SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Tue Mar 19, 2024 3:11 am

All times are UTC




Post new topic Reply to topic  [ 5 posts ] 
Author Message
 Post subject: Assassin 338 X 18s
PostPosted: Sun Aug 07, 2016 10:30 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 692
Location: Saudi Arabia
Assassin 338 X 18s

I tried an X with knotted corners and multiple diagonal 18s.

It is X.
Careful with the knotted cages.

The Assassin: SS gives 1.4 and JS uses 3 fishes.
The Main Puzzle (because I found the solution path pleasant): SS gives 1.1 and JS no fishes.
The Hard one: SS gives 1.75 and JS uses 20 fishes.

The Assassin:


Image

JS Code:
3x3:d:k:3073:1797:4882:4882:4375:4375:4617:3335:4611:1797:3073:4882:4375:4375:4617:4618:4611:3335:4625:4625:3073:4375:4617:4618:4611:3597:3093:4625:16:22:24:4618:25:3597:26:3093:27:28:4619:4620:29:3597:30:3093:31:32:4619:4620:33:2574:34:5907:35:36:4619:4620:4612:2574:2575:37:3074:5907:5907:3336:4612:2574:2575:38:39:4372:3074:1798:4612:3336:2575:40:41:4372:4372:1798:3074:

My Main Puzzle:
Image

My Main Puzzle:
3x3:d:k:3073:1797:4882:4882:4375:4375:4617:3335:4611:1797:3073:4882:4375:4375:4617:4618:4611:3335:4625:4625:3073:4375:4617:4618:4611:3597:3093:4625:16:22:6170:4618:6170:3597:24:3093:25:27:4619:4620:6170:3597:28:3093:29:30:4619:4620:6170:2574:6170:5907:31:32:4619:4620:4612:2574:2575:33:3074:5907:5907:3336:4612:2574:2575:34:35:4372:3074:1798:4612:3336:2575:36:37:4372:4372:1798:3074:

The Hard One:

Image

Hard Version:
3x3:d:k:3073:1797:4882:4882:16:22:4617:3335:4611:1797:3073:4882:23:24:4617:4618:4611:3335:4625:4625:3073:25:4617:4618:4611:3597:3093:4625:26:27:28:4618:29:3597:30:3093:31:32:4619:4620:33:3597:34:3093:35:36:4619:4620:37:2574:38:5907:39:40:4619:4620:4612:2574:2575:41:3074:5907:5907:3336:4612:2574:2575:42:43:4372:3074:1798:4612:3336:2575:44:45:4372:4372:1798:3074:

Solution:
238574169
416329857
759186423
675841932
824963571
193257684
567412398
981735246
342698715


Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 338 X 18s
PostPosted: Sat Aug 20, 2016 8:19 pm 
Offline
Grand Master
Grand Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Thanks HATMAN. I do do all the puzzles - but am falling behind in the WTs! Here is my WT for the Assassin.
The main puzzle was much more straightforward. I haven't tried the hard one. (Missing the 17(5) cage in n2).

Assassin 338 X 18s WT:
1. Innies D\ -> D\ in n5 = +21(3) -> No (123)
Innies D/ -> D/ in n5 = +9(3) -> No (789)
-> r5c5 from (456)
-> r4c4,r6c6 = two of (789)
Also -> r4c6,r6c4 = two of (123)

2. The 7(2)s in n1 and n9 prevent the 12(3)s in n1 or n9 being {246}
-> 6 in D\. Either r5c5 = 6 or 12(3) in n1 or n9 is {156} -> r5c5 = 4.
-> r5c5 from (46)
-> Innies D\ in n5 from <849> or <867>. I.e., 8 locked in D\ in n5.
-> Innies D/ in n5 from <162> or <243>. I.e., 2 locked in D/ in n5.

3. 23(3)r6c7 = {689}
-> None of (689) in r789c7
-> (Since 8 in D\ in n5) -> 8 in n9 in r7c89
-> Outies n9 = [r6c7,r9c6] = +14(2) = [68] or [95]
But the latter leaves no solution for 17(3)r8c7
-> r6c7 = 6, r9c6 = 8
-> r7c89 = {89}
Also -> HS 8 in n5 -> r4c4 = 8
-> Innies D\ in n5 from [867] or [849]
Also -> HS 8 in c5/n2 -> r3c5 = 8

4. (58) in D/ in n3 and n7.
But since +(18)3 cannot contain both (58)
-> One each of (58) in D/ in n3 and n7
-> 13(2) in n3 and n7 cannot be {58}
-> HS 8 in n7 -> r8c2 = 8
-> 5 in D/ in n3.

5. HS 8 in n3 -> r2c7 = 8
-> HS 8 in n1 -> r1c3 = 8
Also -> remaining innies n3 = [r1c7,r3c8,r3c9] = {123} with 2 in r3c89.
-> 18(3)r1c7 from [198] or [378]
-> NP r26c6 = {79}

6! Innies - Outies n1 -> whatever goes in r4c1 also goes in r2c3 -> also goes in n7 in r79c2
r6c6 from (79) and +18(3)r5c4 -> r7c2 cannot be 2!
-> 2 not in r79c2
-> r4c1 not 2
-> r1c4 not 9. (Outies n1 = +11(2)).
-> HS 9 in n2 -> r2c6 = 9!

7. Continuing
-> r1c7 = 1, r3c89 = {23}
Also -> r6c6 = 7
-> r5c5 = 6
Since 17(5)n2 must contain (123)
-> 18(3)r2c7 = [864]
-> 17(5)n2 = {12347}
-> r1c4 = 5
-> r2c3 = r4c1 = 6
-> r3c12 = {57}
-> 12(3)n1 = {129}, 7(2)n1 = {34}
-> 12(3)n9 = {345}, 7(2)n9 = {16}, -> r89c7 = {27}
etc.


Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 338 X 18s
PostPosted: Sun Sep 04, 2016 11:28 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks HATMAN for these puzzles.

Oops! :oops: I was careless when I first 'solved' this puzzle. I've now re-worked it; it wasn't as easy as I originally thought.

Here is my re-worked walkthrough for Assassin 338 X 18s:
Prelims

a) 7(2) cage at R1C2 = {16/25/34}, no 7,8,9
b) 13(2) cage at R1C8 = {49/58/67}, no 1,2,3
c) 13(2) cage at R8C1 = {49/58/67}, no 1,2,3
d) 7(2) cage at R8C9 = {16/25/34}, no 7,8,9
e) 19(3) cage at R1C3 = {289/379/469/478/568}, no 1
f) 10(3) cage at R6C5 = {127/136/145/235}, no 8,9
g) 23(3) cage at R6C7 = {689}
h) 10(3) cage at R7C5 = {127/136/145/235}, no 8,9
i) 17(5) cage at R1C5 = {12347/12356}, no 8,9

Steps resulting from Prelims
1a. 23(3) cage at R6C7 = {689}, CPE no 6,8,9 in R789C7
1b. 17(5) cage at R1C5 = {12347/12356}, 1,2,3 locked for N2

2. 45 rule on D\ 3 innies R4C4 + R5C5 + R6C6 = 21 = {489/579/678}, no 1,2,3
2a. 45 rule on D/ 3 innies R4C6 + R5C5 + R6C4 = 9 = {126/135/234}, no 7,8,9
2b. R5C5 = {456} -> no 4,5,6 in R46C46

3. 45 rule on N1 2(1+1) outies R1C4 + R4C1 = 11 = [47/56/65/74/83/92], no 1,8,9 in R4C1
3a. Max R4C1 = 7 -> min R3C12 = 11, no 1 in R3C12

4. 45 rule on N9 2(1+1) outies R6C7 + R9C6 = 14 = [68/86/95]
4a. 17(3) cage at R8C7 = {278/458/467} (cannot be {368} because 6,8 only in R9C6), no 1,3
4b. 6,8 only in R9C6 -> R9C6 = {68} -> R6C7 = {68}
4c. Naked pair {68} in R6C7 + R9C6, CPE no 8 in R6C6
4d. 23(3) cage at R6C7 = {689}, 9 locked for R7 and N9

5. 45 rule on N3 4 innies R12C7 + R3C89 = 14 = {1238/1247/1256/1346/2345}, no 9

6. 12(3) cage at R1C1 = {129/138/147/156/237/345} (cannot be {246} which clashes with 7(2) cage at R1C2)
6a. 17(3) cage at R8C7 (step 4a) = {278/458/467} -> R89C7 = {27/45/47}
6b. 12(3) cage at R7C7 = {156/237/345} (cannot be {138} which clashes with 12(3) cage at R1C1, cannot be {147/246} which clash with R89C7), no 8
6c. 8 in N9 only in R7C89, locked for R7 and 23(3) cage at R6C7 -> R6C7 = 6, R9C6 = 8 (step 4) -> R89C7 = {27/45}, clean-up: no 5 in R8C1
6d. Killer pair 5,7 in 12(3) cage at R7C7 and R89C7, locked for N9, clean-up: no 2 in 7(2) cage at R8C9
6e. 12(3) cage at R1C1 = {129/156/237} (cannot be {138/147/345} which clash with 12(3) cage at R7C7, no 4,8
6f. 7(2) cage at R1C2 = {16/34} (cannot be {25} which clashes with 12(3) cage at R1C1)
6g. R4C4 = 8 (hidden single in D\) -> R5C5 + R6C6 = 13 (step 2) = [49/67], clean-up: no 3 in R4C1 (step 3)
6h. R4C6 + R5C5 + R6C4 (step 2a) = {126/234}, 2 locked for N5 and D/
6i. R3C5 = 8 (hidden single in N2) -> R1C7 + R2C6 = 10 = [19/37/46]

7. 18(3) cage at R1C9 = {189/378/459/567} (cannot be {468} which clashes with R5C5, cannot be {369} which clashes with R4C6 + R5C5 + R6C4)
7a. 18(3) cage at R7C3 = {189/378/459/567} (cannot be {468} which clashes with R5C5, cannot be {369} which clashes with R4C6 + R5C5 + R6C4)
7b. 13(2) cage at R1C8 = {49/67} (cannot be {58} which clashes with 18(3) cage at R1C9), no 5,8
7c. 13(2) cage at R8C1 = {49/67} (cannot be [85] which clashes with 18(3) cage at R7C3), no 5,8
7d. R8C2 = 8 (hidden single in N7), placed for D/ -> 18(3) cage at R7C3 = {189/378}, no 4,5,6, no 1 in R9C1
7e. Killer pair 7,9 in 18(3) cage at R7C3 and 13(2) cage at R8C1, locked for N7
7f. R2C7 = 8 (hidden single in N3) -> R1C7 + R3C89 (step 5) = {123}, locked for N3, 2 also locked for R3, clean-up: no 6 in R2C6 (step 6i)
7g. Naked pair {79} in R26C6, locked for C6
7h. Naked pair {79} in R26C6, CPE no 7,9 in R2C2 using D\
7i. R2C7 = 8 -> R3C6 + R4C5 = 10 = {46}
7j. Naked pair {46} in R45C5, locked for C5 and N5
7k. 9 in C5 only in R89C5, locked for N8
7l. Killer pair 4,6 in 17(5) cage at R1C5 and R3C6, locked for N2, clean-up: no 5,7 in R4C1 (step 3)
7m. R1C3 = 8 (hidden single in N1) -> R1C4 + R2C3 = 11 = [56/74/92]
7n. 9 in N5 only in R5C4 + R6C6, CPE no 9 in R6C3

8. 18(3) cage at R5C4 = {369/459/567} (cannot be {279} because [972] clashes with R6C6), no 1,2
8a. {369} must be [936] -> no 3 in R5C3 + R7C2
8b. 18(3) cage at R5C3 = {279/369/459/567}, no 1
8c. 2 of {279} must be in R7C1 -> no 2 in R5C3 + R6C2
8d. 1 in N7 only in R789C3, locked for C3

9. 12(3) cage at R1C1 (step 6e) = {129/156/237}
9a. 9 on {129} must be in R3C3 -> no 9 in R1C1
9b. 9 in N1 only in R3C123, locked for R3
9c. 9 in C7 only in R45C7, locked for N6

10. 18(3) cage at R3C1 = {279/369/459/567}
10a. 4,6 of {369/459/567} -> no 4,6 in R3C12

11. 45 rule on N1 1 outies R4C1 = 1 remaining innie R2C3
11a. R2C3 + R4C1 = [44/66] (cannot be [22] which clashes with R7C1 + R89C3), clean-up: no 9 in R1C4 (step 3)
11b. R2C6 = 9 (hidden single in N2) -> R1C7 = 1 (cage sum), naked pair {23} in R3C89, locked for R3, clean-up: no 4 in R1C8, no 6 in R2C1
11c. R6C6 = 7, placed for D\, R5C5 = 6 (step 6g), placed for both diagonals
11d. 12(3) cage at R1C1 (step 6e) = {129} (only remaining combination) = [219], placed for D\, clean-up: no 6 in R1C2
11e. Naked pair {34} in 7(2) cage at R1C2, locked for N1 -> R2C3 = 6, R1C4 = 5 (cage sum), R4C1 = 6 (step 3)
11f. Naked pair {57} in R3C12, locked for R3 -> R3C7 = 4, R2C9 = 7, R1C9 = 9, placed for D/, clean-up: no 1 in R7C3 (step 7d)
11g. Naked pair {37} in R7C3 + R9C1, locked for N7 and D/, clean-up: no 6 in R9C2
11h. Naked pair {49} in 13(2) cage at R8C1, locked for N7 -> R7C1 = 5, R7C2 = 6 -> R5C4 + R6C3 = 12 = [93]
11i. R7C1 = 5 -> R5C3 + R6C2 = 13 = [49]

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

Rating Comment:
I'll rate my re-worked walkthrough at Easy 1.5 because of step 11a which is effectively a "clone" step. It has the same effect as wellbeback's breakthrough step 6; two different ways of seeing the key step.

When there's an easy version, I usually do it first. However in this case the start of the Main puzzle was so easy that I decided to do the Assassin first.
Here is my start for the Main puzzle:
Prelims and step 1 as for the Assassin

2. 45 rule on D\ 3 innies R4C4 + R5C5 + R6C6 = 21 = {489/579/678}, no 1,2,3
2a. 45 rule on D/ 3 innies R4C6 + R5C5 + R6C4 = 9 = {126/135/234}, no 7,8,9
2b. These 21(3) and 9(3) hidden cages overlap, forming the 24(5) cage at R4C4 -> R5C5 = 6, placed for both diagonals, R4C4 + R6C6 = {78}, locked for N5 and D\, R4C6 + R6C4 = {12}, locked for N5 and D/

Then continue, as for my walkthrough for the Assassin, simplifying as appropriate.


HATMAN wrote:
The Main Puzzle (because I found the solution path pleasant)
I only did the start for this puzzle. If you found something interesting in your solving path, please post it.

I'll probably try the Hard version later, but first I've got a backlog of puzzles to catch up with.


Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 338 X 18s
PostPosted: Thu Sep 08, 2016 10:58 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 692
Location: Saudi Arabia
Andrew

As I remember it, it was the flow of the puzzle rather than a particular step.

Maurice


Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 338 X 18s
PostPosted: Sat Oct 22, 2016 4:17 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Removing the 17(5) cage made a big difference.

Having discovered the careless error in my original WT for Assassin 338 X I also had to re-work my WT for the Hard version, but this time before posting my WT.

Here is my walkthrough for Assassin 338 X Hard:
Since the 17(5) cage in the Assassin was mostly effective toward the end of my solving path, I’ve used as much of that as possible. The first major difference is at the end of step 6, when a hidden single in N2 is no longer available, while much of the original step 7 is still valid.

Prelims

a) 7(2) cage at R1C2 = {16/25/34}, no 7,8,9
b) 13(2) cage at R1C8 = {49/58/67}, no 1,2,3
c) 13(2) cage at R8C1 = {49/58/67}, no 1,2,3
d) 7(2) cage at R8C9 = {16/25/34}, no 7,8,9
e) 19(3) cage at R1C3 = {289/379/469/478/568}, no 1
f) 10(3) cage at R6C5 = {127/136/145/235}, no 8,9
g) 23(3) cage at R6C7 = {689}
h) 10(3) cage at R7C5 = {127/136/145/235}, no 8,9

1. 23(3) cage at R6C7 = {689}, CPE no 6,8,9 in R789C7

2. 45 rule on D\ 3 innies R4C4 + R5C5 + R6C6 = 21 = {489/579/678}, no 1,2,3
2a. 45 rule on D/ 3 innies R4C6 + R5C5 + R6C4 = 9 = {126/135/234}, no 7,8,9
2b. R5C5 = {456} -> no 4,5,6 in R46C46

3. 45 rule on N1 2(1+1) outies R1C4 + R4C1 = 11 = {29/38/47/56}, no 1

4. 45 rule on N9 2(1+1) outies R6C7 + R9C6 = 14 = [68/86/95]
4a. 17(3) cage at R8C7 = {278/458/467} (cannot be {368} because 6,8 only in R9C6), no 1,3
4b. 6,8 only in R9C6 -> R9C6 = {68} -> R6C7 = {68}
4c. Naked pair {68} in R6C7 + R9C6, CPE no 8 in R6C6
4d. 23(3) cage at R6C7 = {689}, 9 locked for R7 and N9

5. 45 rule on N3 4 innies R12C7 + R3C89 = 14 = {1238/1247/1256/1346/2345}, no 9

6. 12(3) cage at R1C1 = {129/138/147/156/237/345} (cannot be {246} which clashes with 7(2) cage at R1C2)
6a. 17(3) cage at R8C7 (step 4a) = {278/458/467} -> R89C7 = {27/45/47}
6b. 12(3) cage at R7C7 = {156/237/345} (cannot be {138} which clashes with 12(3) cage at R1C1, cannot be {147/246} which clash with R89C7), no 8
6c. 8 in N9 only in R7C89, locked for R7 and 23(3) cage at R6C7 -> R6C7 = 6, R9C6 = 8 (step 4) -> R89C7 = {27/45}, clean-up: no 5 in R8C1
6d. Killer pair 5,7 in 12(3) cage at R7C7 and R89C7, locked for N9, clean-up: no 2 in 7(2) cage at R8C9
6e. 12(3) cage at R1C1 = {129/156/237} (cannot be {138/147/345} which clash with 12(3) cage at R7C7, no 4,8
6f. 7(2) cage at R1C2 = {16/34} (cannot be {25} which clashes with 12(3) cage at R1C1)
6g. Killer pair 1,3 in 12(3) cage at R1C1 and 7(2) cage at R1C2, locked for N1
6h. R4C4 = 8 (hidden single in D\) -> R5C5 + R6C6 = 13 (step 2) = [49/67], clean-up: no 3 in R1C4 + R4C1 (step 3)
6i. R4C6 + R5C5 + R6C4 (step 2a) = {126/234}, 2 locked for N5 and D/

7. 18(3) cage at R1C9 = {189/378/459/567} (cannot be {468} which clashes with R5C5, cannot be {369} which clashes with R4C6 + R5C5 + R6C4)
7a. 18(3) cage at R7C3 = {189/378/459/567} (cannot be {468} which clashes with R5C5, cannot be {369} which clashes with R4C6 + R5C5 + R6C4)
7b. 13(2) cage at R1C8 = {49/67} (cannot be {58} which clashes with 18(3) cage at R1C9), no 5,8
7c. 13(2) cage at R8C1 = {49/67} (cannot be [85] which clashes with 18(3) cage at R7C3), no 5,8
7d. R8C2 = 8 (hidden single in N7), placed for D/ -> 18(3) cage at R7C3 = {189/378}, no 4,5,6, no 1 in R9C1
7e. Killer pair 7,9 in 18(3) cage at R7C3 and 13(2) cage at R8C1, locked for N7
7f. Killer pair 1,3 in R4C6 + R6C4 and 18(3) cage at R7C3, locked for D/
7g. Naked quint {45679} in 13(2) cage at R1C8 + 18(3) cage, locked for N3

8. 18(3) cage at R1C7 = {189/279/369/378/468} (cannot be {459/567} because R1C7 only contains 1,2,3,8), no 5
8a. 2 of {279} must be in R1C7 -> no 2 in R2C6 + R3C5
8b. 18(3) cage at R2C7 = {189/369/378/468} (cannot be {459/567} because R2C7 only contains 1,2,3,8, cannot be {279} because 2{79} clashes with R6C6), no 2,5
8c. 8 of {189} must be in R2C7 -> no 1 in R2C7
8d. 18(3) cage at R5C3 = {189/279/369/378/459/468/567}
8e. 1,2 of {189/279} must be in R7C1 -> no 1,2 in R5C3 + R6C2
8f. 18(3) cage at R5C4 = {189/369/378/459/468/567} (cannot be {279} because {79}2 clashes with R6C6), no 2
8g. 1 of {189} must be in R7C2 -> no 1 in R5C4 + R6C3
8h. 1 in N3 only in R1C7 + R3C89, CPE no 1 in R3C5

[It looks like it’s time to start using forcing chains.]
9. 8 in N1 only in R12C3 + R3C1
9a Consider permutations for R1C4 + R4C1 (step 3) = {29/47/56}
R1C4 = 2 -> R12C3 = 17 = {89}
or R1C4 = 4 => R4C1 = 7 => R3C12 = 11 = {29/56} => R12C3 = 15 = {78}
or R1C4 = 5 => R12C3 = 14 = {68}
or R1C4 = 6 => R4C1 = 5 => R3C12 = 13 = {49/67} => R12C3 = 13 = {58}
or R1C4 = 7 => R12C3 = 12 = {48}
or R1C4 = 9 => R4C1 = 2 => R3C12 = 16 = {79} => R12C3 = 10 = {28}
-> R12C3 = {28/48/58/68/78/89}, 8 locked for C3 and N1
9b. 18(3) cage at R5C3 (step 8d) = {279/369/459/567}, no 1
9c. 18(3) cage at R5C4 (step 8f) = {369/459/567}, no 1
9d. 1 in N7 only in R789C3, locked for C3
9e. 8 in R3 only in R3C589, CPE no 8 in R1C7
9f. 18(3) cage at R1C7 (step 8) = {189/279/369/378} (cannot be {468} because R1C7 only contains 1,2,3), no 4
9g. R1C7 = {123} -> no 1,3 in R2C6 + R3C5

10. 2 in N7 only in R7C1 + R89C3
10a. 45 rule on N1 2 innies R12C3 = 1 outie R4C1 + 8 -> R12C3 + R4C1 = {48}4/{58}5/{68}6/{78}8/{89}9 (cannot be {28}2) which clashes with R7C1 + R89C3) -> no 2 in R12C3, no 2 in R4C1, clean-up: no 9 in R1C4 (step 3)

11. 18(3) cage at R1C7 (step 9a) = {189/279/369/378}
11a. Consider placement of 8 in N3
R2C7 = 8 => R3C5 = 8 (hidden single in R3) => 18(3) cage at R1C7 = {189/378}
or 8 in R3C89 => R2C7 = 3 => 18(3) cage at R1C7 = {189/279}
-> 18(3) cage at R1C7 = {189/279/378}, no 6
11b. Naked pair {79} in R26C6, locked for C6
11c. 18(3) cage at R2C7 (step 8b) = {189/369/378/468}
11d. 9 of {189/369} must be in R4C5 -> no 1,3 in R4C5

12. 18(3) cage at R1C7 (step 11a) = {189/279/378}, R4C6 + R5C5 + R6C4 (step 2a) = {126/234}, R5C5 + R6C6 (step 6g) = [49/67], 18(3) cage at R7C3 (step 7d) = {189/378}, 12(3) cage at R7C7 (step 6b) = {156/237/345}
12a. Consider combinations for R89C7 (step 6c) = {27/45}
R89C7 = {27}, locked for C7
or R89C7 = {45} => 12(3) cage at R7C7 = {237}, locked for D\, R6C6 = 9 => R5C5 = 4, R4C6 + R6C4 = {23}, locked for D/ -> R7C3 + R9C1 = [19], placed for D/ => R3C7 = 7
-> 7 in R3C7 + R89C7, locked for C7
12b. Consider placements for R1C7 = {123}
R1C7 = 1 => R2C6 + R3C5 = [98] => R2C7 = 8 (hidden single in N3)
or R1C7 = 2 => R89C7 = {45} => 12(3) cage at R7C7 = {237} => R7C7 = 3 => R2C7 = 8
or R1C7 = 3 => R2C7 = 8
-> R2C7 = 8
12c. R1C3 = 8 (hidden single in N1)
12d. R3C5 = 8 (hidden single in N2) -> R1C7 + R2C6 = [19/37]
12e. 2 in N3 only in R3C89, locked for R3
12f. 2 in N3 only in R3C89, CPE no 2 in R5C8
12g. 2 in N1 only in 12(3) cage at R1C1, locked for D\
12h. 12(3) cage at R1C1 (step 6e) = {129/237}, no 5,6
12i. 9 of {129} must be in R3C3 -> no 9 in R1C1 + R2C2
12j. 9 on D\ only in R3C3 + R6C6, CPE no 9 in R6C3
12k. 2 in N9 only in R89C6 = {27}, locked for C6 and N9
[The first key breakthrough; some 8s which were fairly easy in the normal Assassin have now been placed and R89C6 has been reduced to one combination.]

[As will be apparent from the diagonals the 7(2) cages at R1C2 and R8C9 must have different combinations as must the 13(2) cages at R1C8 and R8C1; but I didn’t find a way to use this.]
13. 12(3) cage at R1C1 = {129/237}, 12(3) cage at R7C7 = {156/345}, 18(3) cage at R1C9 = {459/567}, 18(3) cage at R7C3 = [189]/{378}, R4C6 + R5C5 + R6C4 = {126/234}, R5C5 + R6C6 = [49/76], 18(3) cage at R4C1 = {459/567}
13a. Consider combinations for 18(3) cage at R7C3 = [189]/{378}
18(3) cage at R7C1 = [189], placed for N7 and D/ => 13(2) cage at R8C1 = {67}, 18(3) cage at R1C9 = {567}, locked for D/ => {67}5 => R5C5 + R6C6 = [49], 9 placed for D\ => 12(3) cage at R1C1 = {237}, locked for N1 => 7(2) cage at R1C2 = {16} => caged X-Wing for 6 in 7(2) cage and 13(2) cage at R8C1, no other 6 in C12 => 18(3) cage at R3C1 = {459} = [495]
or 18(3) cage at R7C3 = {378}, locked for N7 and D/ => 13(2) cage at R8C1 = {49}, 18(3) cage at R1C9 = {459}, locked for D/ => R5C5 + R6C6 = [67], 7 placed for D\ => 12(3) cage at R1C1 = {129}, locked for N1 => 7(2) cage at R1C2 = {34} => caged X-Wing for 4 in 7(2) cage and 13(2) cage at R8C1, no other 4 in C12 => 18(3) cage at R3C1 = {567}
-> 18(3) cage at R3C1 = [495]/{567}, no 9 in R34C1, no 4 in R3C2 + R4C1, clean-up: no 2,7 in R1C4 (step 3)
13b. 19(3) cage at R1C3 = {478/568}
13c. 4 of {478} must be in R1C4 -> no 4 in R2C3
13d. 9 in N1 only in R3C23, locked for R3

[Now the same forcing chain from a different starting point, or I could have taken one of the previous ones further to a contradiction.]
14. Consider combinations for 18(3) cage at R3C1 = {459/567}
18(3) cage at R3C1 = {459} = [495] => R1C4 = 6 (step 3) => 7(2) cage at R1C2 = [16] => 18(3) cage at R1C9 = {459}
or 18(3) cage at R3C1 = {567} => 9 in N1 only in R3C3, placed for D\ => R5C5 + R6C6 = [67], 6 placed for D/ => 18(3) cage at R1C9 = {459}
-> 18(3) cage at R1C9 = {459}, locked for N3 and D\ -> R5C5 + R6C6 = [67], placed for D\
[Cracked. The rest is straightforward.]
14a. R5C5 = 6 -> R4C6 + R6C4 = 3 (step 2a) = {12}, locked for N5 and D/
14b. Naked pair {37} in R7C3 + R9C1, locked for N7, clean-up: no 6 in 13(2) cage at R8C1
14c. Naked pair {49} in 13(2) cage at R8C1, locked for N7
14d. 12(3) cage at R1C1 = {129} (only remaining combination) -> R3C3 = 9, R1C1 + R2C2 = {12}, locked for N1 and D\, clean-up: no 6 in 7(2) cage at R1C1
14e. Naked pair {34} in 7(2) cage at R1C2, locked for N1
14f. 7(2) cage at R8C9 = {16} (hidden pair in N9)
14g. 1 in R7 only in R7C456, locked for N8
14h. 4 in C3 only in R456C3, locked for N4
14i. 9 in C7 only in R45C7, locked for N6

15. R3C5 = 8 -> R1C7 + R2C6 = 10 = [19]
15a. 18(3) cage at R5C4 (step 8f) = {369/459} -> R5C4 = 9, R6C3 + R7C2 = [36/45], R4C5 = 4 -> R3C6 = 6 (cage sum)
15b. Naked pair {57} in R3C12, locked for R3, N1 and 18(3) cage at R3C1, R2C3 = 6 -> R1C4 = 5 (cage sum), R2C3 = 6
15c. R7C2 = 6 (hidden single in N7) -> R6C3 = 3

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

Rating Comment:
I'll rate my WT for A338X Hard at least Hard 1.5, based on the number and length of my forcing chains.


Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 5 posts ] 

All times are UTC


Who is online

Users browsing this forum: No registered users and 12 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:  
cron
Powered by phpBB® Forum Software © phpBB Group