The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |5..|63.|..9|
 |..7|...|.5.|
 |8..|2..|1..|
 |---+---+---|
 |.2.|8..|...|
 |.7.|...|..6|
 |..6|..7|4.8|
 |---+---+---|
 |6..|9..|.7.|
 |.3.|.28|...|
 |..9|...|3.1|
 *-----------*


Play/Print this puzzle online

[SCLT]

Code: Select all

+---------------------+----------------+--------------+
|  5     a14*  2      |  6   3   a14*  |  7   8   9   |
|  134    6    7      |  14  8    9    |  2   5   34  |
|  8      9    34     |  2   7    5    |  1   6   34  |
+---------------------+----------------+--------------+
| a1349*  2   a1345*  |  8   6   a14*  |  59 b13  7   |
|  1349   7    8      | d35  149  2    |  59 c13  6   |
|  139   f5-1  6      | e35  19   7    |  4   2   8   |
+---------------------+----------------+--------------+
|  6      145  145    |  9   14   3    |  8   7   2   |
|  7      3    14     |  14  2    8    |  6   9   5   |
|  2      8    9      |  7   5    6    |  3   4   1   |
+---------------------+----------------+--------------+


Almost Sashimi Finned X-Wing (Grouped Skyscraper??):

[1* r1c2 = r1c6 - r4c6 = r4c13] = 1r4c8 - (1=3)r5c8 - (3=5)r5c4 - r6c4 = r6c2

-1r6c2; stte

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 5    b14    2     | 6     3    c14    | 7     8     9     |
 | 134   6     7     | 14    8     9     | 2     5     34    |
 | 8     9     34    | 2     7     5     | 1     6     34    |
 *-------------------+-------------------+-------------------|
 | 1349  2     1345  | 8     6    d14    | 59    13    7     |
 | 1349  7     8     |e35   e149   2     | 59   e13    6     |
 | 139 ac15    6     | 3-5  d19    7     | 4     2     8     |
 *-------------------+-------------------+-------------------|
 | 6    b145   145   | 9     14    3     | 8     7     2     |
 | 7     3     14    | 14    2     8     | 6     9     5     |
 | 2     8     9     | 7     5     6     | 3     4     1     |
 *-----------------------------------------------------------*


(5=1)r6c2 - 1r17c2 = 1r1c6&r6c2 - 1r4c6,r6c5 = (135)r5c458 => -5 r6c4 ; stte

[Ngisa]

Code: Select all

+----------------------+------------------+----------------+
| 5       g14     2    | 6     3      g14 | 7     8     9  |
| 134      6      7    | 14    8       9  | 2     5     34 |
| 8        9      34   | 2     7       5  | 1     6     34 |
+----------------------+------------------+----------------+
| 1349     2     a134-5| 8     6      f14 |b59*   13    7  |
|d1349     7      8    | 35  ec149     2  |c59    13    6  |
| 139    hb15     6    | 35   b19*     7  | 4     2     8  |
+----------------------+------------------+----------------+
| 6        145    145  | 9     14      3  | 8     7     2  |
| 7        3      14   | 14    2       8  | 6     9     5  |
| 2        8      9    | 7     5       6  | 3     4     1  |
+----------------------+------------------+----------------+


(5)r4c3 - (5=9*)r4c7&(5=19*)r6c25 - (9)r5c57 = (9-4)r5c1 = r5c5 - r4c6 = (41)r1c26 - (1=5)r6c2 =>
- 5r4c3; stte

Clement

[Cenoman]

After SCLT's nice solution, a foolish one:

Code: Select all

 +-----------------------------+--------------------+-----------------+
 |     5       Y14      2      |  6      3    X14   |  7    8    9    |
 |    a13+4     6       7      |  14     8     9    |  2    5    34   |
 |     8        9       34     |  2      7     5    |  1    6    34   |
 +-----------------------------+--------------------+-----------------+
 |  mAb49+13    2     Aa35+14  |  8      6    W14   |  59   13   7    |
 |  Mmb14+39    7       8      | x35  VwN49+1  2    |  59  x13   6    |
 |  nAb39+1 znBb15      6      | y35    n19    7    |  4    2    8    |
 +-----------------------------+--------------------+-----------------+
 |     6     ZPA4+1-5  T15+4   |  9    UO14    3    |  8    7    2    |
 |     7        3       14     |  14     2     8    |  6    9    5    |
 |     2        8       9      |  7      5     6    |  3    4    1    |
 +-----------------------------+--------------------+-----------------+

BUG+11

Code: Select all

(4)r2c1|r4c3 - (4=1395)b4p1478                          (a,b)
(1)b4p137|r7c2 - (1=5)r6c2                              (A,B)
(3)r45c1 - (3=195)r6c125                                (m,n)
(9-4)r5c1 = r5c5 - r7c5 = (4)r7c2                       (M,N,O,P)
(1)r5c5 - (1=35)r5c48 - r6c4 = (5)r6c2                  (w,x,y,z)
(4)r7c3 - r7c5 = r5c5 - r4c6 = r1c6 - r1c2 = (4)r7c2    (T,U,V,W,X,Y,Z)

=> -5 r7c2; ste

[Sudtyro2]

Code: Select all

+---------------------+---------------+-------------+
|    5     D14   2    |  6    3   C14 |  7   8   9  |
|    134    6    7    |  14   8    9  |  2   5   34 |
|    8      9    34   |  2    7    5  |  1   6   34 |
+---------------------+---------------+-------------+
| wAa1349   2   c1345 |  8    6   B14 | b59  13  7  |
|    1349   7    8    |  35   149  2  |  59  13  6  |
|   x139  zd5-1  6    | y35   19   7  |  4   2   8  |
+---------------------+---------------+-------------+
|    6      145  145  |  9    14   3  |  8   7   2  |
|    7      3    14   |  14   2    8  |  6   9   5  |
|    2      8    9    |  7    5    6  |  3   4   1  |
+---------------------+---------------+-------------+

Kraken cell (1349)r4c1 => -1 r6c2; stte

Code: Select all

9r4c1 - (9=5)r4c7 - r4c3 = 5r6c2 - 1r6c2; abcd
4r4c1 - (4=1)r4c6 - r1c6 = 1r1c2 - 1r6c2; ABCD
3r4c1 - r6c1 = (3-5)r6c4 = 5r6c2 - 1r6c2; wxyz
1r4c1                            - 1r6c2;


From some p&p multi-coloring...not very elegant.

SteveC

[SpAce]

original: Show

Code: Select all

.----------------------------.--------------------.--------------.
|   5       d14      2       | 6     3      e1(4) | 7    8    9  |
|  c134      6       7       | 14    8       9    | 2    5    34 |
|   8        9      c34      | 2     7       5    | 1    6    34 |
:----------------------------+--------------------+--------------:
| ab39+1[4]  2     ab15+3[4] | 8     6       1-4  | 59+  13+  7  |
|   1349     7       8       | 35+  a19[+4]  2    | 59+  13+  6  |
|  b39+1     15+     6       | 35+   19+     7    | 4    2    8  |
:----------------------------+--------------------+--------------:
|   6        15+4    15+4    | 9    a4[#1]   3    | 8    7    2  |
|   7        3       14      | 14    2       8    | 6    9    5  |
|   2        8       9       | 7     5       6    | 3    4    1  |
'----------------------------'--------------------'--------------'

DP(1359)b4567+8 (no solution) using mixed +internals/#external

(4)r4c13|(4,1)r57c5 == (1)r46c1|(3)r4c3 - (13=4)b1p49 - r1c2 = (4)r1c6 => -4 r4c6; stte

Code: Select all

.-----------------------.------------------------.------------------.
|  5       d14     2    | 6       3        d1(4) | 7      8      9  |
| c134      6      7    | 14      8         9    | 2      5      34 |
|  8        9      34   | 2       7         5    | 1      6      34 |
:-----------------------+------------------------+------------------:
|  1349     2      1345 | 8       6         1-4  | 59     13     7  |
|  1349     7      8    | 3'5"+  a1"9'[+4]  2    | 5'9"+  1'3"+  6  |
| b3'9"+1   1"5'+  6    | 3"5'+   1'9"+     7    | 4      2      8  |
:-----------------------+------------------------+------------------:
|  6        145    145  | 9       14        3    | 8      7      2  |
|  7        3      14   | 14      2         8    | 6      9      5  |
|  2        8      9    | 7       5         6    | 3      4      1  |
'-----------------------'------------------------'------------------'

IQ(1359+2)r56 using internals (IQ: "incompatible quads"; a no-solution-DP)

(4)r5c5 == (1)r6c1 - r2c1 = (1,4)r1c26 => -4 r4c6; stte

[eleven]

Code: Select all

 *-----------------------------------------------------------*
 |  5      14    2      |  6    3     14   |  7    8    9    |
 |  134    6     7      |  14   8     9    |  2    5    34   |
 |  8      9     34     |  2    7     5    |  1    6    34   |
 |----------------------+------------------+-----------------|
 |  1349   2     1345   |  8    6     14   |  59   13   7    |
 |  1349   7     8      |  35   19+4  2    |  59   13   6    |
 |  139    15    6      |  35   19    7    |  4    2    8    |
 |----------------------+------------------+-----------------|
 |  6      145   145    |  9    14    3    |  8    7    2    |
 |  7      3     14     |  14   2     8    |  6    9    5    |
 |  2      8     9      |  7    5     6    |  3    4    1    |
 *-----------------------------------------------------------*

DP all cells (no solution) => r5c5=4, stte

I mean, you should show, why your pattern does not have a solution.

[SpAce]

DP all cells (no solution) => r5c5=4, stte

Touché. Not quite comparable, though.

I mean, you should show, why your pattern does not have a solution.

It's all bivalue/bilocation stuff so Medusa coloring does the job quickly and easily. Much easier to understand and verify manually than some MUGs, don't you think? In fact, I don't think we even need box 7:

Code: Select all

:-------------------------+-----------------+-----------------:
| 3'9"            1"5'    |                 | 5"9'  1'3"      |
|                         | 3"5'   1"9'     | 5'9"  1"3'      |
| 3"9'     1'5"           | 3'5"   1'9"     |                 |
:-------------------------+-----------------+-----------------:


As far as I see, both parities produce contradictions (e.g. two 5's in row 5, and two 5"s in row 6). Thus no solution, right? (I wonder if some generalized pattern could be extracted from that. Here we have the same naked quad, formed of bivalue cells, in all three lines and boxes of a chute, and every box has two pairs from the same set of digits. All possible pairings of the four digits exist in the pattern.)

Skipping box 7 would simplify the chain too, using just internals:

(4)r4c13,r5c5 == (1,3)r46c1,r4c3 - (13=4)b1p29 - r1c2 = (4)r1c6 => -4 r4c6; stte

Added. Seems that we need only two rows for the "incompatible-quads" DP, as long as one box contains two pairs and all six pairings exist:

Code: Select all

:-----------------+-----------------+-----------------:
| a'b"      c"d'  |                 | a"c'      b'd"  |
|                 |                 |                 |
| a"b'      c'd"  |  a'd"      b"c' |                 |
:-----------------+-----------------+-----------------:


It shouldn't even matter where the non-paired bivalues are located in their rows (I just drew them in different boxes for clarity). Is this a known pattern? Can it be further generalized? Is it any useful?

[eleven]

Much easier to understand and verify manually than some MUGs, don't you think?

To prove yes, to spot no.

[SpAce]

Much easier to understand and verify manually than some MUGs, don't you think?

To prove yes, to spot no.

I disagree on my part. I did spot this one, after all! As you know, some of the MUGs I've "spotted" have been invalid, so I'm not very comfortable with them at all.

What do you think of the simplified two-row pattern (added to the previous post)? If that logic is accepted, then we could simply use the two-row DP in r56 and get a pretty nice solution:

Code: Select all

:---------------------+-----------------+-----------------:
|                     |                 |                 |
|                     | 3'5"   1"9'+4   | 5'9"  1'3"      |
| 3'9"+1   1"5'       | 3"5'   1'9"     |                 |
:---------------------+-----------------+-----------------:

IQ(1359+2)r56 using internals:

(4)r5c5 == (1)r6c1 - r2c1 = (1,4)r1c26 => -4 r4c6; stte

If that pattern works out as I think, it should be very easy to spot! Don't you agree?

In this case we have two other instances of that pattern in the same chute:

Code: Select all

:-------------------------+-----------------+-----------------:
| 3'9"+14         1"5'+34 |                 | 5"9'  1'3"      |
|                         | 3"5'   1'9"+4   | 5'9"  1"3'      |
|                         |                 |                 |
:-------------------------+-----------------+-----------------:


(1|4)r4c1 == (3|4)r4c3 == (4)r5c5

Code: Select all

:-------------------------+-----------------+-----------------:
| 3'9"+14         1"5'+34 |                 | 5"9'  1'3"      |
|                         |                 |                 |
| 3"9'+1   1'5"           | 3'5"   1"9'     |                 |
:-------------------------+-----------------+-----------------:


(1|4)r4c1 == (3|4)r4c3 == (1)r6c1

Obviously they just don't produce as neat solutions as the first one (as demonstrated by my original solution which used all of those guardians at once).

Is this a new technique perhaps? Either way, I think it could be quite useful (though I have no idea how often the pattern exists). The key feature is those two pairs in a box, which should be easy to spot. They don't even have to be aligned (as evidenced by the 15-pair in box 4), just in the same lines chute-wise. Then it's just a matter of completing the incompatible quads in those same lines. To be incompatible they must include all six pairings of the four digits (two in the pair-box, the other four elsewhere in the lines), two of each in both lines. Or, at least that's how I currently see it. Any objections or refinements? Have I missed something obvious?

PS. If it's new, or previously unnamed, I'd like to dub it "Incompatible Quads" or "IQ".

[eleven]

What do you think of the simplified two-row pattern (added to the previous post)?

Yes, this is a pattern, i should have found myself.

though I have no idea how often the pattern exists

I fear, that it is as rare as MUG's.