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FNC Windoku Killer
http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=13&t=41		 Page 1 of 1
Author:  HATMAN [ Thu May 08, 2008 5:19 pm ]
Post subject:  FNC Windoku Killer
This one is FNC (Ferz non-consecutive) and Windoku.

I've avoided the fish - but it is a little bit softer than I would like. This is unique with just two cages (14(2) and 13(2) in W4) and solvable with 8 cages (but very fishy).

I've been trying to get a Colour Pyramid FerzNC - but I cannot seem to find a solution grid.

Image
Author:  udosuk [ Fri May 09, 2008 11:59 am ]
Post subject:  Re: FNC Windoku Killer
Solution:

Hidden Text:
951647283
768132594
243598671
692783145
587416932
314925867
176854329
435269718
829371456


I don't agree it's soft. In fact I needed to apply a few T&E steps to solve it. :bigoops:

Obviously I've missed a critical move. Perhaps I'll post a "stuck state" later to see which move I missed. :brickwall:
Author:  Glyn [ Fri May 09, 2008 6:16 pm ]
Post subject:  Re: FNC Windoku Killer
Struggled through. Needed to try permutations of the windows at some points, especially to track down a locked candidate in the bottom left window.
Author:  Jean-Christophe [ Sat May 10, 2008 8:10 am ]
Post subject:  Re: FNC Windoku Killer
Surely not easy. Here is my walkthrough
Hidden Text:
1. All diagonal cages of 2 with odd sum have one consecutive combination which cannot work with FNC
a. the three diagonal 9/2 <> {45}
b. 15/2 @ n3 <> {78} = {69} (NP @ n3, w:r234c678)

2a. 10/2 @ r23c6 = {28|37} = {2|3..} -> 5/2 @ r4c78 <> {23} = {14} (NP @ r4, w:r234c678, n6)
b. 9/2 @ r4c34 = {27|36}

3a1. Innies @ w:r678c678 -> r6c6+r7c7+r8c8 = 9
a2. <> {234} because it would violate the FNC rule (no possible cell to place the 3 without it being diagonally adjacent to a 2 or 4).
a3. -> {1(26|35)} = {5|6..} -> 1 locked for w:r678c678
b. 14/2 @ r6c78 = {59|68} = {5|6..}; KNP {56} with h9/3 @ w:r678c678
c. 9/2 @ n9 = {27} (NP @ n9, w:r678c678)
d. 13/2 @ r78c6 = {49} (NP @ n8, c6, w:r678c678)
e. 14/2 @ r6c78 = {68} (NP @ n6, r6, w:r678c678); FCN -> r57c6..9 <> 7
f. 9/2 @ n9: r7c8 = 2, r8c7 = 7

4a. 13/2 @ r6c34 = {49} (NP @ r6, w:r678c234)
b. 10/2 @ r78c4 = [82|73] = {2|7..} -> 9/2 @ n7 <> {27} = {18|36}
c. Since r8c4 = {23}, FNC -> r7c35,r9c5 <> {23} (Note: cannot remove {23} from r9c3 since it's a NOT a buddy/peer of r8c4)
d. Innies @ w:r678c234 -> r67c2+r8c3 = 13; 5 locked for w:r678c234 -> {5(17|26)}
e. FNC -> r7c2,r8c3 <> {56} -> r6c2 <> 2

5a. Innies @ w:r234c234 -> r2c3+r34c2 = 21 (no {123})
b. 2 @ c2 locked @ r1259c2; CPE -> r1c3 <> 2 (either in n1 or hw:r159c234)
c. 4 @ c2 locked @ r1359c2; CPE -> r1c3 <> 4
d. 6/2 @ r1 = {15} (NP @ r1, n1)
e. 9/2 @ n1 = {27|36}
f. two 9/2 @ w:r234c234 = NQ {2367} @ w:r234c234
g. 6/2 @ r23c4 = {15} (NP @ n2, c4, w:r234c234)
h. h21/3 @ r2c3+r34c2 = {489}
i. Since r4c2 = {89}; FNC -> r5c13 <> {89}

6a. h13/3 @ r67c2+r8c3 = {157|256}; FNC -> r7c2,r8c3 <> {56} -> r67c2 = {17|56|57} = {1|5..}
b. KNP {15} @ c2 with r1c2 -> r8c2 <> 1 = {38}
c. 9/2 @ n7 -> r7c3 = {16}

7a. h21/3 @ r2c3+r34c2 = {489}
b. Since r6c3 = {49} -> r2c3,r4c2 <> [49] -> r3c2 <> 8 = {49}, r2c3,r4c2 = {4|9..} (Note: one may prefer using ALS-XZ here)
c. r6c3 and r2c3,r4c2 = KNP {49} -> 4 locked @ r26c3 for c3
d. r269c3 = HT {489} @ c3 -> r9c3 = {89}
e. FNC -> r8c2 = 3, r7c3 = 6, r78c4 = [82], r6c34 = [49]
...

Edited to explain a step
Author:  udosuk [ Sat May 10, 2008 11:24 am ]
Post subject:  Re: FNC Windoku Killer
JC, great walkthrough! :applause: :salute: ;clapclap;

About this move:
Hidden Text:
3a. Innies @ w:r678c678 -> r6c6+r7c7+r8c8 = 9 = {1(26|35)} = {5|6..} -> 1 locked for w:r678c678

You might like to add the following bit:
Hidden Text:
r6c6+r7c7+r8c8 = 9 can't be {234} because it would violate the FNC rule (no possible cell to place the 3 without it being diagonally adjacent to a 2 or 4).

And these are the critical moves that I missed:
Hidden Text:
5b. 2 @ c2 locked @ r1259c2; CPE -> r1c3 <> 2 (either in n1 or hw:r159c234)
5c. 4 @ c2 locked @ r1359c2; CPE -> r1c3 <> 4
7b. Since r6c3 = {49} -> r2c3,r4c2 <> [49] -> r3c2 <> 8 = {49}, r2c3,r4c2 = {4|9..} (Note: one may prefer using ALS-XZ here)
7c. r6c3 and r2c3+r4c2 = KNP {49} -> 4 locked @ r26c3 for c3

Maurice do you really regard these moves as being "soft"? :pallid:
Author:  Jean-Christophe [ Sat May 10, 2008 2:26 pm ]
Post subject:  Re: FNC Windoku Killer
udosuk wrote:
And these are the critical moves that I missed:
Hidden Text:
5b. 2 @ c2 locked @ r1259c2; CPE -> r1c3 <> 2 (either in n1 or hw:r159c234)
5c. 4 @ c2 locked @ r1359c2; CPE -> r1c3 <> 4
7b. Since r6c3 = {49} -> r2c3,r4c2 <> [49] -> r3c2 <> 8 = {49}, r2c3,r4c2 = {4|9..} (Note: one may prefer using ALS-XZ here)
7c. r6c3 and r2c3+r4c2 = KNP {49} -> 4 locked @ r26c3 for c3

I coudn't spot them without the help of JSudoku.

Now, I too may have missed some easier moves. Maurice... ?
Author:  HATMAN [ Tue May 13, 2008 2:47 pm ]
Post subject:  Re: FNC Windoku Killer
JC

I was the same as you up to 4 and for 5 I went more simply but less purely with:

Hidden Text:
6(2) @ r23c4 <> {24} as -> r8c4 = 3 -> r4c4<>3 but r4c3<>FNC hence = {15}
LOL N1W1 -> r1c23 = {15}


and it seemed to go OK from there - however I'll try it again.

Maurice

On trying it again I cannot seem to find where I fixed the
Hidden Text:
4 in r6c3
- having looked at your walkthrough I guess I must have "luckied it" and not noticed.
Author:  HATMAN [ Tue May 13, 2008 2:58 pm ]
Post subject:  Re: FNC Windoku Killer
ZD 60A FNC Windoku Repeat

I found this one harder - I'm posting an easier one on DJApe's site.

It is windoku and ferz non-consecutive.

It is also repeat so all cages must contain repeated numbers.

The chequered pattern indicates overlapping cages.


Image[/
Author:  udosuk [ Wed May 14, 2008 8:56 am ]
Post subject:  Re: FNC Windoku Killer
HATMAN wrote:
I found this one harder - I'm posting an easier one on DJApe's site.

Not yet? :scratch:

Here is the solution and my key move for ZD60A:
Hidden Text:
725813964
914765823
863924715
482579631
671432589
539681472
158246397
347198256
296357148

My key move:
Code:
+-------------------------------+-----------------------------+--------------------+
| 123456789 123456789 123456789 | 123456789 12356789 12345789 |  35789 356 3456789 |
|   346789   1234567   12346789 |  3456789   356789   3456789 |  35789  12 3456789 |
|     89        46       3457   |   345679     12      34679  |  35789  12  356789 |
+-------------------------------+-----------------------------+--------------------+
|   34689      #89        12    |     57      @79      35689  |   46    35    12   |
|  1234567    345678    123457  |    @46      12358     12    |  12359  89  12359  |
|   *589     12345689   *139    |   123689     48      12389  |   46    78  12357  |
+-------------------------------+-----------------------------+--------------------+
|  1235789    *589     12345789 |  12345789    46       26    |  1235   79    78   |
|  12356789 123456789 123456789 |  1234789   1235789  123489  |  12359 345  123679 |
| 123456789 123456789 123456789 |  12345789  1235789 12345789 | 123789 346 1236789 |
+-------------------------------+-----------------------------+--------------------+

FNC: r4c5+r5c4 can't be [76] => r4c5=9 or r5c4=4
If r4c5=9 => r4c2=8
If r5c4=4 => r6c3 can't be 3 (FNC)
Either way, 19/3 @ r6c13+r7c2 can't be [838]
=> 19/3 @ r6c13+r7c2 = [595|919]
=> 9 @ r6,n4 locked @ r6c13, 9 @ r678c234 locked @ r6c3+r7c2

:ugeek:
Author:  HATMAN [ Wed May 14, 2008 1:20 pm ]
Post subject:  Re: FNC Windoku Killer
A neat key move.

I'm having difficulty finding the right level of "easier".
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