The New Sudoku Players' Forum

[mith]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . 3 . |
| . . . | 1 . . | . . 4 |
| 1 5 . | 9 . 2 | . . . |
+-------+-------+-------+
| . 6 . | . . . | . 5 3 |
| 5 . 8 | . . . | 9 . 7 |
| 9 3 . | . . . | . 2 . |
+-------+-------+-------+
| . . . | 3 . 8 | . 4 6 |
| 2 . . | . . 6 | . . . |
| . 4 . | . . . | . . . |
+-------+-------+-------+
.......3....1....415.9.2....6.....535.8...9.793.....2....3.8.462....6....4.......

[denis_berthier]

Code: Select all

Resolution state after Singles:
   68        2789      2469      45678     45678     47        1         3         25       
   368       278       236       1         35678     37        25        9         4         
   1         5         34        9         34        2         6         7         8         
   4         6         12        27        1279      179       8         5         3         
   5         12        8         24        1234      134       9         6         7         
   9         3         7         68        68        5         4         2         1         
   7         19        159       3         1259      8         25        4         6         
   2         189       1359      457       14579     6         357       18        59       
   368       4         13569     257       12579     179       2357      18        259
146 candidates, 622 csp-links and 622 links. Density = 5.88%

There's an easy solution in BC4:

easy solution in BC4: Show

naked-pairs-in-a-column: c7{r2 r7}{n2 n5} ==> r9c7 ≠ 5, r9c7 ≠ 2, r8c7 ≠ 5
hidden-pairs-in-a-column: c4{n6 n8}{r1 r6} ==> r1c4 ≠ 7, r1c4 ≠ 5, r1c4 ≠ 4
whip[1]: c4n5{r9 .} ==> r7c5 ≠ 5, r8c5 ≠ 5, r9c5 ≠ 5
naked-pairs-in-a-row: r1{c1 c4}{n6 n8} ==> r1c5 ≠ 8, r1c5 ≠ 6, r1c3 ≠ 6, r1c2 ≠ 8
hidden-pairs-in-a-block: b2{n6 n8}{r1c4 r2c5} ==> r2c5 ≠ 7, r2c5 ≠ 5, r2c5 ≠ 3
singles ==> r1c5 = 5, r1c9 = 2, r2c7 = 5, r7c7 = 2, r7c3 = 5
whip[1]: b2n7{r2c6 .} ==> r4c6 ≠ 7, r9c6 ≠ 7
naked-pairs-in-a-block: b8{r7c5 r9c6}{n1 n9} ==> r9c5 ≠ 9, r9c5 ≠ 1, r8c5 ≠ 9, r8c5 ≠ 1
naked-pairs-in-a-column: c6{r4 r9}{n1 n9} ==> r5c6 ≠ 1
x-wing-in-rows: n1{r5 r7}{c2 c5} ==> r8c2 ≠ 1, r4c5 ≠ 1
biv-chain-rc[3]: r7c2{n1 n9} - r8c2{n9 n8} - r8c8{n8 n1} ==> r8c3 ≠ 1
singles ==> r8c8 = 1, r9c8 = 8, r8c2 = 8
naked-triplets-in-a-column: c3{r1 r3 r8}{n9 n4 n3} ==> r9c3 ≠ 9, r9c3 ≠ 3, r2c3 ≠ 3
biv-chain-rc[4]: r5c4{n2 n4} - r5c6{n4 n3} - r2c6{n3 n7} - r2c2{n7 n2} ==> r5c2 ≠ 2
stte

but I guess you want us to apply (e.g. to digits 368, block b6 and column c1) a trick based on uniqueness as in your EndorFin puzzle.

[Cenoman]

Two steps (my preference):

Code: Select all

 +---------------------+--------------------+-----------------+
 |  68*   79    49     |  68*   5      47   |  1    3    2    |
 |  68+3* 278   236    |  1     68*    37   |  5    9    4    |
 |  1     5     34     |  9     34     2    |  6    7    8    |
 +---------------------+--------------------+-----------------+
 |  4     6     12     |  27    1279   19   |  8    5    3    |
 |  5     12    8      |  24    1234   34   |  9    6    7    |
 |  9     3     7      |  68*   68*    5    |  4    2    1    |
 +---------------------+--------------------+-----------------+
 |  7    a19    5      |  3     19     8    |  2    4    6    |
 |  2    b189   39-1   |  457   47     6    |  37  b18   59   |
 |  368   4     1369   |  257   27     19   |  37   18   59   |
 +---------------------+--------------------+-----------------+

1. DP(68)r12c1, b2p15, r6c45 (BUG-lite), having a single internal => +3 r2c1
2. XYZ-wing (1=9)r7c2 - (9=81)r8c28 => -1 r8c3; ste

...or one step:

Hidden Text: Show

Code: Select all

 +---------------------+--------------------+-----------------+
 |  68   a79    49     |  68    5     a47   |  1    3    2    |
 |  368   278   236    |  1     68     37   |  5    9    4    |
 |  1     5     34     |  9     34     2    |  6    7    8    |
 +---------------------+--------------------+-----------------+
 |  4     6     2-1    |  27    1279  D19   |  8    5    3    |
 |  5    c12    8      | c24    1234  b34   |  9    6    7    |
 |  9     3     7      |  68    68     5    |  4    2    1    |
 +---------------------+--------------------+-----------------+
 |  7    A19    5      |  3    B19     8    |  2    4    6    |
 |  2    y189  z139    |  457   47     6    |  37  y18   59   |
 |  368   4     1369   |  257   27    C19   |  37   18   59   |
 +---------------------+--------------------+-----------------+

Kraken column (9)r178c2
(9-74)r1c26 = r5c6 - (4=21)r5c24
(9-1)r7c2 = r7c5 - r9c6 = (1)r4c6
(9-81)r8c28 = (1)r8c3
=> -1 r4c3; ste

[jco]

Hello,

After basics

Code: Select all

 1     2     3       4    5      6    7    8   9
.------------------+-----------------+-------------.
| 68    79    49   |  68   5      47 | 1    3   2  | 1
| 368 Aa278   236  |  1    68    B37 | 5    9   4  | 2
| 1     5     34   |  9    34     2  | 6    7   8  | 3
|------------------+-----------------+-------------|
| 4     6    e12   |  27   1279  e19 | 8    5   3  | 4
| 5     1-2   8    | C24   1234  C34 | 9    6   7  | 5
| 9     3     7    |  68   68     5  | 4    2   1  | 6
|------------------+-----------------+-------------|
| 7     19    5    |  3    19     8  | 2    4   6  | 7
| 2    b189   139  |  457  47     6  | 37  c18  59 | 8
| 368   4     1369 |  257  27    d19 | 37  d18  59 | 9
'------------------+-----------------+-------------'

Kraken Cell (278)r2c2 => -2 r5c2; ste
(2)r2c2
(7)r2c2-(7=3)r2c6-(3=42)r5c46
(8)r2c2-r8c2=r8c8-(8=19)r9c68-(9=12)r4c36

Two steps with coloring:

Hidden Text: Show

Code: Select all

  1    2      3      4    5      6    7   8   9
.------------------+----------------+------------.
| 68  "7'9   '4"9  | 68   5     "4'7| 1   3   2  | 1
| 368 `2'78 ``236  | 1    68    '3"7| 5   9   4  | 2
| 1    5     '3"4  | 9   "3'4    2  | 6   7   8  | 3
|------------------+----------------+------------|
| 4    6    ``1`2  | 27   1279   19 | 8   5   3  | 4
| 5   `1``2   8    | 24 ``12'34 "3'4| 9   6   7  | 5
| 9    3      7    | 68   68     5  | 4   2   1  | 6
|------------------+----------------+------------|
| 7    19     5    | 3    19     8  | 2   4   6  | 7
| 2    189    139  | 457  47     6  | 37  18  59 | 8
| 368  4      1369 | 257  27     19 | 37  18  59 | 9
'------------------+----------------+------------'

(',") and (`,``) are two pairs of opposite colors.
Due to cell b8, ` and ' cannot be both true colors,
so `` or " must be true. Since ('3)r5c5 sees (``2)r5c5
and ("3)r5c6, it must be false, so all '-colored digits
are false (all "-colored digits are true). This gives
7 placements. In terms of an AIC:

(1)r5c5=(1-2)r5c2=(2-7)r2c2=(7-3)r2c6=(3)r5c6 => -3 r5c5

Code: Select all

  1    2      3      4     5      6     7   8     9
.------------------+------------------+---------------.
| 68   7      9    | 68    5      4   | 1   3     2   | 1
| 368 '2"8   "236  | 1     68     7   | 5   9     4   | 2
| 1    5      4    | 9     3      2   | 6   7     8   | 3
|------------------+------------------+---------------|
| 4    6     "1'2  | 27    1279  `1``9| 8   5     3   | 4
| 5   '1"2    8    | 24   "124    3   | 9   6     7   | 5
| 9    3      7    | 68    68     5   | 4   2     1   | 6
|------------------+------------------+---------------|
| 7    19     5    | 3     19     8   | 2   4     6   | 7
| 2    1'89   13   | 4`57  47     6   | 37 '1"8 ``5`9 | 8
| 36"8 4      136  | 2``57 27   ``1`9 | 37 "1'8  `5``9| 9
'------------------+------------------+---------------'

Again, (',") and (`,``) are two pairs of opposite colors.
Due to row 9, (``1)r9c6 and ("1)r9c8, `` and " cannot
be both true colors, so ` or ' must be true. Since ("1)r4c3
sees ('2)r4c3 and (`1)r4c6, it must be false, and so all
"-colored digits are false (all '-colored digits are true).
In terms of an AIC:

(1)r4c6=r9c6-(1=8)r9c8-r9c1=r8c2-(8=2)r2c2-r2c3=(2)r4c3 => -1 r4c3; ste

Regards,
jco

Edit: added solution with coloring in two steps.

[mith]

but I guess you want us to apply (e.g. to digits 368, block b6 and column c1) a trick based on uniqueness as in your EndorFin puzzle.

Denis, maybe I'm reading too much into this, but my posting a puzzle relying on uniqueness* in no way implies that I want you to use uniqueness on another puzzle. If you're not happy with the trick in Endor Fins, that's fine; there's no reason to make little jabs like this in other threads. I post a wide variety of puzzles, and not everyone is going to like every puzzle I post. ~shrug~ (FWIW, though, when I posted this elsewhere I explicitly challenged people to find a solution without uniqueness. But some people here have no issue using uniqueness, and I have no problem with people finding such solutions. The real treat in this puzzle for a manual solver, IMO, is the number of naked singles needed, thus the title.)

It's entirely possible you didn't mean this in a negative way, and I'm just being overly sensitive, so apologies in advance if that is the case.

*which I do not believe is the case in the Endor Fins puzzles, see that thread; I have certainly posted uniqueness puzzles in the past though, such as Thunderstorm.

[denis_berthier]

but I guess you want us to apply (e.g. to digits 368, block b6 and column c1) a trick based on uniqueness as in your EndorFin puzzle.

Denis, maybe I'm reading too much into this,

Nothing to add. My guess must have been wrong.