## Contrary "17" Puzzles

Everything about Sudoku that doesn't fit in one of the other sections

### Re: re: # 2919

Pat wrote: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

Good point and nice solution!

Drat! I keep forgetting to look for conjugate cells. My (old) solver indicated that four of the five candidates in [r5c3] led to a contradiction using Singles in short networks. I just stayed with it and checked each for a usable chain.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

This one looks like fun.

Code: Select all
`....2...18.4......3...........6.8.4..2....7.....3.....6..4...8..7..1.5........... #40423 +--------------------------------------------------------------------------------+ |  579     569     579     |  589     2       34569   |  34689   3569    1       | |  8       1569    4       |  1579    3569    135679  |  369     2       35679   | |  3       1569    2       |  15789   45689   14569   |  4689    5679    45679   | |--------------------------+--------------------------+--------------------------| |  1579    359     13579   |  6       579     8       |  1239    4       2359    | |  459     2       368     |  159     459     1459    |  7       36      368     | |  14579   48      56789   |  3       4579    2       |  169     1569    5689    | |--------------------------+--------------------------+--------------------------| |  6       359     1359    |  4       359     3579    |  1239    8       2379    | |  249     7       389     |  289     1       369     |  5       369     3469    | |  12459   48      13589   |  25789   35689   35679   |  13469   13679   34679   | +--------------------------------------------------------------------------------+`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

daj95376 wrote:This one looks like fun.

Only if you are interested in solutions with 7 Nice Loops (plus 2 Remote Pairs) or as an alternative, 9 ALS moves (that's the best my solver comes up with)
hobiwan
2012 Supporter

Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

daj95376 wrote:This one looks like fun.

Code: Select all
`....2...18.4......3...........6.8.4..2....7.....3.....6..4...8..7..1.5........... #40423`

I'm able to get it down to 6 relatively short forcing chains interspersed with STSS to solve. Not pretty but a bit shorter than hobiwan...

Cheers...

- drac
Draco

Posts: 143
Joined: 14 March 2008

Those last puzzles were a bit too hard for my taste. After long tries i found a solution with 4 chains.
The first eliminated 4 in r8c1:
Either r8c1=2 or (r8c4=2 -> r8c3=8 -> r9c2=4)
Code: Select all
` *-----------------------------------------------------------------------------* | 579     569     579     | 589     2      #34569   | 48     #3569    1       | | 8       1569    4       | 1579    3569    135679  | 369     2       35679   | | 3       1569    2       | 15789   45689   14569   | 48      5679    5679    | |-------------------------+-------------------------+-------------------------| | 1579    359     13579   | 6       579     8       | 1239    4       2359    | | 459     2       368     | 159     459     1459    | 7      *36      368     | | 14579   48      56789   | 3       4579    2       | 169     1569    5689    | |-------------------------+-------------------------+-------------------------| | 6       359     1359    | 4       359     3579    | 1239    8       2379    | | 29      7       389     | 289     1      #369     | 5      #369     4       | | 12459   48      13589   | 25789   35689   35679   | 1369    13679   3679    | *-----------------------------------------------------------------------------*`
Here from r5c8=36 you get:
Either r1c6=3 or r8c6=6, i.e. r1c6<>6 and r8c6<>3. This gives a strong link for 3 in r8.
Code: Select all
` *-----------------------------------------------------------------------------* | 579     569     579     |#589     2      @34-59   |#48     @3569    1       | | 8       1569    4       | 1579    3569    135679  | 369     2       35679   | | 3       1569    2       | 15789   45689   14569   | 48      5679    5679    | |-------------------------+-------------------------+-------------------------| | 1579    359     13579   | 6       579     8       | 1239    4       2359    | | 459     2       368     | 159     459     1459    | 7      -36      368     | | 14579   48      56789   | 3       4579    2       | 169     1569    5689    | |-------------------------+-------------------------+-------------------------| | 6       359     1359    | 4       359     3579    | 1239    8       2379    | | 29      7     #@389     |#289     1       69      | 5      @369     4       | | 12459   48      13589   | 25789   35689   35679   | 1369    1-3679  3679    | *-----------------------------------------------------------------------------*`
Now the kite for 8 and the skyscraper for 3 are connected by a strong link for 4 in r1.
This gives a cycle with eliminations:
r1c6<>59, r59c8<>3, r8c3<>9, r39c4<>8
But still it doesn't solve it.
Code: Select all
` *--------------------------------------------------------------------* | 579    6      579    | 589    2     @34     | 48    @359    1      | | 8      159    4      | 1579   3569   13579  | 369    2      35679  | | 3      159    2      | 1579   45689  1459   | 48     579    5679   | |----------------------+----------------------+----------------------| | 1579   359    1579   | 6      579    8      | 1239   4      2359   | | 459    2      38     | 159    459    1459   | 7      6      38     | | 14579  48     6      | 3      4579   2      | 19     159    589    | |----------------------+----------------------+----------------------| | 6      359    159    | 4      359    3579   | 1239   8      279    | | 29     7     #38     | 289    1      6      | 5     @39     4      | | 12459 #48     159    | 2579 #@3589  *3579   |*1369   179    679    | *--------------------------------------------------------------------*`
r8c8=3 eliminates 3 in both r9c67 -> r9c5=3 -> r9c2=8 -> r8c3=3
eleven

Posts: 1863
Joined: 10 February 2008

eleven wrote:Those last puzzles were a bit too hard for my taste.

Yes, I went too far in my search for puzzles that present a challenge while still being fun. The last couple of puzzles weren't fun. I'll try to rectify this shortcoming in my next posts.

What I did find interesting is that everyone (seems to) look for eliminations and misses/ignores common assignments. On the last puzzle, a forcing chain assignment results in several eliminations and exposes a Hidden Pair for several more eliminations. After that, a couple of long forcing chains help, but I subsequently lost interest.

Code: Select all
`[r9c2]=4              [r8c9]=4[r9c2]=8 [r8c368]=369 [r8c9]=4  c7    -  48    Hidden Pair[r6c2]=4 [r9c2]=8 [r8c4]=8 [r1c7]=8 [r1c6]=4 ...         [r1c8]=3 [r5c8]=6 [r8c8]=9 [r8c3]=3 [r5c3]=8 => [r5c9]<>6 [r6c3]<>8[r6c2]=8 [r5c9]=8                                     => [r5c9]<>6 [r6c3]<>8[r3c7]=4 [r1c6]=4 [r1c8]=3 [r5c8]=6 [r8c8]=9 ...         [r8c1]=2 [r8c4]=8 [r8c3]=3 [r5c3]=8 => [r3c4]<>8 [r9c34]<>8[r3c7]=8 [r1c4]=8 [r9c5]=8                   => [r3c4]<>8 [r9c34]<>8`

Yes, carrying the forcing chain assignments one step further would result in common eliminations, but where's the fun in that?
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

daj95376 wrote:Yes, I went too far in my search for puzzles that present a challenge while still being fun. The last couple of puzzles weren't fun. I'll try to rectify this shortcoming in my next posts.

Don't be too hard on yourself, after all it's you who does most of the work by choosing the puzzles for us to have fun. I think a big Thank You is in order (and I am looking forward to whatever you will throw at us)
hobiwan
2012 Supporter

Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

Thanks hobiwan for the kind words. I do what I can with what I currently have at hand.

I decided to skip these three 17/61s because they seemed to lack the fun aspect. You may have a different opinion.

Code: Select all
`....3...2..6...5...1.4...........16.....8..4.2.....3.....7.6...3.......5...1..... # 3661....3...26.....5...1.7.........524...74...........1......8...1.2.3......5........ #40762....3...26.....5...1.4.........527...74...........1......8...1.2.3......5........ #40763`

This one looks complicated, but it has an Achilles Heel that shouldn't be too difficult to find.

Code: Select all
`...2.7..4.3.5.....6.....9..15..4.....2.....7.......3..8...6.......7...5.......... # 7910 *--------------------------------------------------------------------------------------* | 59       189      189      | 2        1389     7        | 1568     1368     4        | | 2479     3        12489    | 5        189      6        | 1278     128      1278     | | 6        178      1258     | 1348     138      1348     | 9        1238     123578   | |----------------------------+----------------------------+----------------------------| | 1        5        7        | 3689     4        2389     | 268      2689     2689     | | 349      2        34689    | 1689     158      189      | 14568    7        1689     | | 49       4689     4689     | 1689     7        12589    | 3        124689   125689   | |----------------------------+----------------------------+----------------------------| | 8        1479     123459   | 1349     6        13459    | 1247     12349    12379    | | 2349     1469     123469   | 7        1238     13489    | 12468    5        123689   | | 234579   14679    123469   | 13489    12358    13489    | 124678   1234689  123689   | *--------------------------------------------------------------------------------------*`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

#7910:

I am not down to one move, but I have two Nice Loops, that together eliminate 17 candidates:

Continuous Nice Loop [r1c1]-9-[r6c1]-4-[r6c8]=4=[r5c7]=5=[r1c7]-5-[r1c1] => [r5c7]<>168, [r6c23]<>4, [r2589c1]<>9
Locked Candidates Type 2 (Claiming): 4 in c2 => [r789c3],[r89c1]<>4
Continuous Nice Loop [r5c1]-3-[r8c1]-2-[r8c5]=2=[r9c5]=5=[r5c5]-5-[r5c7]-4-[r5c1] => [r9c5]<>1, [r8c379]<>2, [r9c15]<>3, [r5c3]<>4, [r9c5]<>8

After that another chain solves the puzzle:
Discontinuous Nice Loop [r7c3]=5=[r3c3]=2=[r2c1]=7=[r9c1]=5=[r7c3] => [r7c3]<>1, [r7c3]<>2, [r7c3]<>3, [r7c3]<>9
hobiwan
2012 Supporter

Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

daj95376 wrote:This one looks complicated, but it has an Achilles Heel that shouldn't be too difficult to find.
This solves it:
r3c9=7 -> r3c3=5 -> r1c1=9 -> r1c23=18 -> r3c2=7
eleven

Posts: 1863
Joined: 10 February 2008

With the right (wrong?) selection in [c1], a subset count contradiction results in [b1]:

Code: Select all
`[r1c1]=9 [r6c1]=4 [r5c1]=3 [r8c1]=2 [r23c3]=245; => [r1c1]<>9`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

daj95376 wrote:I decided to skip these three 17/61s because they seemed to lack the fun aspect. You may have a different opinion.

Code: Select all
`....3...2..6...5...1.4...........16.....8..4.2.....3.....7.6...3.......5...1..... # 3661....3...26.....5...1.7.........524...74...........1......8...1.2.3......5........ #40762....3...26.....5...1.4.........527...74...........1......8...1.2.3......5........ #40763`
At least its interesting, that they can be solved with the same trick:
Take a skyscraper and look, what you can do with the pincers.
Code: Select all
` *---------------------------------------------------------------------* | 45789   45789    45789   | 5689  3      15789  | 46789  1789   2    | |*4789    23       6       | 289   1279   12789  | 5      13789 #134  | | 5789    1        23      | 4     2679   25789  | 6789   3789   36   | |--------------------------+---------------------+--------------------| | 45789   345789   345789  | 2359  2479   24579  | 1      6      789  | |#15679   35679    13579   | 3569  8      1579   | 2      4      79   | | 2       46789    14789   | 69    14679  1479   | 3      5      789  | |--------------------------+---------------------+--------------------| |#14589   24589    124589  | 7     2459   6      | 489    12389 #134  | | 3       24679    12479   | 289   249    2489   | 4679   1279   5    | |*456789  2456789  245789  | 1     2459   3      | 46789  2789  *46   | *---------------------------------------------------------------------*`
Skysrcaper for 1, either r2c9=1 or r5c1=1.
r2c9=1 -> r2c1=4
r5c1=1 -> r9c1=6 -> r9c9=4
i.e. r2c9<>4, r9c1<>4

Second puzzle:
Code: Select all
` *--------------------------------------------------------------------* | 4789  459   5789  |#1569  3      45689  |*16789   46789    2       | | 6     2349  2789  | 129   12489  489    | 5       34789    134789  | | 3489  1     2589  | 7     24689  45689  | 3689    34689    34689   | |-------------------+---------------------+--------------------------| | 1389  369   689   | 39    5      2      | 4       3789     13789   | | 139   7     4     | 369   689    3689   |*1239   #2359     1359    | | 389   25    25    | 4     7      1      | 3689    3689     3689    | |-------------------+---------------------+--------------------------| | 479   469   679   | 8     2469   34569  | 2369    1        34569   | | 2     4689  3     |#1569  1469   45679  | 6789   #456789   456789  | | 5     4689  1     | 2369  2469   34679  | 236789  2346789  346789  | *--------------------------------------------------------------------*`
Skysrcaper for 5, either r1c4=5 or r5c8=5.
r1c4=5 -> r1c7=1
r5c8=5 -> r5c7=2
i.e. r5c7<>1
Code: Select all
` *------------------------------------------------------------------* | 4789  459   5789  | 569   3      45689  | 1       46789   2      | | 6     2349  2789  |#129   12489  489    | 5       34789   34789  | | 3489  1     2589  | 7     24689  45689  | 3689    34689   34689  | |-------------------+---------------------+------------------------| | 1389  369   689   | 39    5      2      | 4       3789    13789  | | 139   7     4     | 369   689    3689   | 239    #2359    1359   | | 389   25    25    | 4     7      1      | 3689    3689    3689   | |-------------------+---------------------+------------------------| | 479   469   679   | 8     2469   34569  | 2369    1       34569  | | 2     4689  3     |*1569  1469   45679  | 6789   *45689   45689  | | 5     4689  1     |#2369  2469   34679  | 236789 #234689  34689  | *------------------------------------------------------------------*`
Skysrcaper for 2, either r2c4=2 or r5c8=2.
r2c4=2 -> r8c4=1
r5c8=2 -> r8c8=5
i.e. r8c4<>5

The third puzzle solves exactly the same way (only differs in 2 4-7 changes).
eleven

Posts: 1863
Joined: 10 February 2008

I could not get this one to cooperate. However, it should give hobiwan some forcing chains to investigate.

Code: Select all
`.4..1..........5.6......3..5.38.....7......2..........6..5.7....2.....1....3..4.. #39462+--------------------------------------------------------------------------------------+|  389      4        56789   |  679      1        35689   |  2789     789      2789    ||  12389    13789    12789   |  2479     34789    3489    |  5        4789     6       ||  289      56789    256789  |  24679    456789   45689   |  3        4789     1       ||----------------------------+----------------------------+----------------------------||  5        169      3       |  8        4679     2       |  1679     679      479     ||  7        1689     14689   |  1469     34569    34569   |  1689     2        34589   ||  12489    1689     124689  |  14679    35679    469     |  16789    356789   35789   ||----------------------------+----------------------------+----------------------------||  6        1389     1489    |  5        2489     7       |  289      389      2389    ||  3489     2        45789   |  469      4689     4689    |  6789     1        35789   ||  89       5789     5789    |  3        2689     1       |  4        56789    25789   |+--------------------------------------------------------------------------------------+`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

daj95376 wrote:I could not get this one to cooperate. However, it should give hobiwan some forcing chains to investigate.

Code: Select all
`.4..1..........5.6......3..5.38.....7......2..........6..5.7....2.....1....3..4.. #39462`

That was a mouthful; from your PM's my solver needed 7 (fairly short) FC's for STSS to solve; the last one is really a Forcing Net but still a simple one. I'd be happy to transcribe 'em if you want to see the list -- well perhaps happy is the wrong word... ;) but certainly willing.

Cheers...

- drac
Draco

Posts: 143
Joined: 14 March 2008

#39462:
It is funny how much the difficulty of a sudoku depends on the techniques used (and their order). This is one my solver had no problems with (even without Forcing Chains). A possible solution:

Code: Select all
`Continuous Nice Loop [r1c1]=3=[r1c6]=5=[r1c3]-5-[r8c3]=5=[r8c9]=3=[r8c1]-3-[r1c1] => [r2c1]<>3, [r39c3]<>5, [r1c6]<>689, [r8c9]<>789Discontinuous Nice Loop [r8c9]-3-[r7c8]=3=[r6c8]=5=[r9c8]=6=[r8c7]=7=[r8c3]=5=[r8c9] => [r8c9]<>3Singles (plus 1 Finned Jellyfish)`

But you are right, lots of Forcing Chains!
hobiwan
2012 Supporter

Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

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