The New Sudoku Players' Forum

[tarek]

Bank Holiday Next week:D , These Kazagurumas should keep you entertained:) . Puzzle #3 for the interested has a small challenge attached to it:idea: . This was posted on theSudokuSolver Forum uder the same heading. All Kazagurumas have the Centre grid as Vanilla & the 4 satellite grids as windoku.

The 1st is a taster, minimal intersections needed:

Centre grid is Vanilla & the 4 Satellite Grids are Windoku

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Bank Holiday 0808 Kazaguruma #1
..7....9....7....68..15............974.............2...7......3.68.......3...7...
....4.2..746.5.....9......1......81.......3..3...........7.............6..2..5.8.
.....3..............7...3..1.........................2..8...7..............8.....
.3.8..1..5.............5...........8..5.......49......3......4.....5.291..7.6....
...7...8.......24.8......6...3.............377............81..42....7....4....5..

The next is slightly more difficult, Intersections Vs. Hidden doubles .... Who will win ???!!!!

Centre Grid is Vanilla & the 4 Satellite Grids are Windoku

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Bank Holiday 0808 Kazaguruma #2
....35....9......7......52....1..............6.8........4........6...8......5....
....3......3......4.......9..7.........1.3..........6..7..............72....45...
........7...8......5..............7.....9....7..............4....3...........5...
.8..........6...........7..4............7...3....8......5............4.......7...
...4............4...5......5.......1.............6...5.7....9...3.....2....1.7...

The next puzzle harbours a challenge. It is A Superior Level Puzzle (Needs one or more out of Triples or X-wings to solve). In the abscence of fruitful Intersections AND doubles, can you spot the fruitful X-wing which ultimately is not needed to solve?

Centre Grid is Vanilla & the 4 Satellite Grids are Windoku

WARNING: Numerous Intersections

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Bank Holiday 0808 Kazaguruma #3
...8.1...6.......7.5.............9......12...1.9.............1............7......
.....4..7..1......7.......5......47..6...........8...........8..5.2..........1...
....1...........6...............8..........5....5.6.........6....1...............
.....1.....9...........2...6..8.............19.........7.............52....4.....
...6...........1........6..2............8...44...............9..92.........3.....

tarek

[tarek]

Bank Holiday 0808 Kazaguruma Special Solutions

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Kazaguruma #01 (Easy Kazaguruma)
127836594453729816896154327382415679745962138619378245274581963968243751531697482
815349267746152938293867541427536819689421375351978624964783152538214796172695483
581963427243751689697482351175238964462197538839546172918325746324679815756814293
934826175581937462726415839673542918815679324249381756352198647468753291197264583
325746189679815243814293765463578912581962437792134856957681324238457691146329578

Kazaguruma #02 (Hidden Doubles Vs. Intersections)
162735498593824617847619523425168739739542186618973245374286951256391874981457362
689432715713859426425617839347926158256183947198574263571268394864391572932745681
286951347391874256457362198964238571532197864718546932625783419843619725179425683
283751964741698532659234718478319625916572843532486179165843297397125486824967351
783419562619725843425683719548372691367951284291864375174236958936548127852197436

Kazaguruma #03 (The Challenge)
724861395691435287853297164278654931365912748149783526982576413536149872417328659
625194837831725694749638215982563471563417928174982356416359782358276149297841563
576413982149872563328659174957238416462197358813546297794385621281964735635721849
862341957139785462745692813621853794357964281984217635276539148493178526518426379
385621947964735128721849635253914786619287354478563219136478592892156473547392861

The answer regarding Kazaguruma #02 is that Hidden Doubles win over intersections as using them 1st would lead to a shorter solution path.

I'll give a detailed rundown of techniques for each by the end of the week.

Regarding the challenge of Kazaguruma #03: I will give a hint regarding that hopefully by the end of today

tarek

[tarek]

The solution path reaches its Zenith when there are no more Singles, intersections nor doubles available.

Look in grid 5 for a very nice naked triple (not needed)
The hidden triple that kills the puzzle can be seen in grid 3
However, the 2 x-wings available (with a similar effect & both not needed) are in grid 4

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Grid 4 of Kazaguruma #03
------------------------.------------------------.------------------------
| 2378    2368    2378   | 367     4       1      | 239     359    -2357   |
| 1       2345    9      | 357     358     358    | 3467    367     2347   |
| 357     3456    3457   | 3567    9       2      | 348     1       348    |
 ------------------------+------------------------+------------------------
| 6       1235    1235   | 8       2357    357    | 3479    3579    3457   |
| 23578   2358    23578  | 9       6       4      | 238     358     1      |
| 9       3458    3458   | 1235    12357   37     | 3678    3678    235678 |
 ------------------------+------------------------+------------------------
| 2358    7       3568   | 235     2358    9      | 1       4       368    |
| 4       9       368    | 13      1378    3678   | 5       2       368    |
| 2358    12358   12358  | 4       2358    3568   | 367     3678    9      |
'------------------------'------------------------'------------------------'

[Glyn]

Tarek It might not be immediately obvious that the X-wing is of a type generalized to Windoku.

The 2's in the base set row 6+top stiles are sufficient to cover box 5 and column 9. => r1c9<>2.

In the PM of Grid 4 below I've labelled the two base sets X and Y for those unfamiliar with Windoku hidden groups.

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------------------------.------------------------.--------------------------
| 2378    2368    2378   | 367     4       1      | 239     359     -2357   |
| 1       2345    9      | 357     358     358    | 3467    367     2347Y   |
| 357     3456    3457   | 3567    9       2      | 348     1       348     |
 ------------------------+------------------------+-------------------------
| 6       1235    1235   | 8       2357Y   357    | 3479    3579    3457    |
| 23578   2358    23578  | 9       6       4      | 238     358     1       |
| 9       3458    3458   | 1235X   12357X  37     | 3678    3678    235678X |
 ------------------------+------------------------+-------------------------
| 2358    7       3568   | 235     2358    9      | 1       4       368     |
| 4       9       368    | 13      1378    3678   | 5       2       368     |
| 2358    12358   12358  | 4       2358    3568   | 367     3678    9       |
'------------------------'------------------------'-------------------------'

[tarek]

Glyn,

That is correct & well done. The x-wing is an x-wing .... not being apparant is part of the challenge , these are tricky to spot especially the w9 group (r159c159) one.

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X-wings in Kazaguruma #03:
------------------------.------------------------.------------------------
|*2378    2368    2378   | 367     4       1      | 239     359    -2357   |
| 1       2345    9      | 357     358     358    | 3467    367     2347   |
| 357     3456    3457   | 3567    9       2      | 348     1       348    |
 ------------------------+------------------------+------------------------
| 6       1235    1235   | 8       2357    357    | 3479    3579    3457   |
|*23578   2358    23578  | 9       6       4      | 238     358     1      |
| 9       3458    3458   | 1235    12357   37     | 3678    3678    235678 |
 ------------------------+------------------------+------------------------
|*2358    7       3568   |*235    *2358    9      | 1       4       368    |
| 4       9       368    | 13      1378    3678   | 5       2       368    |
|*2358    12358   12358  | 4      *2358    3568   | 367     3678    9      |
'------------------------'------------------------'------------------------'
2 forms an x-wing in g4c1b8/g4r7w9 ===> [g4r1c9]<>2 (which can also be written as [g3r4c3]<>2)
w9: r159c159

------------------------.------------------------.------------------------
| 2378    2368    2378   | 367     4       1      | 239     359    -2357   |
| 1       2345    9      | 357     358     358    | 3467    367    *2347   |
| 357     3456    3457   | 3567    9       2      | 348     1       348    |
 ------------------------+------------------------+------------------------
| 6       1235    1235   | 8      *2357    357    | 3479    3579    3457   |
| 23578   2358    23578  | 9       6       4      | 238     358     1      |
| 9       3458    3458   |*1235   *12357   37     | 3678    3678   *235678 |
 ------------------------+------------------------+------------------------
| 2358    7       3568   | 235     2358    9      | 1       4       368    |
| 4       9       368    | 13      1378    3678   | 5       2       368    |
| 2358    12358   12358  | 4       2358    3568   | 367     3678    9      |
'------------------------'------------------------'------------------------'
2 forms an x-wing in g4r6w7/g4c9b5 ===> [g3r4c3]<>2 (which can also be written as [g3r4c3]<>2)
w7: r234c159

tarek

[tarek]

Putting an end to this Bank Holiday Kazaguruma Saga is the rundown of techniques needed to solve Kazaguruma #02. If you spot hidden doubled before intersections then you will enjoy a shorter solution path

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1. Kazaguruma #02 intersections before hidden doubles:
81 x intersections
6 x Hidden doubles

2. Kazaguruma #02 hidden doubles before intersections:
19 x Hidden doubles
21 x intersections

tarek