The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |8..|...|...|
 |..7|..5|96.|
 |...|.6.|.48|
 |---+---+---|
 |.7.|1..|..6|
 |1..|6.8|..9|
 |5..|..9|.7.|
 |---+---+---|
 |73.|.4.|...|
 |.25|3..|6..|
 |...|...|..3|
 *-----------*


Play/Print this puzzle online

[SpAce]

Code: Select all

.-----------------.---------------------.-------------------------.
| 8    569  23469 | 2479   1239   12347 |   1357    135      57-1 |
| 34   1    7     | 48     38     5     |   9       6        2    |
| 239  59   239   | 279    6     b1237  | a(1)357   4        8    |
:-----------------+---------------------+-------------------------:
| 239  7    2389  | 1      5      234   |   2348    238      6    |
| 1    4    23    | 6      7      8     |   235     235      9    |
| 5    68   2368  | 24     23     9     |   2348-1  7      c(1)4  |
:-----------------+---------------------+-------------------------:
| 7    3    189   | 2589   4      6     |   1258    12589    15   |
| 49   2    5     | 3      189   b17    |   6       189     c47   |
| 6    89   1489  | 25789  1289   127   |   47      12589    3    |
'-----------------'---------------------'-------------------------'

(1)r3c7 = (1,7)r38c6 - (7=41)r86c9 => -1 r1c9,r6c7; stte

That was a fun coloring exercise. Found quite a few not so useful eliminations as well:

Coloring: Show

coloring.png (76.53 KiB) Viewed 633 times

[Ngisa]

Code: Select all

+---------------------+--------------------------+--------------------------+
| 8      569    23469 | 2479      1239     12347 | 1357       135       157 |
| 34     1      7     | 48        38       5     | 9          6         2   |
| 239    59     239   | 279       6       b1237  |c1357       4         8   |
+---------------------+--------------------------+--------------------------+
| 239    7      2389  | 1         5        234   | 2348       238       6   |
| 1      4      23    | 6         7        8     | 235        235       9   |
| 5      68     2368  | 24        23       9     |d12348      7        e14  |
+---------------------+--------------------------+--------------------------+
| 7      3      189   | 2589      4        6     | 1258       12589     15  |
| 49     2      5     | 3         189     a17    | 6          189      f4-7 |
| 6      89     1489  | 25789     1289     127   | 47         12589     3   |
+---------------------+--------------------------+--------------------------+


Almost like SpAce
(7=1)r8c6 - r3c6 = r3c7 - r6c7 = (1-4)r6c9 = (4)r8c9 => - 7r8c9; stte

Clement

[Wecoc]

This is what my algorithm came up with.

There's an X-wing of 6 on r1c2-r1c3-r6c2-r6c3, you can easily reach until that point with basic strategies (singles, pointing pairs, etc)
Then a little guess was needed to eliminate candidate 2 on r6c4 (trial and error of each candidate [24] of that cell). From there it's pretty much solved.

Code: Select all

+--------------------------+
| 8 5x 6x | 2  9 4 | 1 3 7 |
| 4 1  7  | 8  3 5 | 9 6 2 |
| 3 9  2  | 7  6 1 | 5 4 8 |
+--------------------------+
| 2 7  9  | 1  5 3 | 4 8 6 |
| 1 4  3  | 6  7 8 | 2 5 9 |
| 5 6x 8x | 4* 2 9 | 3 7 1 |
+--------------------------+
| 7 3  1  | 9  4 6 | 8 2 5 |
| 9 2  5  | 3  8 7 | 6 1 4 |
| 6 8  4  | 5  1 2 | 7 9 3 |
+--------------------------+
x = X-wing, 4* = guessed via elimination

[Leren]

Code: Select all

*--------------------------------------------------------*
| 8   569 23469 | 2479  1239  12347 | 1357   135    57-1 |
| 34  1   7     | 48    38    5     | 9      6      2    |
| 239 59  239   | 279   6    d1237  |e1357   4      8    |
|---------------+-------------------+--------------------|
| 239 7   2389  | 1     5     234   | 2348   238    6    |
| 1   4   23    | 6     7     8     | 235    235    9    |
| 5   68  2368  | 24    23    9     | 2348-1 7     a14   |
|---------------+-------------------+--------------------|
| 7   3   189   | 2589  4     6     | 1258   12589  15   |
| 49  2   5     | 3     189  c17    | 6      189   b47   |
| 6   89  1489  | 25789 1289  127   | 47     12589  3    |
*--------------------------------------------------------*

XY Wing with transport : (1=4) r6c9 - (4=7) r8c9 - (7=1) r8c6 - r3c6 = (1) r3c7 => - 1 r1c9, r6c7; stte

Leren

[SpAce]

There's an X-wing of 6 on r1c2-r1c3-r6c2-r6c3

Technically yes, there's an X-Wing -- but it's in a single chute (the same stack of boxes) so simpler methods (hidden single or claiming) exist for the same effect. In this case it's a hidden single 6 in r9c1. So, you really don't need the X-Wing (though it's actually a useful spotting aid in these situations), which is kind of important because it would be counted as a non-basic technique and the goal of these daily puzzles is to solve them with just one. These would never be solved with a single X-Wing anyway, so it's never used here in its pure form (except in special puzzles requiring multiple steps).

you can easily reach until that point with basic strategies (singles, pointing pairs, etc)

I already tried to point out to you elsewhere that they're not strategies (another SudokuWiki misnomer) but tactics or techniques or patterns or pretty much anything but strategies. Your overall plan of attack for the whole puzzle is a strategy, and having one gets more important when multiple steps are needed (otherwise you may end up with lots of ineffective steps). Individual tactics are helping to implement that strategy. But don't worry, even some veteran solvers have been known to make the mistake of confusing those two concepts. Yeah, I'm a nitpicker, but I just can't stand it

Then a little guess was needed to eliminate candidate 2 on r6c4 (trial and error of each candidate [24] of that cell). From there it's pretty much solved.

I'm nitpicking again, but guessing and T&E (trial and error) are not the same thing in this context. T&E is a valid (though not very elegant) solving method because it produces a proof by contradiction (when only "errors" are considered) that can be documented as a reasoning step. Guessing implies hoping to place a true candidate and solving the puzzle with it -- and accepting such a solution without any a priori logic why that candidate had to be placed. We're not interested in solutions but the reasoning leading to them, so guessed solutions are worthless. T&E, on the other hand, is ok, as long as it's documented properly. Because you didn't provide any documentation it's impossible to determine whether you used guessing or T&E with the cell r6c4 to arrive at the solution.

Here's an example of how it could have been documented with a self-contradicting chain (Discontinuous Nice Loop (DNL), actually):

(2)r6c4 - (2=3)r6c5 - (3=8)r2c5 - (8=4)r2c4 - r2c1 = r8c1 - (4=7)r8c9 - (7=1)r8c6 - r3c6 = r3c7 - r6c7 = (1-4)r6c9 = (4)r8c9 - r8c1 = r2c1 - (4=8)r2c4 - (8=3)r2c5 - (3=2)r6c5 - (2)r6c4 => -2 r6c4; stte (*)

In other words, the chain proves that if you try to place 2r6c4 it will get eliminated -- thus it can't be a valid placement and the candidate can be eliminated (and we can place 4r6c4). However, if we look at that huge chain a bit more closely, we'll notice that it has a lot of redundant nodes being mirror images of each other (before and after the colored part), so it could probably be simplified. In fact, if we look at the colored part only, it's another self-contradicting DNL but this time proving a placement (basically saying: if r8c9 is not 4, then it must be 4 -> contradiction -> thus it must be 4). If we place 4r8c9 the puzzle gets solved as well, so we don't really need the head and tail parts of the chain at all. Yet, we can still shorten it by using an AIC instead of a DNL:

(4=7)r8c9 - (7=1)r8c6 - r3c6 = r3c7 - r6c7 = (1)r6c9 => -4 r6c9; stte

That chain proves that either r8c9 is 4 or r6c9 is 1 (or both), and in neither case r6c9 can be 4 (so it can be eliminated). It's not a contradiction but a verity, which is usually considered a more elegant type of proof. The end result is the same as before because after that elimination 4r8c9 becomes a hidden single (and 1r6c9 a naked single). We could also cut the chain a bit differently and get yet another proof:

(7=1)r8c6 - r3c6 = r3c7 - r6c7 = (1-4)r6c9 = (4)r8c9 => -7 r8c9; stte

Where have we seen that before? Oh yes, take a look at Clement's solution! (The chain almost contains mine too, but not quite. Leren's solution is the same as mine, just named and written differently. In fact, all stte solutions for this puzzle probably require the same core pattern, so there's not much room for variance.)

In other words, you had the right idea but ended up with an unnecessarily complicated (and undocumented) elimination. It's a start anyway!

(*) stte : "singles to the end" -> the puzzle is solvable with just singles after the move

[rjamil]

Probably the same as SpAce OTP, but different move:

Code: Select all

8..........7..596.....6..48.7.1....61..6.8..95....9.7.73..4.....253..6..........3
 +-----------------+----------------------+---------------------+
 | 8    569  23469 | 2479   1239  (1)2347 | (1)357  135   57-1  |
 | 34   1    7     | 48     38    5       | 9       6     2     |
 | 239  59   239   | 279    6     1237    | 1357    4     8     |
 +-----------------+----------------------+---------------------+
 | 239  7    2389  | 1      5     234     | 2348    238    6    |
 | 1    4    23    | 6      7     8       | 235     235    9    |
 | 5    68   2368  | 24     23    9       | 2348-1  7      (14) |
 +-----------------+----------------------+---------------------+
 | 7    3    189   | 2589   4     6       | 1258    12589  15   |
 | 49   2    5     | 3      189   (17)    | 6       189    (47) |
 | 6    89   1489  | 25789  1289  127     | 47      12589  3    |
 +-----------------+----------------------+---------------------+

XY-Wing Transport: 147 @ r8c69 r6c9. 1 @ r1c67 => -1 @ r1c9 r6c7; stte

Hidden Text: Show

Otherwise, my Transport routine become corrupted due code shrinking.

R. Jamil

[SpAce]

Probably the same as SpAce OTP, but different move:
XY-Wing Transport: 147 @ r8c69 r6c9. 1 @ r1c67 => -1 @ r1c9 r6c7; stte

Hi rjamil. There's no strong link with 1s on row 1, so that can't work. It works with row 3, but then it's exactly the same as Leren's transport move (which is effectively the same as mine). Or you could use the ERI in b2 for the strong link, but that would only eliminate r1c9 (which doesn't solve the puzzle).

Otherwise, my Transport routine become corrupted due code shrinking.

Seems that way.

[rjamil]

Probably the same as SpAce OTP, but different move:
XY-Wing Transport: 147 @ r8c69 r6c9. 1 @ r1c67 => -1 @ r1c9 r6c7; stte

Hi rjamil. There's no strong link with 1s on row 1, so that can't work. It works with row 3, but then it's exactly the same as Leren's transport move (which is effectively the same as mine). Or you could use the ERI in b2 for the strong link, but that would only eliminate r1c9 (which doesn't solve the puzzle).

Hi SpAce,

I think it's similar to as "A) XY-Wing Type 1 Transport (Row-Column wise)" pattern 41 to 44.

It should be read as:
XY-Wing Transport: 147 @ r8c69 r6c9, ERIs 1 @ b23r1c67 => -1 @ r1c9 r6c7; stte

R. Jamil

[SpAce]

It should be read as:
XY-Wing Transport: 147 @ r8c69 r6c9, ERIs 1 @ b23r1c67 => -1 @ r1c9 r6c7; stte

That works, but then you should have written it that way. I don't think it's a fair assumption to have your readers see "1 @ r1c67" as two connected ERIs, unless it's explicitly stated. Besides, such complexity -- while correct -- makes little practical sense when you have the direct r3 strong link available.

[rjamil]

Hi SpAce,

That works, but then you should have written it that way. I don't think it's a fair assumption to have your readers see "1 @ r1c67" as two connected ERIs, unless it's explicitly stated. Besides, such complexity -- while correct -- makes little practical sense when you have the direct r3 strong link available.

I have mentioned ERIs before 1 @ r1c67. However, need more time and thorough study in order to shrink/concise step description. Till then apology for ambiguity.

BTW, two ERIs in b2 and b3 make same effect as r3 strong link. Trying to detect slightly variation.

R. Jamil