## Bank Holiday 0808 Kazaguruma Special

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Bank Holiday 0808 Kazaguruma Special

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

Code: Select all
`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

Code: Select all
`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

Code: Select all
`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
Last edited by tarek on Thu Dec 19, 2019 6:33 pm, edited 2 times in total.

tarek

Posts: 3759
Joined: 05 January 2006

Bank Holiday 0808 Kazaguruma Special Solutions

Code: Select all
`Kazaguruma #01 (Easy Kazaguruma)127836594453729816896154327382415679745962138619378245274581963968243751531697482815349267746152938293867541427536819689421375351978624964783152538214796172695483581963427243751689697482351175238964462197538839546172918325746324679815756814293934826175581937462726415839673542918815679324249381756352198647468753291197264583325746189679815243814293765463578912581962437792134856957681324238457691146329578Kazaguruma #02 (Hidden Doubles Vs. Intersections)162735498593824617847619523425168739739542186618973245374286951256391874981457362689432715713859426425617839347926158256183947198574263571268394864391572932745681286951347391874256457362198964238571532197864718546932625783419843619725179425683283751964741698532659234718478319625916572843532486179165843297397125486824967351783419562619725843425683719548372691367951284291864375174236958936548127852197436Kazaguruma #03 (The Challenge)724861395691435287853297164278654931365912748149783526982576413536149872417328659625194837831725694749638215982563471563417928174982356416359782358276149297841563576413982149872563328659174957238416462197358813546297794385621281964735635721849862341957139785462745692813621853794357964281984217635276539148493178526518426379385621947964735128721849635253914786619287354478563219136478592892156473547392861`

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
Last edited by tarek on Thu Dec 19, 2019 6:34 pm, edited 1 time in total.

tarek

Posts: 3759
Joined: 05 January 2006

### Kazaguruma #03 Challenge Hint

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

Code: Select all
`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      |'------------------------'------------------------'------------------------'`
Last edited by tarek on Thu Dec 19, 2019 6:35 pm, edited 1 time in total.

tarek

Posts: 3759
Joined: 05 January 2006

### Kazagurama #03

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.

Code: Select all
`------------------------.------------------------.--------------------------| 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       |'------------------------'------------------------'-------------------------' `
Glyn

Posts: 357
Joined: 26 April 2007

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.

Code: Select all
`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

Posts: 3759
Joined: 05 January 2006

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
Code: Select all
`1. Kazaguruma #02 intersections before hidden doubles:81 x intersections6 x Hidden doubles2. Kazaguruma #02 hidden doubles before intersections:19 x Hidden doubles21 x intersections`

tarek

tarek

Posts: 3759
Joined: 05 January 2006