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 Post subject: Fers NC Windoku pairs 1
PostPosted: Wed Mar 06, 2013 12:16 pm 
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Grand Master
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Location: Saudi Arabia
Fers NC W pairs 1 (pointing practice)

Fers NC: diagonally adjacent cells are non-consecutive.

Windoku: remember the hidden windows

Not too hard a puzzle with a nice solution path.


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PostPosted: Fri Jan 22, 2016 5:44 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
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Another interesting puzzle which I found while looking back through this forum for interesting puzzles for which nobody had posted a walkthrough. Thanks HATMAN.

HATMAN wrote:
Windoku: remember the hidden windows
The way I solved it there wasn't any need to remember the hidden windows, so I didn't include my usual note about them.

I haven't done many Fers NC puzzles, so it took me a bit of time to find steps 6b and 6c. Then while checking my walkthrough I noticed a better way to express these steps. Probably part of what HATMAN was referring to as a nice solution path.

Here is my walkthrough:
This puzzle is Fers NC and a Windoku.

I’ll skip Prelims, because there are some NCs in the pairs, which are all diagonally-connected.

1a. 5(2) cage at R2C8 = {14} (cannot be {23} which is NC), locked for N3 and W2
1b. 7(2) cage at R2C7 = {25}, locked for W2
1c. 12(2) cage at R3C8 = {39}, locked for W2
1d. R2C6 = {678} -> no 7 in R13C5 (Fers NC)
1e. R4C6 = {678} -> no 7 in R5C5 (Fers NC)
1f. R4C8 = {678} -> no 7 in R5C79 (Fers NC)

2a. 7(2) cage at R2C3 = {16/25} (cannot be {34} which is NC)
2b. 14(2) cage at R3C2 = {59/68}
2c. Killer pair 5,6 in 7(2) and 14(2) cages, locked for W1
2d. 11(2) cage at R2C2 = {29/38/47}, no 1

3a. 7(2) cage at R7C4 = {16/25} (cannot be {34} which is NC)
3b. 9(2) cage at R6C3 = {18/27/36} (cannot be {45} which is NC), no 4,5,9
3c. 11(2) cage at R7C3 = {29/38/47} (cannot be {56} which clashes with 7(2) cage), no 1,5,6

4a. 16(2) cage at R7C7 = {79}, locked for N9 and W4
4b. 10(2) cage at R6C7 = {28/46}
4c. 9(2) cage at R7C6 = {18/36} (cannot be {45} which is NC)
4d. Killer pair 6,8 in 9(2) and 10(2) cage, locked for W4
4e. R8C8 = {79} -> no 8 in R7C9 + R9C79 (Fers NC)

5. 7(2) cage at R2C3 (step 2a) = {16/25}, 14(2) cage at R3C2 (step 2b) = {59/68} -> combined cage = {16}{59}/{25}{68} -> 11(2) cage at R2C2 (step 2d) = {38/47} (cannot be {29} which clashes with combined cage)
5a. 45 rule on W1 3 innies R2C4 + R4C24 = 13 = {139/238/247} (cannot be {148} which clashes with 11(2) cage)
[I noted that 5,6 cannot be diagonally-adjacent -> either R24C3 = {56} or R3C24 = {56}
I’ll need to wait until later to use this.]

6. 7(2) cage at R7C4 (step 3a) = {16/25}, 9(2) cage at R6C3 (step 3b) = {18/27/36} -> combined cage = {16}{27}/{25}{18}/{25}{36}, 2 locked for W3 -> 11(2) cage at R7C3 (step 3c) = {38/47}
6a. 45 rule on W3 R6C24 + R8C4 = 18 contains 9 = {189/369/459}, no 7
6b. Triple combined cages 7(2), 9(2) and 11(2) = {25}{18}{47}/{25}{36}{47} (cannot be {16}{27}{38} which clash with hidden cage R6C24 + R8C4 = {459}, Fers NC for either of 3,8 in R7C3) -> 7(2) cage = {25}, locked for W3, 11(2) cage = {47}, locked for N7 and W3
6c. 11(2) cage = {47} -> hidden cage R6C24 + R8C4 = {189} (cannot be {369} because of Fers NC, whichever of 4,7 is in R7C3) -> 9(2) cage = {36}
[With hindsight, I didn’t need to reduce 11(2) cage to one combination first. 11(2) cage = {38/47} eliminates {369/459} from hidden cage R6C24 + R8C4 using Fers NC and W3.]
6d. Hidden cage R6C24 + R8C4 = {189} -> no 7 in R7C3 (Fers NC)
6e. R7C3 = 4, R8C2 = 7, R8C8 = 9, R7C7 = 7, R3C8 = 3, R4C7 = 9
6f. R3C8 = 3 -> no 2,4 in R2C79 + R4C9
6g. R2C7 = 5, R3C6 = 2
6h. Clean-up: no 8 in R2C2, no 5 in R3C2, no 6 in R6C7
6i. 2 in R2 only in R2C13, locked for N1
6j. 2 in R2 only in R2C13 -> no 1,3 in R1C2 (Fers NC)
6k. R2C2 = {34} -> no 3,4 in R1C13 + R3C1 (Fers NC)
6l. 3 in N1 only in R2C12, locked for R2
6m. R3C3 = {78} -> no 7,8 in R2C4 + R4C24 (Fers NC + W1)
6n. Other Fers NC eliminations: no 4,6 in R1C68, no 1,3 in R24C5, no 8 in R5C68, no 6,8 in R7C1 + R9C13

7. R2C4 + R4C24 (step 5a) = {139} (only remaining combination) -> R2C4 = 9, R4C24 = {13}, locked for R4 and W1, R2C2 = 4 -> R3C3 = 7, R2C8 = 1, R3C7 = 4
7a. R2C3 = 2 (hidden single in W1) -> R3C4 = 5, R7C4 = 2, R8C3 = 5
7b. Fers NC eliminations: no 8 in R1C35 + R3C5, no 1,3 in R1C4, no 4,6 in R2C5 + R4C35, no 1,3 in R6C35 + R8C5, no 4,6 in R7C2 + R9C24
7c. R4C3 = 8, R3C2 = 6, R6C3 = 6, R7C2 = 3, R4C24 = [13], R6C2 = 9, R5C3 = 3
7d. Naked pair {67} in R4C68, locked for R4 and W2 -> R2C6 = 8, R2C159 = [376], R4C159 = [425], R7C19 = [91], R7C568 = [568], R8C7 = 3, R6C78 = [24], R68C6 = [51]

and the rest is naked singles, without using Fers NC or the windows.

Solution:
+-------+-------+-------+
| 1 5 9 | 4 6 3 | 8 2 7 |
| 3 4 2 | 9 7 8 | 5 1 6 |
| 8 6 7 | 5 1 2 | 4 3 9 |
+-------+-------+-------+
| 4 1 8 | 3 2 7 | 9 6 5 |
| 5 2 3 | 6 9 4 | 1 7 8 |
| 7 9 6 | 1 8 5 | 2 4 3 |
+-------+-------+-------+
| 9 3 4 | 2 5 6 | 7 8 1 |
| 6 7 5 | 8 4 1 | 3 9 2 |
| 2 8 1 | 7 3 9 | 6 5 4 |
+-------+-------+-------+


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