates in one step, but needs a second loop:
Continuous Nice Loop [r2c2]=6=[r5c2]-6-[r5c7]=6=[r8c7]=3=[r6c7]-3-[r6c6]=3=[r4c4]=1=[r5c4]=4=[r9c4]=5=[r9c5]=6=[r2c5]-6-[r2c2] => [r8c7]<>2, [r6c9]<>3, [r8c7]<>5, [r25c3],[r5c8]<>6, [r59c4],[r8c7],[r9c5]<>7, [r459c4],[r9c5]<>8

[eleven]

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 *--------------------------------------------------------------------------------------*
 | 2        1348     13478    | 3578     5789     3789     | 578      14578    6        |
 | 479      4689     46789    | 578      26       1        | 25789    3        245789   |
 | 179      5       #136789   |#378      4        26       | 2789     12789    12789    |
 |----------------------------+----------------------------+----------------------------|
 | 19       7       *12689    |#138      289      5        | 4       *12689    12389    |
 | 3        124689   124689   | 1478     2789     24789    |*256789   1256789  125789   |
 | 5        12489    12489    | 6        2789    #234789   |#23789    12789    123789   |
 |----------------------------+----------------------------+----------------------------|
 | 6        149      14579    | 2        3        478      | 5789     45789    45789    |
 | 8        234      2-3457   | 9        1        47       |#23567    24567    23457    |
 | 479      2349     23479    | 4578     5678     4678     | 1        2789     234789   |
 *--------------------------------------------------------------------------------------*


A bit easier to see is this first step (including only 2 digits):
The #'s mark 3 strong links for 3, that allow to eliminate 3 in r8c3, because either r3c3 or r8c7 must be 3 (already done in daj95376's grid).
But there is also a kite for 6 in the * cells plus r8c7, either r4c3=6 or r8c7=6.
So we have: Either r3c3=3 or r8c7=3 -> r4c3=6, i.e. r3c3<>6.
It results in the same grid as hobiwan's above, i.e. solvable with 2 w-wings and UR (type 3 or 4).

[hobiwan]

A bit easier to see is this first step (including only 2 digits):
The #'s mark 3 strong links for 3, that allow to eliminate 3 in r8c3, because either r3c3 or r8c7 must be 3 (already done in daj95376's grid).
But there is also a kite for 6 in the * cells plus r8c7, either r4c3=6 or r8c7=6.
So we have: Either r3c3=3 or r8c7=3 -> r4c3=6, i.e. r3c3<>6.
It results in the same grid as hobiwan's above, i.e. solvable with 2 w-wings and UR (type 3 or 4).

Really nice! I like the way how you combine basic patterns that are really chains underneath to complex chains.

I had your pattern as Nice Loop:
[r3c3]=3=[r3c4]-3-[r4c4]=3=[r6c6]-3-[r6c7]=3=[r8c7]=6=[r5c7]-6-[r4c8]=6=[r4c3]-6-[r3c3] => [r3c3]<>6
How long does it take you to find such a pattern?

[hobiwan]

A chain very similar to eleven's is applicable right after the first hidden pair (no fish needed):

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Hidden Single: [r8c5]=1
Hidden Pair: 2,6 in [r2c5],[r3c6] => [r3c6]<>3789 [r2c5]<>5789
.-----------------------------.-----------------------------.----------------------------.
| 2         13489     134789  |  3578     5789      3789    |  5789     145789   6       |
| 479      *4689      46789   |  578      26        1       |  25789    3        245789  |
| 179       5        *136789  | *378      4         26      |  2789     12789    12789   |
:-----------------------------+-----------------------------+----------------------------:
| 19        7         12689   | *138      289       5       |  4        12689    12389   |
| 3        *124689    1245689 |  1478     2789      24789   | *256789   1256789  125789  |
| 1459      12489     124589  |  6        2789     *234789  | *235789   125789   1235789 |
:-----------------------------+-----------------------------+----------------------------:
| 6         149       14579   |  2        3         478     |  5789     45789    45789   |
| 8         234       23457   |  9        1         467     | *23567    24567    23457   |
| 4579      2349      234579  |  4578     5678      4678    |  1        2456789  2345789 |
'-----------------------------'-----------------------------'----------------------------'
Discontinuous Nice Loop [r3c3]=3=[r3c4]-3-[r4c4]=3=[r6c6]-3-[r6c7]=3=[r8c7]=6=[r5c7]-6-[r5c2]=6=[r2c2]-6-[r3c3] => [r3c3]<>6
Singles, W-Wing, UR

[ronk]

Deleted: Incorrect read of eleven's post and fully quoted anyway.

[eleven]

How long does it take you to find such a pattern?

This is very different. I only started to look for them with those harder 17 clue puzzles, because they have only a few bivalue cells and you have to concentrate on strong links. And i think, that in random puzzles such patterns are more rare.
I guess, this one took me less than 10 minutes, with a program, that highlights single numbers, because only 1, 3 and 6 had potential strong links. But i tried other things before without success.
Edit: made it more english (i hope)

[hobiwan]

But there is also a kite for 6 in the * cells plus r8c7, either r4c3=6 or r8c7=6.
So we have: Either r3c3=3 or r8c7=3 -> r4c3=6, i.e. r3c3<>6.

Agree with r3c3<>6, but not with r4c3=6.

I don't think that was meant as a result. I read it as:
r3c3=3 -> r3c3<>6
r3c3<>3 -> r8c7=3 -> r8c7<>6 -> r4c3=6 -> r3c3<>6

[ronk]

I don't think that was meant as a result. I read it as:
r3c3=3 -> r3c3<>6
r3c3<>3 -> r8c7=3 -> r8c7<>6 -> r4c3=6 -> r3c3<>6

You're likely correct.

[daj95376]

Depends on what qualifies as "advanced":

True. For me, advanced doesn't have much of a threshold. My new solver lacks chains for now. My old solver was implemented with networks. Any time a puzzle forces me to manually dig through a list of network results, and I can only find a long or complex chain, then I say the puzzle needs an advanced step. For this puzzle, I used two implication chains. My first chain is the same as eleven's with intermediate assignments.

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[r3c3]=6 [r3c4]=3 [r4c9]=3 [r8c7]=3 [r8c8]=6 [r4c3]=6 [r3c3]<>6
SSTS
[r9c3]=7 [r9c6]=8 [r9c8]=9 [r3c9]=9 [r5c9]=7 [r8c9]=5 [r8c3]=7 [r9c3]<>7
SSTS


[eleven]

But there is also a kite for 6 in the * cells plus r8c7, either r4c3=6 or r8c7=6.
So we have: Either r3c3=3 or r8c7=3 -> r4c3=6, i.e. r3c3<>6.

Agree with r3c3<>6, but not with r4c3=6.

Its a pity, that we dont have a notation, that can be understood by everyone without having to study it (and its hard to find definitions). For mine it might be better to use paranthesis: r3c3=3 or (r8c7=3 -> r4c3=6)

[ronk]

Its a pity, that we dont have a notation, that can be understood by everyone ...

At one time, the de facto standard notation for this forum was the nice loop notation. Despite some differences, that's what hobiwan and I have been using.

[daj95376]

This puzzle can be cracked through several backdoor singles. However, getting to them doesn't appear easy. My solver indicates attacking cell [r5c3] ... of all things!

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....1.6..3......2.7...........7.2....1....8..5..3........2...354.......7.6....... # 2919

 +--------------------------------------------------------------------------------+
 |  289     24589   24589   |  4589    1       345789  |  6       45789   3489    |
 |  3       4589    16      |  45689   45679   456789  |  14579   2       1489    |
 |  7       4589    16      |  45689   2       345689  |  13459   14589   13489   |
 |--------------------------+--------------------------+--------------------------|
 |  689     3489    3489    |  7       45689   2       |  13459   1459    13469   |
 |  269     1       23479   |  4569    4569    4569    |  8       4579    23469   |
 |  5       24789   24789   |  3       4689    1       |  2479    479     2469    |
 |--------------------------+--------------------------+--------------------------|
 |  189     789     789     |  2       4679    4689    |  149     3       5       |
 |  4       23589   23589   |  1589    359     589     |  129     6       7       |
 |  129     6       23579   |  1459    34579   4579    |  1249    1489    12489   |
 +--------------------------------------------------------------------------------+


[hobiwan]

This puzzle can be cracked through several backdoor singles. However, getting to them doesn't appear easy. My solver indicates attacking cell [r5c3] ... of all things!

Continuous Nice Loop -[r1c8]=7=[r1c6]=3=[r1c9]-3-[r5c9]=3=[r5c3]=7=[r5c8]-7-[r1c8]= => [r5c3]<>249, [r1c6]<>4589, [r34c9]<>3, [r6c8]<>7

The rest is too tough for me. I do have some eliminations, but nothing that really advances the puzzle.

[daj95376]

Well, I attacked cell [r5c3] and ended up with a contradiction in [r5] for all of the incorrect candidates.

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[r5c3]=2|4|9 [r5c9]=3 [r1c6]=3 [r1c8]=7                            ~[r5]
[r5c3]=7     [r5c9]=3 [r1c6]=3 [r1c8]=7 [r6c7]=7 [r6c9]=2 [r6c5]=6 ~[r5]
[r5c3]=3     puzzle solves w/Singles


[Pat]

This puzzle can be cracked through several backdoor singles.
However, getting to them doesn't appear easy.
My solver indicates attacking cell r5c3 ... of all things!

# 2919

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....1.6..3......2.7...........7.2....1....8..5..3........2...354.......7.6.......



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289     24589   24589   |  4589    1       345789  |  6       45789   3489
3       4589    16      |  45689   45679   456789  |  14579   2       1489
7       4589    16      |  45689   2       345689  |  13459   14589   13489
------------------------+--------------------------+-----------------------
689     3489    3489    |  7       45689   2       |  13459   1459    13469
269     1       23479   |  4569    4569    4569    |  8       4579    23469
5       24789   24789   |  3       4689    1       |  2479    479     2469
------------------------+--------------------------+-----------------------
189     789     789     |  2       4679    4689    |  149     3       5
4       23589   23589   |  1589    359     589     |  129     6       7
129     6       23579   |  1459    34579   4579    |  1249    1489    12489



Well, I attacked cell r5c3
and ended up with a contradiction in [r5] for all of the incorrect candidates

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[r5c3]=2|4|9 [r5c9]=3 [r1c6]=3 [r1c8]=7                            ~[r5]
[r5c3]=7     [r5c9]=3 [r1c6]=3 [r1c8]=7 [r6c7]=7 [r6c9]=2 [r6c5]=6 ~[r5]
[r5c3]=3     puzzle solves w/Singles



well, once we know where to look---

if r5c9=3
then r1c6=3, r1c8=7, r6c7=7, r6c9=2, r6c5=6,
conflict in r5: {2,6,7} must all fit in just 2 cells r5c13