The New Sudoku Players' Forum

[novi]

And one more Sudoku Windmill Diagonal Windoku.

[dyitto]

If one starts putting one arbitrary valid Windoku-X grid in the middle grid (the 'axis'), the result will mostly be invalid.

For example:



In the middle grid, 7 in R4C1 & R7C3 is OK. But left-bottom they break the windoku rule.

[novi]

I am not sure what you are trying to say. An ** arbitrary ** valid Windoku-X grid cannot be used here because some numbers are part of two grids where there are ** overlapping ** windoku regions. This puzzle really is OK, see the attached solution image file which shows the one ** valid ** solution to the given puzzle.

[dyitto]

An ** arbitrary ** valid Windoku-X grid cannot be used here because some numbers are part of two grids where there are ** overlapping ** windoku regions.

That's indeed what I was trying to say.
Your moderate puzzle was indeed valid.

Creating my own new random complete grid seems to be quite difficult. May I ask you how you've created yours?

[dyitto]

Code: Select all

left-top:
...|...|...
...|...|..2
16.|...|...
---+---+---
...|...|..8
...|...|...
.9.|...|...
---+---+---
..3|...|...
...|1..|...
...|...|...

right-top:
...|...|...
6..|...|...
.7.|...|...
---+---+---
..3|...|.7.
.5.|...|8..
...|...|...
---+---+---
...|...|...
...|...|2..
...|.85|...

right-bottom:
...|...|...
...|...|...
...|...|..3
---+---+---
...|..8|...
..7|...|...
...|...|...
---+---+---
...|...|...
...|...|8..
.8.|.2.|..5

left-bottom:
...|..6|...
...|...|...
...|...|...
---+---+---
..5|3..|...
...|...|...
...|...|...
---+---+---
...|...|..9
...|...|...
...|2..|4..

middle:
...|...|...
...|.4.|...
...|...|...
---+---+---
...|...|...
...|...|...
..7|...|...
---+---+---
...|3..|...
...|...|...
...|...|..1


www.scrybqj.com/images_diversen/windoluX_windmill_20110507.pdf { PDF ]

[novi]

JSudoku software was used to create the puzzle. I put a new post concerning it in the Software part of the forum.

[BryanL]

Hi Novi,

your above windmill has a deadly pattern in the right 9x9.

69r78c47

When I spotted it, there was a single 2 available to break the pattern but it lead to an inconsistency...

Bryan

[JasonLion]

That isn't a deadly pattern because of the diagonals. Swapping the 6s & 9s causes the 9 moved to R7C7 to conflict with a clue 9 in R3C3 on the anti-diagonal, and so is not a valid solution.

[BryanL]

That isn't a deadly pattern because of the diagonals.

Doh! I didn't even take note of the diagonals. Crikey, how many houses are there in those things??? Interesting exercise to code all of them in...

[Pat]

how many houses are there in those things???

each WinDoku-X has

27 houses of plain 3x3 SuDoku
+ 4 windows
+ diagonal
+ anti-diagonal
= 33 houses

x5 would make 165
-8 boxes (overlap) --> 157 houses

[dyitto]

Additionally, windoku has 5 implicit houses that can be derived from the 4 defined houses.

[tarek]

I took an interest in generating windoku kazagurumas in the 0808 bank holiday special. My feeling is that due to the overlap and rotational symmetry, the middle grid should be free from any extra constraints unless they are 90 degree symmetrical only ( not fully symmetrical ). To me that looked more aesthetically pleasing and was behind my decision to leave the central grid empty from any extra constraints and more recently free from any clues at all.

[RW]

Hi novi,

thank you for these puzzles! Did the easy and moderate. The easy was perhaps a bit too easy but the moderate was just the right difficulty. More of these please! I've done some diagonals earlier, but I'm completely new to both windoku and windmills. Didn't think of the 5 implicit houses mentioned by dyitto, perhaps they would have made it easier. Don't know how many inherent solving features of the windmill I catched or missed.

About the representation, on my b/w printout, the diagonal lines are very faint. Especially in the beginning when I wasn't yet used to the format, it was hard to follow where exactly the middle puzzle was on the sheet as I couldn't see the diagonal clearly. Though after a while I got used to it and it's no problem anymore. But perhaps they would be a bit more solver friendly if the diagonals were just a bit darker?

RW

[Pat]

Didn't think of the 5 implicit houses mentioned by dyitto,
perhaps they would have made it easier.

the 5 extra houses are implied by the 4 windows,
therefore they cannot add any information

[RW]

the 5 extra houses are implied by the 4 windows,
therefore they cannot add any information

Perhaps for a computer solver that automatically does all eliminations based on the 4 windows they don't add any information, but for a manual pen and paper solver it sure helps to acknowledge them and for example also look for singles within those houses.

RW