## Contrary "17" Puzzles

Everything about Sudoku that doesn't fit in one of the other sections
daj95376 wrote: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]<>3Singles, 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]<>7Uniqueness Test 3: 5/7 in [r7c39],[r8c39] => [r7c6]<>8Naked Single: [r7c6]=7Full House: [r9c6]=8W-Wing: 7 in [r5c9],[r9c8] connected through 9 in [r3c89] => [r6c8],[r8c9]<>7Singles`

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
hobiwan
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Location: Klagenfurt

Code: Select all
` *--------------------------------------------------------------------------------------* | 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).
eleven

Posts: 1899
Joined: 10 February 2008

eleven wrote: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.

[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
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Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

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]=1Hidden 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]<>6Singles, W-Wing, UR`
hobiwan
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Location: Klagenfurt

Deleted: Incorrect read of eleven's post and fully quoted anyway.
Last edited by ronk on Sun Apr 06, 2008 11:45 am, edited 1 time in total.
ronk
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hobiwan wrote: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)
Last edited by eleven on Sat Apr 05, 2008 9:17 pm, edited 1 time in total.
eleven

Posts: 1899
Joined: 10 February 2008

ronk wrote:
eleven wrote: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
hobiwan
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Location: Klagenfurt

hobiwan wrote: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.
ronk
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Location: Southeastern USA

hobiwan wrote: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]<>6SSTS[r9c3]=7 [r9c6]=8 [r9c8]=9 [r3c9]=9 [r5c9]=7 [r8c9]=5 [r8c3]=7 [r9c3]<>7SSTS`
daj95376
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ronk wrote:
eleven wrote: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)
eleven

Posts: 1899
Joined: 10 February 2008

eleven wrote: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.
ronk
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Location: Southeastern USA

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!

Code: Select all
`....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   | +--------------------------------------------------------------------------------+`
daj95376
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daj95376 wrote: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.
hobiwan
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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`
daj95376
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### re: # 2919

daj95376 wrote: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
Code: Select all
`....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

Pat

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