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PostPosted: Sat Jun 27, 2009 7:49 pm 
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This is a difficult puzzle.
A human can find a solution, which is simpler and more elegant than what programs do.


Image

020030000560000000407690200000000316600000009183000000006027901000000087000050060


   List with cloaked techniques:
Hidden Text:
Technique                 on Digit(s)              in Grid(s)

Naked Singles on in
Intersection on 8 in r4n5
Hidden Single on 8 in r4c5
Hidden Single on 9 in r4c2
XY-Chain on 4 with 5 cells in r5c2 <> 4
Hidden Single on 7 in r4c4
Naked Singles on - in --
----- on - in --
----- on - in --
----- on - in --
----- on - in --
----- on - in --
----- on - in --
----- on - in --
----- on - in --
----- on - in --
----- on - in --
----- on - in --
----- on - in --
----- on - in --

Hint :
Hidden Text:
Image

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PostPosted: Sat Jun 27, 2009 9:22 pm 
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I almost did it unassisted ....

I confess to not focusing enough on this.

Here is one machine assisted solution
Hidden Text:
Code:
Start
SSTS
*-----------------------------------------------------------------*
| 9      2      1     | 58     3      58    | 6      7      4     |
| 5      6      8     | 27     47     24    | 1      9      3     |
| 4      3      7     | 6      9      1     | 2      5      8     |
|---------------------+---------------------+---------------------|
| 27     9      245   | 57     8      45    | 3      1      6     |
| 6      47     45    | 12357  147    2345  | 8      24     9     |
| 1      8      3     | 29     46     69    | 7      24     5     |
|---------------------+---------------------+---------------------|
| 8      5      6     | 4      2      7     | 9      3      1     |
| 23     14     24    | 139    16     69    | 5      8      7     |
| 37     17     9     | 138    5      38    | 4      6      2     |
*-----------------------------------------------------------------*
Eliminating 5 from r4c3,r5c46(ALS-XZ A=257 in r24c4 B=245 in r24c6 x=2 z=5)
r5c3 MUST be 5 (Hidden Single in Column 3)
Eliminating 4 from r5c5(ALS-XZ A=3458 in r149c6 C=234 in r5c68 x=3 z=4)
SSTS
Solution


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PostPosted: Sun Jun 28, 2009 1:44 pm 
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If it is any comfort:
Hidden Text:
I spent a good hour searching for advanced techniques rated Ultra Hard and below but excluding chains, which would crack the puzzle.

I (of course) found the Hidden Pair [69] in r68c6. Further I found the following Y-Wing, but not the XY-Wing yielding the exact same elimination, which I needed machine assistance to spot.
The Hidden Pair [69] and the elimination r5c3<>2 did however not result in any fruitful advancement.

Image


At this point I was pretty sure that a chain was needed to solve the puzzle. I now had JSudoku solve the puzzle and had a glance at its list of techniques used, but did not at all look at its detailing of the techniques used. It was a bit a chocking that JSudoku needed two XY-Chains plus a final XY-Wing after the two XY-Chains.

Having solved some 50 puzzles of similar difficulty by the same person who has made this one, I had a good hunch that a single XY-Chain would crack the puzzle.

For all bivalue cells I now in strict sequence tried both values to see if eliminating any of them would crack the puzzle resulting in its solving requiring Naked Singles only. All accommodating bivalue cells were marked and I started looking for a single XY-Chain cracking the puzzle. I was however not successful. Having only two bivalue cells in n4 and n5 was a major obstacle. If I remember correctly, I think I found an XYT-Chain cracking the puzzle, but discarded it as too complex.

Next I examined the bivalue cells left over from the previous step and concentrated on those whose solution would solve the puzzle requiring N/H Singles only. First out was r4c1={27}. Solving r4c1=2 -> Hidden Single 7 in r4c4 -> puzzle solves with Naked Singles. And this time I was able to find the following XY-Chain -> r4c1<>7:

Image


Fortunately I immediately saw that r4c1<>7 -> r5c2=7<>4 and then saw that I could use a subchain of the already found XY-Chain to prove r5c7<>4. This then became my final solution. I spent some time looking for a shorter chain, also having other bivalue cells as the target cell, but without finding a shorter or better XY-Chain.

Totally I spent some 3 intense hours arriving at the published solution.

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