SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Fri Apr 19, 2024 11:29 pm

View unanswered posts | View active topics


Board index » Puzzles and Solutions » Killer Puzzles

All times are UTC




Post new topic Reply to topic  Page 1 of 1
  [ 6 posts ] 
  Print view Previous topic | Next topic 
Author Message
HATMAN
 Post subject: Assassin 324 X
PostPosted: Fri Sep 11, 2015 6:19 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
Assassin 12/13 324 X

As often happens with a concept it works OK, but explicit feasible examples bounce from easy to impossible. This is SS 1.25 but I think easier.

Note disjoint cage at R7c13.

I have a new HS that I'm happy is hidden and both programs fail completely. However I'm on my sixth version and still not happy to post these HS as they are still Ruudiculous or very easy. Because I'm happy with the HS bit I want the rest of the puzzle to be at assassin level.

Image


JS Code
3x3:d:k:3073:3073:13:3083:15:16:17:18:3330:19:3073:3073:3083:3337:21:23:3330:3330:24:25:3340:3337:3337:3337:26:3330:27:28:29:30:3340:3333:3333:3079:31:32:33:34:3078:35:3333:3333:3079:3079:36:3078:3078:3078:37:38:39:3079:40:41:3094:3332:3094:3336:3336:3336:42:3342:3342:3332:3332:3348:43:3336:44:3075:3075:45:3332:46:3348:47:48:3338:3338:3075:3075:

Solution:

127896543
863425971
594173826
786931254
932754168
451268397
319642785
248517639
675389412


Last edited by HATMAN on Thu Sep 17, 2015 10:07 am, edited 1 time in total.

Top
 Profile  
Reply with quote  
Andrew
 Post subject: Re: Assassin 324 X
PostPosted: Tue Sep 15, 2015 3:36 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada
It's well over a month since I last did an Assassin.

Thanks HATMAN for an interesting and enjoyable puzzle; I liked the 12/13 concept with 2 and 4 cell cages.

HATMAN wrote:
This is SS 1.25 but I think easier.
Maybe you saw my step 4a as a Human Solvable step, or found an easier way. I've rated my walkthrough a bit higher.

Here is my walkthrough for Assassin 324X:
Prelims

a) 12(4) cage at R1C1 = {1236/1245}, no 7,8,9
b) R12C4 = {39/48/57}, no 1,2,6
c) 13(4) cage at R1C9 = {1237/1246/1345}, no 8,9
d) 13(4) cage at R2C5 = {1237/1246/1345}, no 8,9
e) 13(2) cage at R3C3 = {49/58/67}, no 1,2,3
f) 13(4) cage at R4C5 = {1237/1246/1345}, no 8,9
g) 12(4) cage at R4C7 = {1236/1245}, no 7,8,9
h) 12(4) cage at R5C3 = {1236/1245}, no 7,8,9
i) R7C13 = {39/48/57}, no 1,2,6
j) 13(4) cage at R7C2 = {1237/1246/1345}, no 8,9
k) 13(4) cage at R7C4 = {1237/1246/1345}, no 8,9
l) R7C89 = {49/58/67}, no 1,2,3
m) R89C3 = {49/58/67}, no 1,2,3
n) 12(4) cage at R8C7 = {1236/1245}, no 7,8,9
o) R9C67 = {49/58/67}, no 1,2,3

Steps resulting from Prelims
1a. 12(4) cage at R1C1 = {1236/1245}, 1,2 locked for N1
1b. 13(4) cage at R2C5 = {1237/1246/1345}, 1 locked for N2
1c. 13(4) cage at R1C9 = {1237/1246/1345}, 1 locked for N3
1d. 12(4) cage at R5C3 = {1236/1245}, 1,2 locked for N4
1e. 13(4) cage at R4C5 = {1237/1246/1345}, 1 locked for N5
1f. 12(4) cage at R4C7 = {1236/1245}, 1,2 locked for N6
1g. 13(4) cage at R7C2 = {1237/1246/1345}, 1 locked for N7
1h. 13(4) cage at R7C4 = {1237/1246/1345}, 1 locked for N8
1i. 12(4) cage at R8C7 = {1236/1245}, 1,2 locked for N9

2. 45 rule on N7 1 innie R9C2 = 7, clean-up: no 5 in R7C13, no 6 in R89C3, no 6 in R9C67
2a. R7C13 = {39} (cannot be {48} which clashes with R89C3), locked for R7 and N7, clean-up: no 4 in R7C89, no 4 in R89C3
2b. Naked pair {58} in R89C3, locked for C3 and N7, clean-up: no 5,8 in R4C4
2c. R9C67 = {49} (cannot be {58} which clashes with R9C3), locked for R9
2d. Killer pair 5,6 in R7C89 and 12(4) cage at R8C7, locked for N9
2e. 8 in R7 only in R7C789, locked for N9

3. 45 rule on N2 3 innies R1C56 + R2C6 = 20 = {389/569/578} (cannot be {479} which clashes with R12C4), no 2,4
3a. 1,2 in N2 only in 13(3) cage at R2C5 = {1237/1246}, no 5

[At this stage I saw
8 on D\ only in R6C6 + R7C7, 8 on D/ only in R3C7 + R6C4, X-Wing using diagonals, 8 in R6C46, locked for R6 and N5, 8 in R37C7, locked for C7
However I’ve changed this to a comment after seeing the next step, which is possibly a bit over-the-top because it’s over a month since I’ve worked on an Assassin so I’m a bit out of practice.]

4. 45 rule on N9 3 innies R79C7 + R8C8 = 20 = {389/479}
4a. Consider permutations for R9C67 = {49}
R9C67 = [49] => 13(4) cage at R7C4 = {1237}, 7 locked for R7 => R7C89 = {58}, locked for N9 => R79C7 + R8C8 = {479}
or R9C67 = [94] => R79C7 + R8C8 = {479}
-> R79C7 + R8C8 = {479}, locked for N9, clean-up: no 6 in R7C89
4b. Naked pair {58} in R7C89, locked for R7 and N9
[The rest is fairly straightforward, but not particularly quick.]

5. R6C6 = 8 (hidden single on D\)
5a. R3C7 = 8 (hidden single on D/)
5b. 9 on D\ only in 13(2) cage at R3C3 = {49}, locked for D\ -> R7C7 = 7, placed for D\
5c. Naked pair {49} in 13(2) cage at R3C3, CPE no 4,9 in R3C4 + R4C3

6. 13(4) cage at R7C4 = {1246} (only remaining combination), locked for N8 -> R9C67 = [94], R8C9 = 9

7. R1C56 + R2C6 (step 3) = {569/578} (cannot be {389} because 8,9 only in R1C5), no 3, 5 locked for N2 and C6, clean-up: no 7 in R12C4
7a. 8,9 only in R1C5 -> R1C5 = {89}
7b. Killer pair 4,9 in R12C4 and R4C4, locked for C4

8. R8C34 = {58} (hidden pair in R8)
8a. R8C6 = 7 (hidden single in R8)
8b. R1C56 + R2C6 (step 7) = {569} (only remaining combination) -> R1C5 = 9, R12C6 = {56}, locked for C6 and N2, clean-up: no 3 in R12C4
8c. Naked pair {48} in R12C4, locked for C4 and N2 -> R4C4 = 9, R3C3 = 4, R89C4 = [53], R89C3 = [85], R9C5 = 8, clean-up: no 5 in 12(4) cage at R1C1
8d. R7C3 = 9 (hidden single in C3) -> R7C1 = 3

9. R5C5 = 5 (hidden single on D\), placed for D/
9a. R5C5 = 5 -> 13(4) cage at R4C5 = {1345}, locked for N5

10. Naked quad {1236} in 12(4) cage at R1C1, locked for N1 -> R1C3 = 7
10a. Naked pair {59} in R3C12, locked for R3 and N1 -> R2C1 = 8, R12C4 = [84]
10b. 6 on R3 only in R3C89, locked for N3

11. 12(4) cage at R5C3 = {1245} (cannot be {1236} which clashes with R4C3) -> R56C3 = {12}, locked for C3, R6C12 = {45}, locked for R6 and N4
11a. 3 in R6 only in R6C789, locked for N6
[A couple of hidden singles which have been around for a while]
11b. R2C7 = 9 (hidden single in R2), R6C8 = 9 (hidden single in R6)

12. R4C7 = 2 (hidden single in R4) -> 12(4) cage at R4C7 = {1236} (only remaining combination) -> R6C7 = 3, R5C78 = {16}, locked for R5 and N6 -> R6C9 = 7, R56C3 = [21], R5C14 = [97], R3C12 = [59], R6C12 = [45]
12a. R4C1 = 7 (hidden single in N4)

13. R2C8 = 7 (hidden single on D/) -> 13(4) cage at R1C9 = {1237}, locked for N3 -> R1C78 = [54], R12C6 = [65], R3C9 = 6

14. R8C8 = 3 (hidden single in R8), placed for D\
14a. R2C2 = 6 (hidden single on D\)
14b. R3C56 = [73] (hidden pair in R3), R5C6 = 4, R4C6 = 1, placed for D/

15. Naked pair {12} on D\ in R1C1 + R9C9, CPE no 2 in R1C9 + R9C1 -> R1C9 = 3, R9C1 = 6, placed for D/ -> R6C4 = 2, R3C48 = [12], R2C9 = 1, R9C9 = 2, placed for D\

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

Rating Comment:
I'll rate my walkthrough at Easy 1.5. I used a short forcing chain.

I hope to find time to catch up on the two Assassins and the Human Solvable which I 'missed'.
Top
 Profile  
Reply with quote  
Afmob
 Post subject:
PostPosted: Tue Sep 15, 2015 11:29 am 
Offline
Grand Master
Grand Master

Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for the new Killer, HATMAN! I didn't need to use any chains and found solving it quite straightforward though I had to use two advanced moves.
A324X Walkthrough:
1. R789 !
a) Innie N7 = R9C2 = 7
b) 13(4) @ N7 = 14{26/35} -> 4 locked for N7
c) 12(2) = {39} locked for R7+N7
d) 13(2) @ N7 = {58} locked for C3+N7
e) 13(2) @ N8 = {49} locked for R9 since {58} blocked by R9C3 = (58)
f) 9 locked in Innies N9 = 20(3) = 9{38/47} since {569} blocked by Killer pair (56) of 12(4) @ N9
g) 13(4) @ N8: R8C5 <> 5,7 since R7C456 <> 3
h) ! Innies+Outies R7: 6 = R8C125+R9C1 - R7C7 = {...}-4 / {1246}-7 / {1346}-8 / {246}+2-8 -> CPE: R8C789 <> 4
i) 12(4) = {1236} locked for N9
j) 13(2) @ R7 = {58} locked for R7+N9

2. D\/ !
a) 13(2) <> {58}
b) Hidden Single: R6C6 = 8 @ D\, R3C7 = 8 @ D/, R2C1 = 8 @ N1
c) 9 locked in 13(2) @ D\ = {49} locked for D\
d) R7C7 = 7, R8C9 = 9, R9C7 = 4, R9C6 = 9
e) ! Generalized X-Wing: 9 locked in D\/ for C34
f) Hidden Single: R1C5 = 9 @ N2, R1C4 = 8 @ N2 -> R2C4 = 4, R9C5 = 8 @ C5
g) R4C4 = 9, R3C3 = 4

3. N1245
a) Innies N2 = 11(2) = {56} locked for C6+N2
b) 12(4) = {1236} locked for N1
c) R1C3 = 7
d) 12(4) @ N4 = {1245} since {1236} blocked by R4C3 = (1236) -> R56C3 = {12} locked for C3+N4; 4,5 locked for R6+N4
e) Hidden Single: R5C5 = 5 @ D\, R7C3 = 9 @ D/
f) 13(4) @ N5 = {1345} locked for N5

4. C789+N8
a) 12(4) @ N6 = 12{36/45} -> 1,2 locked for N6
b) Hidden Single: R4C7 = 2 @ R4
c) 12(4) @ N6 = {1236} locked for N6
d) R6C9 = 7
e) Hidden Single: R2C8 = 7 @ D/
f) 13(4) @ N3 = {1237} locked for N3
g) Hidden Single: R3C9 = 6 @ R3
h) 13(4) @ N8 = {1246} locked for N8
i) R1C7 = 5, R1C6 = 6, R7C1 = 3, R9C3 = 5, R9C4 = 3

5. D\
a) Naked pair (12) locked in R1C1+R9C9 for D\; CPE: R1C9+R9C1 <> 1,2
b) R9C1 = 6, R6C4 = 2, R1C9 = 3
c) Naked pair (36) locked in R2C23 for R2
d) Hidden Single: R3C5 = 7 @ C5, R3C6 = 3 @ N2, R4C5 = 3 @ N5, R4C6 = 1 @ R4

6. Rest is singles without considering diagonals.

Rating:
Easy 1.25. I used large Outies and a generalized X-Wing.
Top
 Profile  
Reply with quote  
HATMAN
 Post subject: Re: Assassin 324 X
PostPosted: Fri Sep 18, 2015 11:28 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
Assassin 324 12&13 H1 & H2

I was dissatisfied with the base assassin so decided to try for something harder. I came up with these two, however JS solves one with just an X-wing (SS 1.05) but fails to solve the other one (SS 1.4).

Same solution

Image

JS Code:
3x3:d:k:3073:3073:23:3083:24:25:26:27:3330:28:3073:3073:3083:3337:29:30:3330:3330:31:32:3340:3337:3337:3337:33:3330:34:35:36:37:3340:3333:3333:3079:38:39:40:41:3078:3341:3333:3333:3079:3079:42:3078:3078:3078:43:3341:44:3079:45:46:3094:3332:3094:3336:3336:3336:47:48:49:3332:3332:3348:50:3336:51:3075:3075:52:3332:53:3348:54:55:56:57:3075:3075:




Image

JS Code:
3x3:d:k:3073:3073:15:3083:16:17:18:19:3330:21:3073:3073:3083:3337:22:23:3330:3330:24:25:3340:3337:3337:3337:26:3330:27:28:29:30:3340:3333:3333:3079:31:32:33:34:3078:3341:3333:3333:3079:3079:35:3078:3078:3078:36:3341:37:3079:38:39:40:3332:41:3336:3336:3336:42:3342:3342:3332:3332:3348:43:3336:44:3075:3075:45:3332:46:3348:47:48:49:50:3075:3075:
Top
 Profile  
Reply with quote  
Andrew
 Post subject: Re: Assassin 324 X
PostPosted: Fri Sep 25, 2015 4:15 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada
Thanks HATMAN for posting these variants. The first one proved to be a lot easier, even though it has one fewer cage than the original Assassin.

Just like JSudoku I solved it with a generalised X-Wing, plus lots of hiddens.

Here is my walkthrough for Assassin 324X H1:
Prelims

a) 12(4) cage at R1C1 = {1236/1245}, no 7,8,9
b) R12C4 = {39/48/57}, no 1,2,6
c) 13(4) cage at R1C9 = {1237/1246/1345}, no 8,9
d) 13(4) cage at R2C5 = {1237/1246/1345}, no 8,9
e) 13(2) cage at R3C3 = {49/58/67}, no 1,2,3
f) 13(4) cage at R4C5 = {1237/1246/1345}, no 8,9
g) 12(4) cage at R4C7 = {1236/1245}, no 7,8,9
h) 12(4) cage at R5C3 = {1236/1245}, no 7,8,9
i) 13(2) cage at R5C4 = {49/58/67}, no 1,2,3
j) R7C13 = {39/48/57}, no 1,2,6
k) 13(4) cage at R7C2 = {1237/1246/1345}, no 8,9
l) 13(4) cage at R7C4 = {1237/1246/1345}, no 8,9
m) R89C3 = {49/58/67}, no 1,2,3
n) 12(4) cage at R8C7 = {1236/1245}, no 7,8,9

Steps resulting from Prelims
1a. 12(4) cage at R1C1 = {1236/1245}, 1,2 locked for N1
1b. 13(4) cage at R2C5 = {1237/1246/1345}, 1 locked for N2
1c. 13(4) cage at R1C9 = {1237/1246/1345}, 1 locked for N3
1d. 12(4) cage at R5C3 = {1236/1245}, 1,2 locked for N4
1e. 13(4) cage at R4C5 = {1237/1246/1345}, 1 locked for N5
1f. 12(4) cage at R4C7 = {1236/1245}, 1,2 locked for N6
1g. 13(4) cage at R7C2 = {1237/1246/1345}, 1 locked for N7
1h. 13(4) cage at R7C4 = {1237/1246/1345}, 1 locked for N8
1i. 12(4) cage at R8C7 = {1236/1245}, 1,2 locked for N9

2. 45 rule on N7 1 innie R9C2 = 7, clean-up: no 5 in R7C13, no 6 in R89C3
2a. R7C13 = {39} (cannot be {48} which clashes with R89C3), locked for R7 and N7, clean-up: no 4 in R89C3
2b. Naked pair {58} in R89C3, locked for C3 and N7, clean-up: no 5,8 in R4C4
2c. 8 in R7 only in R7C789, locked for N9

3. 45 rule on N2 3 innies R1C56 + R2C6 = 20 = {389/569/578} (cannot be {479} which clashes with R12C4), no 2,4
3a. 2 in N2 only in 13(4) cage at R2C5 = {1237/1246}, no 5

4. 8 on D\ only in R6C6 + R7C7, 8 on D/ only in R3C7 + R6C4, Generalised X-Wing for 8 using diagonals, no other 8 in R6, C7 and N5, clean-up: no 5 in 13(2) cage at R5C4

5. 8 in N5 only in R6C46
5a. 45 rule on N5 3 innies R4C4 + R6C46 = 19 = {289/568} (cannot be {478} which clashes with 13(2) cage at R5C4) -> R4C4 = {69}, R6C46 = {28/58}, clean-up: no 6,9 in R3C3
5b. R4C4 = 9 (hidden single on D\) -> R3C3 = 4, placed for D\, R6C46 = {28}, locked for R6 and N5, clean-up: no 3, in R12C4, no 4 in 13(2) cage at R5C4
5c. Naked pair {67} in 13(2) cage at R5C2, locked for N5
5d. R6C6 + R7C7 = [87] (hidden pair on D\), R6C4 = 2, placed for D/
5e. R4C7 = 2 (hidden single in R4)
5f. R5C3 = 2 (hidden single in R5)
5g. R3C7 = 8 (hidden single on D/)
5h. R7C3 = 9 (hidden single on D/) -> R7C1 = 3
5i. 1 in R4 only in R4C56, locked for N5
5j. 1 in N4 only in R6C123, locked for R6

6. 12(4) cage at R1C1 = {1236} (only remaining combination), locked for N1 -> R1C3 = 7, clean-up: no 5 in R2C9
6a. Naked pair {59} in R3C13, locked for R3 and N1 -> R2C1 = 8, clean-up: no 4 in R1C4

7. R2C8 = 7 (hidden single on D/) -> 13(4) cage at R1C9 = {1237}, locked for N3 -> R3C9 = 6, R2C4 = 4 -> R1C4 = 8

8. 13(4) cage at R2C5 = {1237} (only remaining combination), locked for N2

9. Naked quad {4569} in R1C5678, 6 locked for R1 and N2

10. R19C5 = [98] (hidden pair in C5) -> R12C6 = [65], R89C3 = [85]
10a. R2C7 = 9 -> R8C9 = 9 (hidden single in N9), R6C8 = 9 (hidden single in N6), R9C6 = 9 (hidden single in N8)

11. R5C5 = 5 (hidden single on D/), placed for D\

12. 12(4) cage at R5C3 = {1245} (cannot be {1236} which clashes with R4C3) -> R6C3 = 1, R6C12 = {45}, locked for R6 and N4

13. 12(4) cage at R4C7 = {1236} (only remaining combination), locked for N6 -> R6C9 = 7, 13(2) cage at R5C4 = [76], R6C7 = 3
13a. Naked pair {16} in R5C78, locked for R5 -> R5C1 = 9, R3C12 = [59], R6C12 = [45]

14. 6 on D/ only in R8C2 + R9C1, locked for N7
14a. R49C1 = [76] (hidden pair in C1), R9C47 = [34], R1C78 = [54]
14b. Naked pair {12} in R9C89, locked for N9 -> R8C7 = 6, R8C8 = 3, placed for D\
14c. R2C2 = 6 (hidden single on D\) -> R2C3 = 3

15. R3C4 = 1, R3C8 = 2, R2C9 = 1, R9C9 = 2, placed for D\

16. R7C4 = 6 (hidden single in R7) -> 13(4) cage at R7C4 = {1246}, locked for N8
16a. R8C6 = 7, R2C6 = 3, R5C6 = 4, R4C6 = 1, placed for D\

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

Rating Comment:
I'll rate this puzzle at 1.0.

It looks like the H2 will be a lot harder without R7C13.
Top
 Profile  
Reply with quote  
Andrew
 Post subject: Re: Assassin 324 X
PostPosted: Sun Sep 27, 2015 3:16 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada
I found the H2 the most enjoyable of these three puzzles.

JS ... but fails to solve the other one (SS 1.4):
I've read many times that JS is good at finding fishes, but maybe it's not good at finding short forcing chains.

Here is my walkthrough for Assassin324X H2:
Prelims

a) 12(4) cage at R1C1 = {1236/1245}, no 7,8,9
b) R12C4 = {39/48/57}, no 1,2,6
c) 13(4) cage at R1C9 = {1237/1246/1345}, no 8,9
d) 13(4) cage at R2C5 = {1237/1246/1345}, no 8,9
e) 13(2) cage at R3C3 = {49/58/67}, no 1,2,3
f) 13(4) cage at R4C5 = {1237/1246/1345}, no 8,9
g) 12(4) cage at R4C7 = {1236/1245}, no 7,8,9
h) 12(4) cage at R5C3 = {1236/1245}, no 7,8,9
i) 13(2) cage at R5C4 = {49/58/67}, no 1,2,3
j) 13(4) cage at R7C2 = {1237/1246/1345}, no 8,9
k) 13(4) cage at R7C4 = {1237/1246/1345}, no 8,9
l) R7C89 = {49/58/67}, no 1,2,3
m) R89C3 = {49/58/67}, no 1,2,3
n) 12(4) cage at R8C7 = {1236/1245}, no 7,8,9

Steps resulting from Prelims
1a. 12(4) cage at R1C1 = {1236/1245}, 1,2 locked for N1
1b. 13(4) cage at R2C5 = {1237/1246/1345}, 1 locked for N2
1c. 13(4) cage at R1C9 = {1237/1246/1345}, 1 locked for N3
1d. 12(4) cage at R5C3 = {1236/1245}, 1,2 locked for N4
1e. 13(4) cage at R4C5 = {1237/1246/1345}, 1 locked for N5
1f. 12(4) cage at R4C7 = {1236/1245}, 1,2 locked for N6
1g. 13(4) cage at R7C2 = {1237/1246/1345}, 1 locked for N7
1h. 13(4) cage at R7C4 = {1237/1246/1345}, 1 locked for N8
1i. 12(4) cage at R8C7 = {1236/1245}, 1,2 locked for N9

2. 45 rule on N2 3 innies R1C56 + R2C6 = 20 = {389/569/578} (cannot be {479} which clashes with R12C4), no 2,4
2a. 1,2 in N2 only in 13(4) cage at R2C5 = {1237/1246}, no 5

3. 45 rule on N5 3 innies R4C4 + R6C46 = 19 = {289/379/469/568} (cannot be {478} which clashes with 13(2) cage at R5C4)

4. 45 rule on N7 3 innies R7C13 + R9C2 = 19 = {289/379/469/568} (cannot be {478} which clashes with R89C3)

5. 45 rule on N9 3 innies R79C7 + R8C8 = 20 = {389/479/578} (cannot be {569} which clashes with R7C89), no 6

6. 45 rule on N5 2 innies R6C46 = 1 outie R3C3 + 6, IOU no 6 in R6C4

7. Consider placements for 8 on D/
R3C7 = 8 => 8 on D\ only in R4C4 + R6C6
or R6C4 = 8
or R7C3 = 8 => 8 on D\ only in R4C4 + R6C6
-> 8 in N5 only in R4C4 + R6C46, locked for N5, clean-up: no 5 in 13(2) cage at R5C4
7a. R4C4 + R6C46 (step 3) contains 8 = {289/568}, no 3,4,7, clean-up: no 6,9 in R3C3
7b. 13(4) cage at R4C5 = {1237/1345} (cannot be {1246} which clashes with R4C4 + R6C46), no 6

8. 7 on D\ only in R3C3 + R5C5 + R7C7, CPE no 7 in R3C7 + R7C3

9. Consider placements for 9 on D\
R4C4 = 9 or R6C6 = 9 or R7C7 = 9 => R6C4 = 9 (hidden single on D/) -> 9 in N5 only in R4C4 + R6C46 (step 7a) = {289}, locked for N5, 2 also locked for R6, clean-up: no 7,8 in R3C3, no 4 in 13(2) cage at R5C4
9a. Naked pair {67} in 13(2) cage at R5C4, locked for N5
9b. R5C3 = 2 (hidden single in N4)
9c. 1 in N4 only in R6C123, locked for R6
9d. R4C7 = 2 (hidden single in N6)
9e. 1 in N6 only in R5C78, locked for R5
9f. R7C7 = 7 (hidden single on D\), clean-up: no 6 in R7C89
9g. R4C4 + R6C6 = {89} (hidden pair on D\), locked for N5 -> R6C4 = 2, placed for D/

10. 6 in N9 only in 12(4) cage at R8C7 = {1236}, locked for N9

11. 12(4) cage at R1C1 = {1236} (cannot be {1245} which clashes with R3C3), locked for N1
11a. Naked quad {1236} in R1C1 + R2C2 + R8C8 + R9C9, locked for D\
11b. Naked pair {45} in R3C3 + R5C5, CPE no 4 in R3C5

12. R3C7 + R7C3 = {89} (hidden pair on D/)
12a. Killer pair 8,9 in R7C3 and R7C89, locked for R7

13. Hidden killer pair 6,7 in 13(4) cage at R1C9 and 13(4) cage at R7C4 for D/, each 13(4) cage can only contain one of 6,7 = {1237/1246}, no 5, 2 locked for N3 and N7
13a. 6,7 are on D/ -> no 6,7 in R2C9 + R3C8 and R7C2 + R8C1
13b. 5 on D/ only in R4C6 + R5C5, locked for N5
13c. R89C3 = {49/58} (cannot be {67} which clashes with 13(4) cage at R7C2), no 6,7
13d. Killer pair 4,5 in R3C3 and R89C3, locked for C3
13e. Killer pair 8,9 in R7C3 and R89C3, locked for C3 and N7 -> R1C3 = 7, clean-up: no 5 in R2C4
[Cracked. The rest is fairly straightforward.
I thought about placing this statement after step 9, but step 13 is the final key step.]

14. 12(4) cage at R5C3 = {1245} (only remaining combination, cannot be {1236} which clashes with R4C3) -> R6C3 = 1, R6C12 = {45}, locked for R6 and N4

15. 12(4) cage at R4C7 = {1236} (only remaining combination because R6C7 only contains 3,6), locked for N6

16. Naked triple {789} in R6C689, locked for R6, 7 also locked for N6 -> R6C5 = 6, R5C4 = 7, R6C7 = 3, clean-up: no 5 in R1C4
16a. Naked pair {16} in R5C78, locked for R5
16b. Killer pair 8,9 in R12C4 and R4C4, locked for C4

17. 5 in N2 only in R1C56 + R2C6 (step 2) = {569/578}, no 3

18. Killer pair 8,9 in R3C12 and R3C7 (because R3C12 cannot be {45} which clashes with R3C3), locked for R3
18a. Hidden killer pair 8,9 in R3C12 and R2C1 for N1, R3C12 contains one of 8,9 -> R2C1 = {89}
18b. Killer pair 4,5 in R3C12 and R3C3, locked for R3

19. R19C5 = {89} (hidden pair in C5)
19a. Killer pair 8,9 in R12C4 and R1C5, locked for N2
19b. R1C56 + R2C6 (step 17) = {569/578}, 5 locked for C6
19c. R5C5 = 5 (hidden single in N5), placed for D\ -> R3C3 = 4, R4C4 = 9, R6C6 = 8, clean-up: no 3 in R12C4, no 9 in R89C3
19d. Naked pair {48} in R12C4, locked for C4 and N2 -> R19C5 = [98] -> R12C6 = 11 = {56}, locked for C6 and N2, clean-up: no 5 in R8C3
19e. R3C9 = 6 (hidden single in R3)

20. R2C8 = 7 (hidden single in N3), placed for D/ -> 13(4) cage at R1C9 = {1237}, locked for N3

21. 13(4) cage at R7C2 = {1246} (only remaining combination), locked for N7
21a. R89C3 = [85], R7C1 = 3, R7C3 = 9, placed for D/, R9C2 = 7, clean-up: no 4 in R7C89
21b. Naked pair {58} in R7C89, locked for R7 and N7

22. R7C4 = 6 (hidden single in R7) -> R89C4 = [53], R3C4 = 1
22a. R7C4 = 6 -> 13(4) cage at R7C4 = {1246}, locked for N8 -> R89C6 = [79], R9C7 = 4, R8C9 = 9

23. 4 in C9 only in R45C1, locked for N6
23a. R1C8 = 4 (hidden single in C8) -> R12C4 = [84], R1C7 = 5, R12C6 = [65]

24. Naked pair {12} in R1C1 + R9C9, locked for D/, CPE no 1 in R1C9 + R9C1
24a. R1C9 = 3, placed for D/, R9C1 = 6, R3C8 = 2, R9C8 = 1, R9C9 = 2, placed for D\
24b. R3C6 = 3, R5C6 = 4, R4C6 = 1, placed for D/

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

Rating Comment:
I'll rate the H2 at Easy 1.5. I used two short forcing chains.
Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  Page 1 of 1
  [ 6 posts ] 

Board index » Puzzles and Solutions » Killer Puzzles

All times are UTC


Who is online

Users browsing this forum: No registered users and 7 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