SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Fri Mar 29, 2024 10:36 am

All times are UTC




Post new topic Reply to topic  [ 4 posts ] 
Author Message
 Post subject: Two Zero Killers
PostPosted: Tue Dec 24, 2013 4:35 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
A couple of puzzles for Christmas - full zero killers.
Green cages are non-consecutive.
Red cages are consecutive


Consecutively Semi Fully Ordered W 4

The non-consecutive cages are ordered (up or down, right or left).

The consecutive cages are fully ordered increasing top left to bottom right.

It is Windoku.

Hardish - a bit above 1.0 I'd guess.


Image
Uploaded with ImageShack.us

Consecutive Fully Ordered W 6


Both consecutive and non-consecutive cages are fully ordered i.e. increasing top-left to bottom-right.

It is Windoku.

Easier - about paper solvable.


Image
Uploaded with ImageShack.us


Top
 Profile  
Reply with quote  
 Post subject: Re: Two Zero Killers
PostPosted: Fri Dec 27, 2013 10:28 pm 
Offline
Grand Master
Grand Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Thanks HATMAN and Merry Christmas! After your puzzle a bit ago with the single number 2 in it, I had thought about what it would take to not have any numbers. I realized that something would have to be done to break the symmetry of exchanging (1-9), (2-8), etc. to get another solution. Your idea of making "fully" ordered cages does that nicely.

Here's my wt of how I actually did the first puzzle. Not the cleanest since it has a chain in it. I haven't really looked for a way around that yet, so I haven't got a "score" which does go around it.
(I have also done your "C FO 3X 7" puzzle - but I'll have to do it again to get a decent wt. The way I did it was all mini-contradictions (which I suppose/hope are fishes).)

Very belated congratulations on your marriage and non-retirement!

Hidden Text:
1. C2, C3, and C4 cages in n2 can only be from:

a) [12] [345] [6789]
b) [12] [789] [3456]
c) [45] [123] [6789]
d) [56] [789] [1234]
e) [89] [123] [4567]
f) [89] [567] [1234]

I.e.
[12] in one of r1c45, r12c6, r23c4
[89] in one of r12c5, r12c6, r3c56

2. 9 in r1 can only be in r1c3 or r1c7
But 9 in r1c3...
puts r1c123 = [789]
puts r3c456 = [789]
puts 9 in r2 in r2c9 which breaks the Red Cage rule
-> r1c7 = 9

3. -> r1c8 is max 7 (NC Cage)
-> r1c9 is max 5 (NC Cage)
But 5 in r1c9 puts 7 in both r1c8 and r3c9
-> r1c9 is max 4
Also r1c9 cannot be 1 which puts 3 in r3c9 and 3 in r3c5
-> r123c9 from [234], [345], [456]
-> r1c8 from (567)
-> (18) in n3 in r23c78

4. C4 cage in n2 can no longer be [3456] (r3c9 from (456))
Also C4 cage in n2 can no longer be [4567] (puts 2 in both r1c5 and r1c9).
-> c4 cage in n2 from [1234] or [6789]

Longish chain here...

But putting C4 cage in n2 as [6789]...
puts 8 in n1 in r1 which puts r1c123 = [678]
which puts r2c78 = {78} which puts 1 in r3c78
which puts r123c1 = [642]
which does not allow a solution for the other two Consec cages in c1

-> C4 cage in n2 is [1234]

5. -> (HS 1 in r1) r1c1 = 1 -> r1c123 = [123]
-> r123c9 = [456]
-> r1c8 = 7
-> C3 cage in n2 is [567] and C2 cage in n2 is [89]
Also -> r2c78 = {23} and r3c78 = {18}
-> r4c678 = {567} - Can only be [675]

6. -> {675} in r23c23 in W1.
Also 8 in n1 in r2 - but cannot go in r2c1 -> 8 in r2c23
-> r123c1 = [149]
-> r4c234 = {349} (W1)

7. -> r4c159 from {128} - can only be [218]
-> r5c169 = [329]

8. r6789c9 from {1237} - can only be [2][137]
-> r9c789 = [567]
-> r8c78 = [89]

9. HS 1 in r5 -> 1 in r5c78
-> 2 not in r7c8
-> r7v78 = [24] and r6c8 = 3

10. Only available option for r789c1 is [678]
->r6c1 = 5
etc.

CPFC currently out of relegation zone!!


Top
 Profile  
Reply with quote  
 Post subject: Re: Two Zero Killers
PostPosted: Sat Dec 28, 2013 5:34 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
A few weeks ago we had Paper Solvable 14 Snakes D CNC ONO with one given number. Now we have two puzzles (and another three days later) with no given numbers. Very clever! What next ?!

I tried the easier one Consecutive Fully Ordered W 6 first. A fun puzzle!

HATMAN wrote "about paper solvable". I'll describe my solving path as more live Human Solvable than Paper Solvable.

Here is my walkthrough for Consecutive Fully Ordered W 6:
The four windows are numbered W1, W2, W3 and W4; the hidden windows will give their cells, for example hidden window R159C159.

Green bordered cage is non-consecutive, fully ordered (NCFO)
Red bordered cages are consecutive, fully ordered (CFO)

Prelims (the two CFO cages in R5 and the CFO cage at R6C5 are covered by step 2)
a) CFO cage at R1C5: no 8,9 in R1C5, no 1,9 in R2C5, no 1,2 in R3C5
b) CFO cage at R2C3: no 9 in R2C3, no 1 in R3C3
c) CFO cage at R2C4: no 9 in R2C4, no 1 in R3C4
d) CFO cage at R2C8: no 8,9 in R2C8, no 1,9 in R2C9, no 1,2 in R3C9
e) CFO cage at R3C2: no 9 in R3C2, no 1 in R4C3
f) CFO cage at R4C4: no 9 in R4C4, no 1 in R4C5
g) CFO cage at R4C7: no 8,9 in R4C7, no 1,9 in R4C8, no 1,2 in R4C9
h) CFO cage at R6C1: no 8,9 in R6C1, no 1,9 in R6C2, no 1,2 in R6C3
i) NCFO cage at R6C1: {135/136/…/479//579}, R6C7 = {12345}, R6C8 = {34567}, R6C9 = {56789}
j) CFO cage at R7C1: no 8,9 in R7C1, no 1,9 in R7C2, no 1,2 in R8C3

1. 1 in N6 only in R46C7, locked for C7

2. The two CFO cages at R5C1 and R5C6 must be [1234/2345/5678/6789], R5C1 and R5C6 = {1256}, R5C2 and R5C7 = {2367}, R5C3 and R5C8 = {3478}, R5C4 and R5C9 = {4589} -> R5C5 = {159}
2a. The CFO cage at R6C5 must contain the same numbers as the CFO cage at R5C1 (can’t be the same as the cage at R5C6 because R5C6 and R6C5 are both in N5), R6C5 = {1256}, R7C5 = {2367}, R8C5 = {3478}, R9C5 = {4589}
2b. R6C5 must be the same as R5C1 -> 1 must be in R5C56 + R6C5, locked for N5

3. CFO cage at R4C4 = [23/34/45/56/67/78/89], no 2 in R4C5
3a. 2 in C5 only in CFO cage at R1C5 = [123/234] or in CFO cage at R6C5 = [1234/2345], 3 locked for C5, no 2 in R4C4, no 3,4 in R1C5, no 4 in R2C5
3b. No 3,4 in R1C5 -> CFO cage at R1C5 cannot be [345/456], no 5 in R2C5, no 5,6 in R3C5

4. NCFO cage at R6C1 cannot contain both of 4,5 -> either CFO cage at R4C7 contains at least one of 4,5 or CFO cage at R5C6 = [1234/2345], which each block CFO cage at R4C7 = [123] -> no 1 in R4C7, no 2 in R4C8, no 3 in R4C9
4a. R6C7 = 1 (hidden single in N6), placed for W4
4b. CFO cage at R6C5 = [2345/5678/6789], no 2 in R7C5, no 3 in R8C5, no 4 in R9C5
4c. CFO cage at R5C1 must contain the same numbers as the CFO cage at R6C5 = [2345/5678/6789], no 1 in R5C1, no 2 in R5C2, no 3 in R5C3, no 4 in R5C4
4d. CFO cage at R6C1: no 1 in R6C1 -> no 2 in R6C2, no 3 in R6C3

5. 9 in N6 only in R456C9, locked for C9
5a. No 9 in CFO cage at R2C8 -> no 7 in R2C8, no 8 in R2C9

6. 2 in N6 only in R45C7, locked for C7
6a. 2 in CFO cage at R4C7 = [234] or 2 in CFO cage at R5C6 = [1234] (locking cages), 3,4 locked for N6
6b. 2 in CFO cage at R4C7 = [234] or 2 in CFO cage at R5C6 = [1234] -> CFO cage at R5C6 cannot be [2345] (locking-out cages), no 2 in R5C6, no 3 in R5C7, no 4 in R5C8, no 5 in R5C9
6c. 2 in CFO cage at R4C7 = [234] or 2 in CFO cage at R5C6 = [1234] -> CFO cage at R4C7 cannot be [345/456] (locking-out cages), no 3,4 in R4C7, no 4,5 in R4C8, no 5,6 in R4C9
6d. Whichever of CFO cage at R4C7 and CFO cage at R5C6 doesn’t contain 2,3,4 must contain 7, locked for N6
6e. CFO cage at R4C7 cannot be [567] (which clashes with R6C8), no 5 in R4C7, no 6 in R4C8, no 7 in R4C9
6f. R6C8 = 5 (hidden single in N6), placed for W4, no 6 in R6C9 because of NCFO cage at R6C7
6g. Whichever of CFO cage at R4C7 and CFO cage at R5C6 doesn’t contain 2,3,4 must contain 6,7,8, locked for N6 -> R6C9 = 9, placed for hidden window R678C159, no 9 in R8C1
6h. no 6 in R5C6, no 7 in R45C7, no 8 in R45C8

7. Naked pair {26} in R45C7, locked for C7
7a. Naked pair {37} in R45C8, locked for C8
7b. Naked pair {48} in R45C9, locked for C9

8. CFO cage at R2C8 = [123/456], R2C8 = {14}, R2C9 = {25}, R3C9 = {36}

9. CFO cage at R6C1 = [234/678], R6C1 = {26}, R6C2 = {37}, R6C3 = {48}
9a. Naked pair {26} in R6C15, locked for R6

10. R6C5 = {26} -> CFO cage at R6C5 = [2345/6789], no 6 in R7C5, no 7 in R8C5, no 8 in R9C5
10a. CFO cage at R5C1 must contain the same numbers as the CFO cage at R6C5 = [2345/6789], no 5 in R5C1, no 6 in R5C2, no 7 in R5C3, no 8 in R5C4
10b. Naked pair {26} in R56C1, locked for C1 and N4
10c. Naked pair {37} in R56C2, locked for C2 and N4
10d. Naked pair {48} in R56C3, locked for C3 and N4

11. CFO cage at R2C3 = [12/23/56/67], no 3,7 in R2C3, no 5,9 in R3C3
11a. CFO cage at R2C4 = [45/89]

12. Naked pair {159} in R4C123, locked for R4
12a. CFO cage at R4C4 = [34/67/78], no 4,8 in R4C4, no 6 in R4C5

13. CFO cage at R5C1 must contain the same numbers as the CFO cage at R6C5 -> R1234C5 must contain the same numbers as the CFO cage at R5C6
13a. CFO cage at R6C5 = [1234/5678] -> R1234C5 = [1234/5678], R1C5 = {15}, R2C5 = {26}, R3C5 = {37}, R4C5 = {48}
13b. R4C45 = [34/78]
13c. Naked pair {37} in R4C38, locked for R4
13d. Naked pair {48} in R4C59, locked for R4 and hidden window R234C159, no 4,8 in R23C1
13e. Naked pair {26} in R4C67, locked for W2
13f. Naked pair {26} in R6C15, locked for hidden window R678C159, no 2,6 in R78C9
13g. Naked triple {159} in R159C5, locked for hidden window R159C159, no 1,5,9 in R19C19

14. CFO cage at R5C6 = [1234/5678]
14a. CFO cage at R5C1 = [6789] (cannot be [2345] which clashes with CFO cage at R5C6) -> CFO cage at R5C6 = [1234], R5C5 = 5, CFO cage at R6C5 = [6789]
14b. CFO cage at R6C1 = [234]
14c. Naked pair {78} in R6C46, locked for N5 -> R4C45 = [34]
14d. CFO cage at R1C5 = [123]
14e. CFO cage at R4C7 = [678], R4C6 = 2
[Catching up on the windows after these placements …]
14f. R23C5 = [23], placed for hidden window R234C159, no 2,3 in R23C19
14g. R4C8 = 7, placed for W2
14h. R5C234 = [789], placed for hidden window R159C234, no 7,8,9 in R19C234
14i. R5C678 = [123], placed for hidden window R159C678, no 1,2,3 in R19C678
14j. R78C5 = [78], placed for hidden window R678C159, no 7,8 in R78C19

15. R23C9 = [56] -> CFO at R2C8 = [456], R2C8 = 4, placed for W2

16. R3C8 = 1 (hidden single in N3)

17. Naked pair {13} in R78C9, locked for C9, N9 and hidden window R678C159, no 1,3 in R78C1
17a. R1C9 = 2 (hidden single in N3), R9C9 = 7, placed for hidden window R159C159, no 7 in R1C1

18. CFO cage at R2C4 = [67] (cannot be [78] which clashes with R6C4) -> R6C46 = [87]

19. Naked pair {45} in R78C1, locked for C1 and N7 -> R234C1 = [791], R3C7 = 8, placed for W2

20. CFO cage at R7C1 = [567] -> R8C1 = 4

and the rest is naked singles, without using the windows.
Solution:
3 5 6 4 1 8 7 9 2
7 8 1 6 2 9 3 4 5
9 4 2 7 3 5 8 1 6
1 9 5 3 4 2 6 7 8
6 7 8 9 5 1 2 3 4
2 3 4 8 6 7 1 5 9
5 6 9 2 7 3 4 8 1
4 1 7 5 8 6 9 2 3
8 2 3 1 9 4 5 6 7

(Non) Rating Comment:
I won't give a rating for my walkthrough. A few steps are technically in the 1.5 range, but this definitely isn't a 1.5 rated puzzle.


Top
 Profile  
Reply with quote  
 Post subject: Re: Two Zero Killers
PostPosted: Wed Jan 08, 2014 4:49 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Consecutive Semi Fully Ordered W4 was, for me, definitely the hardest of the three "real zero killers" posted by HATMAN in December.

It was made harder for me by the fact that, first time through, I accidentally omitted one possible combination: however my re-work did come up with a nice step which simplified my later steps.

Here is my walkthrough for Consecutive Semi Fully Ordered W4:
The four windows are numbered W1, W2, W3 and W4; the hidden windows will give their cells, for example hidden window R159C159.

Green bordered cages are non-consecutive, ordered ascending or descending
Red bordered cages are consecutive, fully ordered (CFO)

Prelims
a) CFO cage at R1C1: no 8,9 in R1C1, no 1,9 in R1C2, no 1,2 in R1C3
b) CFO cage at R1C4: no 8,9 in R1C4, no 1,9 in R1C5, no 1,2 in R2C5
c) CFO cage at R1C6: no 9 in R1C6, no 1 in R2C6
d) CFO cage at R1C9: no 8,9 in R1C9, no 1,9 in R2C9, no 1,2 in R3C9
e) CFO cage at R2C4: no 7,8,9 in R2C4, no 1,8,9 in R3C4, no 1,2,9 in R3C5, no 1,2,3 in R3C6
f) CFO cage at R4C1: no 9 in R4C1, no 1 in R5C1
g) CFO cage at R4C4: no 9 in R4C5, no 1 in R5C6
h) CFO cage at R4C6: no 9 in R4C6, no 1 in R4C7
i) CFO cage at R4C9: no 9 in R4C9, no 1 in R5C9
j) CFO cage at R5C2: no 9 in R5C2, no 1 in R5C3
k) CFO cage at R6C8: no 9 in R6C8, no 1 in R7C8
l) CFO cage at R7C1: no 8,9 in R7C1, no 1,9 in R8C1, no 1,2 in R9C1
m) CFO cage at R8C7: no 9 in R8C7, no 1 in R8C8
n) CFO cage at R9C5: no 9 in R9C5, no 1 in R9C6
o) CFO cage at R9C7: no 8,9 in R9C7, no 1,9 in R9C8, no 1,2 in R9C9
p) Non-consecutive ordered cages, no 1,2,8,9 in the middle cell -> R1C8 + R2C1 + R8C9 + R9C2 = {34567}

1. There are three CFO cages in N2 -> CFO cage at R2C4 = [1234/3456/4567/6789], CFO cage at R1C4 = [123/345/567/789], CFO cage at R1C6 = [12/45/56/89]
R1C4 = {1357}, R1C5 = {2468}, R1C6 = {1458}, R2C4 = {1346}, R2C5 = {3579}, R2C6 = {2569}, R3C4 = {2457}, R3C5 = {3568}, R3C6 = {4679}
1a. 9 in N2 only in R2C56 + R3C6, CPE no 9 in R2C78 using W2

[When I first did this puzzle, I carelessly omitted [56] from CFO cage at R1C6. I’ve therefore done some re-work, including the new step 9 which removes this combination and the new step 7 which removed several combinations from the non-consecutive ordered cage at R9C1.]

2. CFO cage at R1C1 cannot be [567] because R1C45 = [12/34] and there’s no possible non-consecutive cage at R1C7
2a. CFO cage at R1C1 cannot be [789] because R1C45 = [12/34/56] and there’s no possible non-consecutive cage at R1C7
2b. CFO cage at R1C1 = [123/234/345/456/678], no 5,7 in R1C1, no 6,8 in R1C2, no 7,9 in R1C3

3. R1C7 = 9 (hidden single in R1), placed for hidden window R159C678, no 9 in R5C68 + R9C6, clean-up: no 7 in R1C9, no 8 in R2C9, no 8 in R4C5, no 8 in R4C6, no 8 in R9C5
3a. Non-consecutive ordered cage at R1C7 contains 9 in R1C7 -> no 6 in R1C9, clean-up: no 7 in R2C9, no 8 in R3C9
3b. From remaining combinations for CFO cage at R1C1 and in R1C45, remaining possible combinations for non-consecutive ordered cage at R1C7 are {169/179/259/269/359/379/469/479}, no 3,4 in R1C8, no 5 in R1C9, clean-up: no 6 in R2C9, no 7 in R3C9
3c. 8 in N3 only in R23C78, locked for W2, no 8 in R4C78, clean-up: no 7 in R4C6

4. Non-consecutive, ordered cage at R1C1 = [146/158/159/169/259/269/379/479/631/641] (cannot be [13x/24x/35x/46x] which clash with CFO cage at R1C1, cannot be [147/257/258/268/368/369/642] which don’t allow two CFO cages in C1) -> R3C1 = {1689}
4a. CFO cage at R4C1 cannot be [89] (which clashes with non-consecutive, ordered cage at R1C1 or with CFO at R7C1 = [789] when non-consecutive, ordered cage at R1C1 = [146/631/641], no 8 in R4C1, no 9 in R5C1
4b. CFO cage at R7C1 cannot be [567], which clashes with non-consecutive, ordered cage at R1C1, no 5 in R7C1, no 6 in R8C1, no 7 in R9C1

5. Non-consecutive, ordered cage at R9C1 cannot be [531/579] which don’t allow two CFO cages in R9 -> no 5 in R9C1, clean-up: no 4 in R8C1, no 3 in R7C1
5a. CFO cage at R7C1 not [345] -> non-consecutive, ordered cage at R1C1 (step 4) = [146/158/159/169/259/379/479/631/641] (cannot be [269] which clashes with CFO cage at R7C1)

[Since working out interactions between two CFOs and a non-consecutive, ordered cage is rather tedious, I’ll use a short forcing chain which I’ve just spotted.]
6. 9 in R4 only in R4C234, locked for W1 => R3C1 = 9 (hidden single in N1) or R4C8 = 9, locked for W2, no 9 in R3C6
-> no 9 in R3C6, clean-up: no 8 in R3C5, no 7 in R3C4, no 6 in R2C4
6a. 9 in N2 only in R2C56, locked for R2
6b. 8 in N2 only in R1C56, locked for R1, clean-up: no 7 in R1C2, no 6 in R1C1
6c. Non-consecutive, ordered cage at R1C1, max R1C1 = 4 -> no 1 in R3C1
6d. CFO cage at R1C1 = [123/234/345/456] -> CFO cage at R1C4 (step 1) = [123/567/789] (cannot be [345] which clashes with CFO cage at R1C1), no 3 in R1C4, no 4 in R1C5, no 5 in R2C5
6e. CFO cage at R2C4 (step 1) = [1234/3456/4567], 4 locked for N2, clean-up: no 5 in R2C6
6f. 4 in N2 only in R2C4 + R3C46, CPE no 4 in R3C23 using W1

7. 8,9 in R4 only in R4C234 and R4C89
7a. R4C234 cannot contain both of 8,9 because R23C23 must contain at least one of 8,9 for N1
7b. R4C89 cannot contain both of 8,9 because R4C89 = [98] clashes with R45C9 = [89]
7c. Hidden killer pair 8,9 in R4C234 and R4C89 for R4, R4C234 and R4C89 must each contain one of 8,9
7d. R4C234 contains one of 8,9 -> R23C23 must contain one of 8,9 for W1 -> R3C1 = {89}
7e. R4C89 contains one of 8,9 -> R4C8 = 9 or R45C9 = [89], 9 in R4C8 + R5C9, locked for N6

8. CFO cage at R7C1 cannot be [789] which clashes with R3C1, no 7 in R7C1, no 8 in R8C1, no 9 in R9C1

[Removing [56] from CFO cage at R1C6 seems to require either a contradiction move or a forcing chain.]
9. Consider combinations for CFO cage at R1C1 = [123/234/345/456]
CFO cage at R1C1 = [123] => CFO cage at R1C9 = [456] => 6 in R1 only in CFO cage at R1C4 = [567]
or CFO cage at R1C1 = [234] => CFO cage at R1C9 = [123], CFO cage at R1C4 not [123] => 3 in N2 only in R2C4 => CFO cage at R2C4 = [3456]
or CFO cage at R1C1 = [345/456], no 5 in R1C6
-> no 5 in R1C6, no 6 in R2C6

10. Consider combinations for CFO cage at R1C4 = [123/567/789]
CFO cage at R1C4 = [123] => R1C8 = 7 (hidden single in R1)
or CFO cage at R1C4 = [567] => R1C8 = 7 (hidden single in R1)
or CFO cage at R1C4 = [789] => CFO cage at R1C6 = [12] => CFO cage at R1C1 = [345/456] (cannot be [234] which clashes with R1C69, ALS block), 5 locked for R1
-> no 5 in R1C8
10a. 5 in R1 only in R1C234, locked for hidden window R159C234, no 5 in R59C234, clean-up: no 4 in R5C2, no 6 in R5C3
10b. CFO cage at R6C8 cannot be [67], which clashes with R1C8, no 6 in R6C8, no 7 in R7C8

11. 5 in R9 only in CFO cage at R9C5 = [45/56] or in CFO cage at R9C7 = [345/456/567] -> CFO cage at R9C7 cannot be [234] (which doesn’t allow a valid combination for non-consecutive ordered cage at R9C1), no 2 in R9C7, no 3 in R9C8, no 4 in R9C9
11a. CFO cage at R9C5 cannot be [12/34/67] because combined with CFO cage at R9C7 = [345/456/567] they don’t allow valid combinations for non-consecutive ordered cage at R9C1 and CFO at R7C1), no 1,3,6 in R9C5, no 2,4,7 in R9C6
11b. From the remaining combinations for CFO cage at R9C5 = [45/56] and CFO cage at R9C7, combinations for non-consecutive, ordered cage at R9C1 are from three of <1489/4789> (cannot be <1236/1239/1269> because 1,2,9 only in R9C34) = [841/479], R9C4 = {89} clean-up: no 2,5 in R8C1, no 1,4 in R7C1

12. Non-consecutive, ordered cage at R1C1 (step 5a) = [158/159/169/259] (cannot be [146/379/479] which clash with CFO cage at R7C1), no 3,4 in R1C1, clean-up: no 4,5 in R1C2, no 5,6 in R1C3

13. R1C4 = 5 (hidden single in R1) -> CFO cage at R1C4 = [567], 6 placed for hidden window R159C159, no 6 in R5C19 + R9C9
13a. R1C8 = 7, placed for hidden window R159C678, no 7 in R5C67 + R9C7
13b. R3C5 = 3 -> CFO cage at R1C4 = [1234], 1,2 placed for W1, no 1,2 in R234C23, 3 placed for hidden window R234C159, no 3 in R24C19, 4 placed for W2, no 4 in R24C78
13c. CFO cage at R1C6 = [89], 9 placed for W2, no 9 in R4C8
13c. Clean-up: no 2 in R2C9, no 1,2 in R1C9, no 3 in R4C6, no 5 in R4C7, no 8 in R7C8, no 6 in R8C7, no 4,6 in R9C7, no 5,8 in R9C8, no 8,9 in R9C9
[Cracked. The rest is fairly straightforward.
From here on, I’ve only given the most useful hidden window placements.]

14. R1C1 = 1 (hidden single in R1) -> CFO cage at R1C1 = [123], 2,3 placed for hidden window R159C234, no 2,3 in R5C234, CFO cage at R1C9 = [456], 5,6 placed for hidden window R234C159, no 5,6 in R2C1 + R4C15 -> R2C1 = 4, placed for hidden window R234C159, no 4 in R4C5, CFO cage at R7C1 = [678], R3C1 = 9, R4C1 = 2, R4C5 = 1, R5C6 = 2, R9C234 = [419], placed for hidden window R159C234, no 1,4,9 in R5C234, clean-up: no 3 in R4C7, no 8 in R5C2

15. R89C9 = [37] -> non-consecutive, ordered cage at R7C9 = [137], CFO cage at R9C7 = [567], CFO cage at R9C5 = [23], R456C9 = [892], clean-up: no 4,5 in R6C8, no 9 in R7C8

16. R4C234 = {349} (naked triple in W1), locked for R4, 9 and locked for N4 -> R4C8 = 5, R4C67 = [67]

17. Naked triple {678} in R5C234, locked for R5
17a. R6C7 = 6 (hidden single in N6)
17b. R5C2 = 6 (hidden single in N4) -> CFO cage at R5C2 = [67]
17c. R2C23 = [86]

18. R8C8 = 9 (hidden single in N9) -> CFO cage at R8C7 = [89], R3C78 = [18]

19. Naked pair {25} in R8C23 = [52] -> R7C23 = [39], R3C23 = [75], R4C234 = [943], R6C2 = 1, R8C6 = 1

20. R6C8 = 3 -> CFO cage at R6C8 = [34]

and the rest is naked singles, without using the windows.

Rating Comment:
I'll rate my walkthrough for Consecutive Semi Fully Ordered W4 at least 1.5.


Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 4 posts ] 

All times are UTC


Who is online

Users browsing this forum: Bing [Bot] and 6 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
Powered by phpBB® Forum Software © phpBB Group