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PostPosted: Wed Oct 15, 2008 8:56 pm 
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Image

601407000382000000900001003000300200200106009007004000400800006000000928000709304


Hint 1:
Hidden Text:
Image
Hint 2:
Hidden Text:
Image

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Last edited by Børge on Sun Feb 08, 2009 5:41 pm, edited 6 times in total.

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PostPosted: Sat Oct 18, 2008 8:33 am 
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Code:
6.14.7...
382......
9....1..3
...3..2..
2..1.6..9
..7..4...
4..8....6
......928
...7.93.4

The hints given by Børge will lead you to the textbook solution path for this puzzle.

However... we can always explore different "unorthordox" tricks to crack puzzles. Here I will show you a couple:

Hidden Text:
Firstly, let's apply all "basic level" techniques - naked/hidden singles, naked/hidden subsets, box-line intersections (aka locked candidates):

Code:
+----------------+----------------+----------------+
| 6    5    1    | 4    3    7    | 8    9    2    |
| 3    8    2    | 69   69   5    |-147  147  17   |
| 9    7    4    | 2    8    1    | 56   56   3    |
+----------------+----------------+----------------+
| 15   46   59   | 3    579  8    | 2    46  #157  |
| 2    34   358  | 1   @57   6    |*47   38   9    |
| 158  369  7    | 59   2    4    |*16   38  #15   |
+----------------+----------------+----------------+
| 4    39   39   | 8   @15   2    |*157  157  6    |
| 7    1    56   | 56   4    3    | 9    2    8    |
| 58   2    568  | 7    156  9    | 3    15   4    |
+----------------+----------------+----------------+

r57c5 (marked @) prevents r57c7 to be [71].
r46c9 (marked #) prevents r56c7 to be [71].
As a result, r25c7 can't be [47] (since it will lead to r256c7 or r257c7 to be [471]).
Therefore r2c7 can't be 4. And the rest is solvable by singles. :idea:

This path is different to the "textbook solving path" as it uses only one advanced move instead of two to crack the puzzle. However pedantic people will probably refer it as not elegant enough (i.e. feels too much like forcing chain).

Another unorthodox move I discovered is like this (back to the pencilmark grid as above):

Code:
+----------------+----------------+----------------+
| 6    5    1    | 4    3    7    | 8    9    2    |
| 3    8    2    | 69   69   5    | 147  147  17   |
| 9    7    4    | 2    8    1    | 56  #56   3    |
+----------------+----------------+----------------+
| 15   46   59   | 3    579  8    | 2   @46   157  |
| 2    34   358  | 1   #57   6    |@47   38   9    |
| 158  369  7    | 59   2    4    | 16   38   15   |
+----------------+----------------+----------------+
| 4    39   39   | 8   *15   2    | 157  157  6    |
| 7    1    56   | 56   4    3    | 9    2    8    |
| 58   2    568  | 7    156  9    | 3   *15   4    |
+----------------+----------------+----------------+

Naked triples {157} @ both r7c578 & r7c78+r9c8
=> r7c5+r9c8 (marked *) must be [11|55] (i.e. the 2 cells must be identical)
(This could be viewed as a mini version of Law of Leftovers, I call it "cell cloning".)
Now r4c8+r5c7 (marked @) can't be [44] (both @ n6)
=> r3c8+r5c5 (marked #) can't be [67]
=> r7c5+r9c8 (marked *) can't be [55], must be [11].

After that you still need Børge's 2nd hint to crack the puzzle. But it is an alternative as his 1st hint (albeit probably not as simple/elegant).

:ugeek:

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PostPosted: Sat Oct 18, 2008 12:48 pm 
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Suddenly realized that I had forgotten to post the sudoku code for Irregular Challenging Vanilla #1. :bigoops:
It has now been added to the original post.

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PostPosted: Sat Oct 18, 2008 2:21 pm 
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Udosuk,
Thanks a lot for your "unorthordox" views on solving this puzzle.

Based on your observations, here some other "unorthordox" routes for solving this puzzle.
Hidden Text:
Image

Image

Image


The rest of the puzzle can now be solved with Naked Singles only.

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Last edited by Børge on Sun Feb 22, 2009 3:50 pm, edited 6 times in total.

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PostPosted: Sat Oct 18, 2008 7:48 pm 
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As Borge is a certified Sudoku setter :) we know he would only pose a puzzle with a unique solution.

Hidden Text:
Starting after the basic level moves posted by udosuk.

Code:
.------------.------------.------------.
| 6   5   1  | 4   3   7  | 8   9   2  |
| 3   8   2  | 69  69  5  | 147 147 1A7|
| 9   7   4  | 2   8   1  | 56  56  3  |
:------------+------------+------------:
| 1B5 46  59 | 3   579 8  | 2   46  157|
| 2   34  358| 1   57  6  | 47  38  9  |
| 158 369 7  | 59  2   4  | 16  38  15A|
:------------+------------+------------:
| 4   39  39 | 8   15  2  | 157 157 6  |
| 7   1   56 | 56  4   3  | 9   2   8  |
| 5B8 2   568| 7   156 9  | 3   15  4  |
'------------'------------'------------'


To avoid the UR(15) in r46c19 we have
Either r2c9=1 and r6c9=5 (option A)
or r9c1=5 and r4c1=1. (option B)

Net result r4c9<>1 and r6c1<>5. Singles to finish.

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PostPosted: Sat Oct 18, 2008 8:23 pm 
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Glyn,
a brilliant solution :king: :applause: :cheers: :sun: :salute:
JSudoku is unable to find it ... A BUG :?: :mrgreen:

Glyn wrote:
As Borge is a certified Sudoku setter :) we know he would only pose a puzzle with a unique solution.
Where can I obtain the certificate or diploma attesting this?

Just for the record:
I have not created Irregular Challenging Vanilla #1 myself.
I borrowed it from a Norwegian magazine.

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PostPosted: Sun Oct 19, 2008 9:56 pm 
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This puzzle has a Sudoku Explainer rating of 7.1. Incidentally the two eliminations I exposed there with a Unique Rectangle are found by Sudoku Explainer as separate Contradiction Forcing Chains with tariffs of 8.9 each. I guess it would be unlikely a program would suggest these when many easier moves were available. As a uniqueness move they are much less taxing, but I'm not sure whether any programs available would find them .

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