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 Post subject: Anti-kNight X 1 & 1A
PostPosted: Mon Dec 17, 2012 1:28 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
Anti-kNight X1

Not done one of these for a while.

Note it is X.

Note it is Anti-kNight: cells a knights move apart cannot have the same number.

Note the three disjoint cages.

Quite a sweet one - I used a couple of small fishes.



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JS Code
3x3:d:k:13:14:15:16:4868:17:18:19:20:21:6657:3337:22:4868:23:3595:6657:24:3596:3337:2562:25:4868:26:2562:3595:27:3596:28:29:6659:30:6659:31:32:33:4358:4358:4358:34:35:36:3079:3079:3079:37:38:39:6659:40:6659:41:42:43:44:4106:2562:45:3589:46:2562:3080:47:48:6657:4106:49:3589:50:3080:6657:51:52:53:54:55:3589:56:57:58:59:

Solution:
162985743
879342561
543671298
956817324
728493615
314526879
691258437
287134956
435769182



Plus a harder one 1A:

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3x3:d:k:21:22:2834:2834:4868:3087:3087:23:24:25:6657:3337:26:4868:27:3595:6657:28:3596:3337:2562:29:4868:30:2562:3595:31:3596:32:33:6659:34:6659:35:36:37:2318:2318:38:39:40:41:42:43:44:2324:45:46:6659:47:6659:48:49:4109:2324:4106:2562:50:3589:51:2562:3080:4109:52:6657:4106:53:3589:54:3080:6657:55:56:57:3088:3088:3589:2577:2577:58:59:

Same Solution


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 Post subject: Re: Anti-kNight X 1 & 1A
PostPosted: Tue Jan 01, 2013 8:08 pm 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
HATMAN wrote:
Quite a sweet one - I used a couple of small fishes.
Lovely puzzle. Lots of fish of varying sizes. Some wacky eliminations from the AN aspect of the puzzle. Really good variant. Couldn't get very far on the A version.

Thanks and Happy New Year!
Ed


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 Post subject: Re: Anti-kNight X 1 & 1A
PostPosted: Thu Jan 03, 2013 8:00 am 
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Grand Master
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Happy New Year! Thanks HATMAN. It was fun rediscovering the useful implications of the anti-kNight property.
Here is how I started 1A.

Hidden Text:
1. Starting off
Green = {1234}
16/2@r6c9 = {79}
16/2@r7c2 = {79}
-> (79) locked in r7

Innies c5 r456c5 = +12
-> r5c46 = +7 -> no (789)


2. '79' - Breakthrough
Whichever of (79) goes in r6c9 also goes in r7c2
-> must go in r4c13 in n4
-> must go in r5c5 in n5
-> must go in r4c1 in n4

But that cannot be a 7 (in 14/2) -> must be a 9
-> r4c1 = r5c5 = r6c9 = r7c2 = 9
-> r3c1 = 5, r7c9 = 7, r8c3 = 7

Also r46c5 = {12}
-> r5c46 = {34}
Also Pink = {5678}
Also Yellow = {5678}
Also Corners = {1234}


3. Following from that
7 in r8c3 prevents 7 being in 14/3@r6c5
-> 19/3@r1c5 = {478} and 14/3@r7c5 = {356}

Now 3 in r5c46 prevents 3 from being in r7c5
-> 3 in r89c5
which prevents 3 from being in r9c7
-> HS 7 in n8 -> r9c4 = 7
-> r9c3 = 5

Also 9 in n8 only in r89c6
-> 9 in n9 only in r89c7
-> 10/2@r9c6 = {19}

Also 9 in n1 only in r12c3 and 9 in n2 only in r12c4
-> 11/2@r1c3 = {29}
Also -> 9 in n3 can only be in r3c8
-> 14/2@r2c7 = [59]
-> HS 5 in n2 r1c6 = 5
-> 12/2@r1c6 = [57]
-> HS 7 in Yellow r2c2 = 7
-> 13/2@r2c3 = [94]
-> 11/2@r1c3 = [29]

Also HS 7 in Pink r4c6 = 7
Also HS 5 in Yellow r8c8 = 5
-> HS 5 in Pink r6c4 = 5

etc., etc.,


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 Post subject: Re: Anti-kNight X 1 & 1A
PostPosted: Fri Feb 03, 2017 12:17 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
As I said in my recent post for Anti-kNight 2 Non-Consecutive I'd try this one next. So far I've just done the easier one; which is clearly easier since there's an early placement. Even so it wasn't that easy; see rating comment.

Nice cage design, using the AN properties. I particularly enjoyed finding step 7.

Here is my walkthrough for Anti-kNight X 1:
This is Anti-kNight, Killer-X. 26(4) R28C28, 10(4) R37C37 and 26(4) R46C46 are disjoint cages.

Prelims

a) 13(2) cage at R2C3 = {49/58/67}, no 1,2,3
b) 14(2) cage at R2C7 = {59/68}
c) 14(2) cage at R3C1 = {59/68}
d) 16(2) cage at R7C2 = {79}
e) 12(2) cage at R7C8 = {39/48/57}, no 1,2,6
f) 19(3) cage at R1C5 = {289/379/469/478/568}, no 1
g) 26(4) disjoint cage at R28C28 = {2789/3689/4589/4679/5678}, no 1
h) 10(4) disjoint cage at R37C37 = {1234}
i) 26(4) disjoint cage at R46C46 = {2789/3689/4589/4679/5678}, no 1

Steps resulting from Prelims
1a. 16(2) cage at R7C2 = {79}, locked for N7
1b. 16(2) cage = {79} -> no 7,9 in R6C4 (AN)
1c. 10(4) disjoint cage at R37C37 = {1234}, CPE no 1,2,3,4 in R5C5 using diagonals

2. 45 rule on R5 3 innies R5C456 = 16
2a. 45 rule of C5 3 innies R456C5 = 12
2b. Total of 26(4) disjoint cage at R46C46 and two hidden 12(3) and 16(3) cages = 54 with R5C5 used for both hidden cages, i.e. one extra use -> R5C5 = 9, placed for both diagonals
2c. R5C5 = 9 -> no 9 in R37C46 + R46C37 (AN)
2d. R456C5 = 12 = {129} -> R46C5 = {12}, locked for C5 and N5
2e. Naked pair {12} in R46C5 -> no 1,2 in R5C37 (AN)
2f. R5C456 = 16 = {349} -> R5C46 = {34}, locked for R5 and N5
2g. Naked pair {34} in R5C46 -> no 3,4 in R37C5 (AN)
2h. 26(4) disjoint cage at R28C28 = {5678}
2i. Naked quad {5678} in R2C2 + R4C4 + R6C6 + R8C8, locked for D\
2j. Naked quad {5678} in R2C8 + R4C6 + R6C4 + R8C2, locked for D/
2k. 19(3) cage at R1C5 = {478/568}, no 3, 8 locked for C5 and N2
2l. 19(3) cage at R1C5 = {478/568}, no 8 in R2C37 (AN), clean-up: no 5 in R3C2, no 6 in R3C8
2m. 3 in C5 only in 14(3) cage at R7C5, locked for N8
2n. 3 in C5 only in R89C5 -> no 3 in R8C7 + R9C37 (AN), clean-up: no 9 in R7C8

3. 17(3) cage at R5C1 = {278} (only remaining combination), locked for R5 and N5, clean-up: no 6 in R3C1
3a. 17(3) cage at R5C1 = {278} -> no 7,8 in R37C2 (AN) -> 16(2) cage at R7C2 = [97], R5C3 = 8, clean-up: no 4,5,6 in R2C3, no 6 in R3C2, no 5 in R7C8
3b. 13(2) cage at R2C3 = [94], clean-up: no 5 in R3C8, no 5 in R4C1
3c. R3C2 = 4 -> no 4 in R2C4 (AN)
3d. R5C3 = 8 -> no 8 in R7C4 (AN)
3e. Naked pair {56} in R25C7, locked for C7, clean-up: no 7 in R7C8
3f. Naked pair {27} in R5C12 -> no 2 in R7C1 (AN)
3g. Naked triple {156} in 12(3) cage at R5C7, locked for N6
3h. 1 in R5 only in R5C89 -> no 1 in R37C9 (AN)
3i. 10(4) disjoint cage at R37C37 = {1234}, 4 locked for R7, clean-up: no 8 in R8C7
3j. 4 in R7 only in R7C37 -> no 4 in R8C5 (AN)
3k. 26(4) disjoint cage at R28C28 = {5678}, 7 locked for R2
3l. 9 in N2 only in R1C46, locked for R1
3m. 4 on D\ only in R7C7 + R9C9, locked for N9
3n. 4 in R7C7 + R9C9 -> no 4 in R6C9 + R9C6 (AN)
[I carelessly omitted the AN steps after placements for 16(2) cage at R7C2, which would have simplified things slightly. However it’s the same after step 4.]

4. 19(3) cage at R1C5 (step 2k) = {478} (cannot be {568} which clashes with R2C7, AN), locked for C5 and N2
4a. 4 in C5 only in R12C5 -> no 4 in R1C7 (AN)
4b. Naked triple {356} in 14(3) cage at R7C5, locked for N8

5. 7 on D/ only in R2C8 + R4C6, CPE no 7 in R4C8
5a. 7 on D/ only in R2C8 + R4C6 -> no 7 in R4C79 (AN)
5b. 7 in N6 only in R6C789, locked for R6

6. R5C1 = 7 (hidden single in C1)
6a. R5C2 = 2 -> no 2 in R37C3 (AN)
6b. 10(4) disjoint cage at R37C37 = {1234}, 2 locked for C7

7. R3C37 + R4C5 form naked triple triangle (because of AN) = {123}, 3 locked for R3 and 10(4) disjoint cage at R37C37
7a. 2 in R3C7 + R4C5 -> no 2 in R4C9 (AN)
7b. R37C3 + R5C4 form naked triple triangle (because of AN) = {134}, 1 locked for C3 and 10(4) disjoint cage at R37C37
7c. 3 in R3C3 + R5C4 -> no 3 in R1C4 (AN)
7d. 4 in R5C4 + R7C3 -> no 4 in R9C4 (AN)
7e. R37C7 + R5C6 form naked triple triangle (because of AN) = {234} -> no 3 in R1C6, no 4 in R9C6 (AN)
7f. R6C5 + R7C37 form naked triple triangle (because of AN) = {124} -> no 1 in R6C1, no 2 in R6C9 (AN)
7g. 3 in N2 only in R2C46, locked for R2
7h. 1 in N4 only in R46C2, locked for C2
7i. 2 in N6 only in R46C8, locked for C8
7j. 4 in N8 only in R8C46, locked for R8

8. 12(2) cage at R7C8 = [39]
8a. R8C7 = 9 -> no 9 in R6C8 (AN)
8b. 3 on D\ only in R1C1 + R3C3, locked for N1

9. 4 in C1 only in R69C1 -> no 4 in R7C3 (AN)
9a. R7C3 = 1, placed for D/, R3C3 = 3, R3C7 = 2, placed for D/, R7C3 = 4
9b. R3C3 = 3 -> no 3 in R5C4 (AN)
9c. R3C7 = 2 -> no 2 in R1C6 + R4C5 (AN)
9d. R7C3 = 1 -> no 1 in R6C5 + R9C4 (AN)
9e. R7C7 = 4 -> no 4 in R5C6 + R6C9 (AN)
9f. R46C5 = [12] -> no 1 in R2C46, no 2 in R8C46 (AN)
9g. R5C46 = [43], R2C4 = 3 (hidden single in C4), R8C6 = 4 (hidden single in C6)
9h. R4C8 = 2 (hidden single in R4), R6C2 = 1 (hidden single in R6)
9i. R7C3 = 1 -> no 1 in R9C4 (AN)
9j. 1 in R3 only in R3C46, locked for N2

10. R3C8 = 9 (hidden single in C8) -> R2C7 = 5
10a. R2C7 = 5 -> no 5 in R4C6 (AN)
10b. R5C7 = 6 -> no 6 in R3C6 (AN)
10c. Naked pair {15} in R5C89 -> no 5 in R7C9 (AN)
10d. 26(4) disjoint cage at R28C28 = {5678}, 5 locked for R8
10e. 5 in N9 only in R89C8, locked for C8 -> R5C89 = [15]
10f. 5 in R4 only in R4C234 -> no 5 in R6C3 (AN)

[Looks like I need to try forcing chains now.]
11. Consider placement for 2 on D\
R1C1 = 2
or R9C9 = 2 => R8C1 = 2 (hidden single in N7)
-> no 2 in R2C1
11a. R2C6 = 2 (hidden single in R2)

12. Consider placement for 4 in R4
R4C3 = 4 => R9C1 = 4 (hidden single in C1), placed for D/
or R4C9 = 4
-> no 4 in R1C9
12a. R1C9 = 3, placed for D/, R9C1 = 4

13. Consider permutations for R34C1 = [59/86]
R34C1 = [59] => R3C6 = 1, R3C4 = 6 => no 6 in R2C2 (AN)
or R34C1 = [86] => no 6 in R2C2 (AN)
-> no 6 in R2C2 (AN)
13a. Variable hidden killer pair 5,6 in R1C23 and R23C1 for N1, R1C23 cannot be {56} which clashes with R1C46 = {569} -> R23C1 must contain at least one of 5,6 -> R34C1 = [59] (cannot be [86] because R234C1 = [186] doesn’t contain either of 5,6)
13b. R3C1 = 5 -> no 5 in R4C3 (AN)
13c. Naked pair {46} in R46C3, locked for C3 and N4 -> R19C3 = [25], R6C1 = 3, R1C1 = 1, placed for D\
13d. Naked pair {68} in R7C1 + R8C2, locked for N7
13e. Naked pair {68} in R7C1 + R8C2 -> no 6 in R6C3 (AN)
13f. R6C4 = 5 (hidden single on D/)
13g. R46C3 = [64]
13g. Naked pair {78} in R6C78, locked for R6 and N6

14. R2C59 = [41] (hidden pair in R2)
14a. Naked pair {78} in R1C57, locked for R1, R1C2 = 6, R8C2 = 8, placed for D/

and the rest is naked singles, without using anti-knight or diagonals.

Rating Comment:
SS score 1.25. Probably low. In score mode it used X-cycles, which seem to be equivalent to short forcing chains or JSudoku's fishes.


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 Post subject: Re: Anti-kNight X 1 & 1A
PostPosted: Sat Feb 04, 2017 2:44 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
And then I tried the harder one. It proved to be a One-Trick Pony. One fairly early step cracks this puzzle, either wellbeback's elegant clone move or my slightly more mundane forcing chain; after that it's straightforward. For that reason I found the easier version of the puzzle to be the more interesting of the two.

Here is my walkthrough for Anti-kNight X 1A:
This is Anti-kNight, killer-X. 26(4) R28C28, 10(4) R37C37 and 26(4) R46C46 are disjoint cages.

Prelims

a) R1C34 = {29/38/47/56}, no 1
b) R1C67 = {39/48/57}, no 1,2,6
c) 13(2) cage at R2C3 = {49/58/67}, no 1,2,3
d) 14(2) cage at R2C7 = {59/68}
e) R34C1 = {59/68}
f) R5C12 = {18/27/36/45}, no 9
g) R67C1 = {18/27/36/45}, no 9
h) R67C9 = {79}
i) 16(2) cage at R7C3 = {79}
j) 12(2) cage at R7C8 = {39/48/57}, no 1,2,6
k) R9C34 = {39/48/57}, no 1,2,6
l) R9C67 = {19/28/37/46}, no 5
m) 19(3) cage at R1C5 = {289/379/469/478/568}, no 1
n) 26(4) disjoint cage at R28C28 = {2789/3689/4589/4679/5678}, no 1
o) 10(4) disjoint cage at R37C37 = {1234}
p) 26(4) disjoint cage at R46C46 = {2789/3689/4589/4679/5678}, no 1

Steps resulting from Prelims
1a. R67C9 = {79}, locked for C9
1b. R67C9 = {79} -> no 7,9 in R5C8 + R6C7 (AN)
1c. Naked pair {79} in R7C39, locked for R7, clean-up: no 2 in R6C1, no 3,5 in R8C7
1d. 16(2) cage at R7C3 = {79}, locked for N7, clean-up: no 3,5 in R9C4
1e. 16(2) cage at R7C3 = {79} -> no 7,9 in R6C24 (AN)
1f. 10(4) disjoint cage at R37C37 = {1234}, CPE no 1,2,3,4 in R5C5 using diagonals

2. 45 rule on C5 3 innies R456C5 = 12
2a. Min R5C5 = 5 -> max R46C5 = 7, no 7,8,9 in R46C5
2b. 45 rule on N5 (using R456C5 = 12) 2 remaining innies R5C46 = 7 = {16/25/34}, no 7,8,9

3. Consider placements for 7 in N4
One of R4C2 + R5C123 = 7 => no 7 in R7C2 (AN)
or R4C3 = 7 => no 7 in R5C5 (AN) => R5C7 = 7 (hidden single in R5) => R67C9 = [97]
or R6C13 = 7 => R67C9 = [97]
-> R7C2 = 9, R8C3 = 7, R67C9 = [97], clean-up: no 4 in R1C4, no 4 in R2C3, no 6 in R3C2, no 5 in R7C8, no 3 in R9C6
[Cracked; the rest is straightforward]
3a. R7C2 = 9 -> no 9 in R5C3 (AN)
3b. R5C5 = 9 (hidden single in R5), placed for both diagonals
3c. R5C5 = 9 -> no 9 in R3C46 + R4C3 (AN)
3c. 26(4) disjoint cage at R28C28 = {5678}, 7 locked for R2
3d. 26(4) disjoint cage at R46C46 = {5678}, locked for N5
3e. R5C46 (step 2b) = {34}, locked for R5 and N5, clean-up: no 5,6 in R5C12
3f. Naked pair {34} in R5C46 -> no 3,4 in R37C5 (AN)
3g. Naked pair {12} in R46C5, locked for C5
3h. Naked pair {12} in R46C5 -> no 1,2 in R5C37 (AN)

4. R4C1 = 9 (hidden single in R4) -> R3C1 = 5, clean-up: no 6 in R1C4, no 8 in 13(2) cage at R2C3, no 9 in R2C7, no 4 in R67C1

5. 19(3) cage at R1C5 = {478} (cannot be {568} which clashes with R7C5), locked for C5 and N2
5a. Naked triple {478} in 19(3) cage -> no 8 in R2C7 (AN)
5b. Naked triple {356} in 14(3) cage at R7C5, locked for N8
5c. 3 in C5 only in R89C5 -> no 3 in R9C37 (AN)
5c. Clean-up: no 3,4 in R1C3, no 4,5,8 in R1C7, no 6 in R3C8, no 9 in R9C4, no 7 in R9C6, no 4 in R9C7

6. R7C15 = [65] (hidden pair in R7) -> R6C1 = 3
6a. 7 in N4 only in R4C2 + R5C12 -> no 7 in R3C2 (AN)
6b. 13(2) cage at R2C3 = [94]
6c. R3C589 = [798] (hidden triple in R3), R2C7 = 5
6d. 26(4) disjoint cage at R28C28 = {5678}, 5 locked for R8
6e. 10(4) disjoint cage at R37C37 = {1234}, 4 locked for R7
6f. R1C46 = {59} (hidden pair in N2)
6g. Clean-up: no 8 in R1C3, no 2 in R1C4, no 8 in R8C7

7. 4 in C1 only in R89C1, locked for N7, clean-up: no 8 in R9C4
7a. 10(4) disjoint cage at R37C37 = {1234} -> R7C7 = 4, R8C7 = 9 -> R7C8 = 3
7b. R9C46 = [79] (hidden pair in N8) -> R9C37 = [51], R1C46 = [95] -> R1C37 = [27], R7C3 = 1, placed for D/, R3C3 = 3, R3C7 = 2, placed for D/
7c. R8C2 + R9C1 = [84], both placed for D/, R2C8 = 6, placed for D/
7d. R3C3 = 3 -> no 3 in R5C4 (AN) -> R5C46 = [43]
7e. R2C46 = [32] (hidden pair in N2) -> no 2 in R4C5 (AN)
7f. R5C1 = 7 (hidden single in C1) -> R5C2 = 2
7g. Naked pair {68} in R5C37, locked for R5

and the rest is naked singles, without using anti-knight or diagonals.

Rating Comment:
SS score 1.55. It probably didn't solve it the way either wellbeback or I did. My forcing chain will be in the lower half of the 1.5 range.


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