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Børge
PostPosted: Wed Sep 17, 2008 6:32 pm 
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Joined: Mon Apr 21, 2008 10:32 am
Posts: 868
There are four difficulties to choose from.
All four puzzles have the same solution.

A) Novice.
B) Apprentice (mainstream edition).
C) Master (80 Intersections, 2 Naked Pairs, 3 Naked Triplets, 3 Naked Quads, 1 Empty Rectangle in g8). Select to view GRID numbers.
D) Grand Master (90 Intersections, 5 Naked Pairs, 6 Naked Triplets, 5 Naked Quads, 1 X-Wing in g8, 1 Y-Wing in g10, 1 Grouped X-Wing in g1). Select to view GRID numbers.
The 3 advanced techniques are needed in 3 different grids.

I will post a second post with a Walktrough of the Grand Master level puzzle, including an explanation of the Grouped X-Wing.



Regular Clueless Explosion #21A (Novice)

Rating based on required solving techniques:  Moderate

Image

008000002000800000060040700007100000002007000090000006000032005000400000030090600
000700000306000000007005104090000000000000809700500300000000030005000000000600002
000000000208000000000105900000700050000008000806094300000000000609000000004000073
300000000001008000009000803906000000000006000400009018000080701000600000035070200
000720000000000900009400000013008000000003006007000000000100000000000800408000605
036000091000000000070300000100000000000000908092060500000020004500001200000008000
000008000000000001042007005000070000100000900908030010000000009300002000001050730
500000600006000000000062700000090020007003000950007400005304010600000003090500200
000004003000800000050000027000000006005009000001003040004000000706000000000200070



Regular Clueless Explosion #21B (Apprentice)

Rating based on required solving techniques:  Moderate

Image

008000002000800000060040700007100000002007000090000006000032005000400000030090600
000700000306000000007005104090000000000000809700500300000000030005000000000600002
000000000208000000000105900000700050000008000806094300000000000609000000004000073
300000000001008000009000803906000000000006000400009018000000701000600000035070200
000720000100000900009400000013008000000003006007000000000100000000000800408000605
036000091000000000070300000100000000000000008092060500000020004500001200000008000
000008000000000001042007005000000000100000900908030010000000009300002000001050730
500000600406000000000062700000000020007003000950007400005004010000000003090500200
000004003000800000050000027000000006005009000001003040004000000706000000000200070



Regular Clueless Explosion #21C (Master)

Rating based on required solving techniques:  Extra Hard

Image

008000002000800000060040700007100000002007000090000006000032005000400000030090600
000700000306000000007005104090000000000000809700500300000000030005000000000600002
000000000208000000000105900000700050000008000806094300000000000609000000004000073
300000000001008000009000803906000000000006000400009018000000701000600000035070200
000720000100000900009400000003008000000003006007000000000100000000000800408000605
036000091000000000070300000100000000000000008092060500000020004500001200000008000
000008000000000000042007005000000000100000900908030010000000009300002000001050730
500000600406000000000002700000090020007003000950007400005304010000000003090500200
000004003000800000050000027000000006005009000001003040004000000706000000000200070



Regular Clueless Explosion #21D (Grand Master)

Rating based on required solving techniques:  Super Hard

Image

008000002000800000060040700007100000002007000090000006000032005000400000030090600
000700000306000000007005104090000000000000809700500300000000030005000000000600002
000000000208000000000105900000700050000008000806094300000000000609000000004000073
300000000001008000009000803906000000000006000400009018000080701000600000035070200
000720000000000900009400000013008000000003006007000000000100000000000800408000605
036000091000000000070300000100000000000000908092060500000020004500001200000008000
000008000000000001042007005000070000100000900908030010000000009300002000001050730
500000600006000000000002700000090020007003000950007400005304010600000003090500200
000004003000800000050000027000000006005009000001003040004000000706000000000200070

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Børge
PostPosted: Wed Sep 17, 2008 6:34 pm 
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Joined: Mon Apr 21, 2008 10:32 am
Posts: 868
Here a Walktrough of the Grand Master level puzzle, including an explanation of the Grouped X-Wing.
Hidden Text:
In this puzzle all three advanced techniques are needed early, making them pretty difficult to find :twisted:
JSudoku reports two Grouped X-Wing, but only one is needed.

Before analyzing the Grouped X-Wing, lets recapitulate a standard X-Wing.


There is an X-Wing on 1 in g8:r25c27 (green cells) so all seven other pencil 1 in g8:r25 can be eliminated
Image



The two grouped X-Wings here are "a special case" of general Grouped X-Wing since each is grouped through the Clueless cells in a given nonet in the Clueless grid 10.
Perhaps the term Exploded X-Wing would be better.
After finding the X-Wing above and doing its resulting eliminations, there is a Grouped X-Wing on 5 in g8:r3c58.
This Grouped X-Wing is not needed, but is a bit easier to comprehend than the one needed in g1.

All cells in g8 with a pencil 5 have been coloured (blue, green, pink or yellow).
The Grouped X-Wing on 5 in g8:r3c58 consists of the blue and green cells, and the blue cells also belong to nonet 8 in the Clueless grid 10.
The 9 Clueless cells in g8 have a strong relationship since a given value can only be true for one of these 9 cells.
Hence the 3 blue cells also have a strong relationship for 5 since only one of them can take the value 5.
If one of the blue cells is 5, then the two other ones cannot take 5. This is what makes the X-Wing grouped through a strong relationship, or strong links of you prefer.

g8:c5 must have a 5 somewhere. It can either be in g8:r2c5 or g8:r3c5.

1) Assume g8:r2c5 = 5. Then the only cell in g8:c8 that can be 5 is g8:r3c8
=> g8:r3c9 <> 5 (the pink cell)

2) Assume g8:r3c5 = 5.
=> g8:r3c9 <> 5 (the pink cell)

CONCLUSION: Regardless of which of the two cells in g8:c5 that takes the 5, g8:r3c9<>5.

An identical deduction is possible using g8:c8 instead of g8:c5.
In g8:c8 the 5 can be in either g8:r2c8, g8:r8c8 or g8:r3c8.

1) Assume g8:r2c8 or r8c8 = 5. Then the only cell in g8:c5 that can be 5 is g8:r3c5
=> g8:r3c9 <> 5 (the pink cell)

2) Assume g8:r3c8 = 5.
=> g8:r3c9 <> 5 (the pink cell)

CONCLUSION: Regardless of which of the three cells in g8:c8 that takes the 5, g8:r3c9<>5.

Image


How to find an Exploded X-Wing (special case of Grouped X-Wing).

COLUMN BOUND for digit X:
In a single non-cluleless grid find two columns where the digit X can only be in cluless cells plus ONE non-cluless cell.
If the two non-cluless cells are in the same row, then the digit X can be eliminated from all other cells in this row.

ROW BOUND for digit X:
In a single non-cluleless grid find two rows where the digit X can only be in cluless cells plus ONE non-cluless cell.
If the two non-cluless cells are in the same column, then the digit X can be eliminated from all other cells in this column.



There is a Grouped X-Wing on 5 in g1:r4c25.
Hence 5 can be eliminated from all 3 pink cells
=> a Hidden-Single 5 in g1:r5c7
=> a Hidden-Single 5 in g1:r3c8
Image



Finally there is a Y-Wing with strong link on 8 in g10:r7c14 with {48} sattelites in g10:r2c1 + g10:r1c4
=> g10:r2c45 <> 4
Image
How to find a Y-Wing.
Looking for a Y-Wing is similar to looking for a Skyscraper.

1) Find a row, column or nonet where the digit X can only be in two cells A and B.
2) If both cells A and B have a buddy with the pair XY, then Y can be eliminated from all cells that can see both cells with the pair XY.

Image

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