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PostPosted: Mon Jun 02, 2008 11:12 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
This is Part A of the Assassin Forum Archive. Please read the first part of the Archive Index to get the background to this archive including Mike (mhparker)'s original post about ratings.
Old SudokuSolverV3.2 scores:
Killer rating table      
Rounded Score from SSv3.2
pg# on this thread
(E) = Easy (H) = Hard
======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A..1 0.75 0.65|A..5 0.75 0.65|A.12 0.70|
|A..1v2 1.25 1.00|A..6 0.90|A.13 0.65|
|A..2 0.75 0.75|A..7 0.75|Uluru 1.20|
|A..2X 1.50 1.65|A..8 0.65|A.14 0.75 0.65|
|A2X-Lite H1.00 1.00|A..9 0.75 0.65|A.15 0.75 0.70|
|A..3 0.80|A.10 0.75 0.70| |
|A..4 0.70|A.11 0.70| |
|====================================================================|
page #1


======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A.16 1.25 0.95|SKX1 1.00|A.22 0.80|
|UTA H1.50 1.90|A.19 1.00 0.80|SKX2 1.40|
|UTAv2 H1.50 1.50|A.20 1.00 0.75|A.23 0.70|
|A.17 1.00 0.70|A.20v2 1.25 1.20|A.24 1.25|
|A.17v2 E1.50 1.10|A.21 0.70| |
|A.18 1.25 0.95|A.21v2 1.50| |
|====================================================================|
page #2


======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A.25 0.80|SKX3 1.35|A.32 0.90|
|A.25v2 1.65|A.30 0.70|A.32v2 0.80|
|A.26 H1.25 1.40|Bullseye3 2.0(t&E)2.15|A.32v3 0.85|
|A.27 0.90|A New One 2.40| |
|A.28 0.75|A.31 H1.0 0.95| |
|A.29 0.90|Last06 H1.25 1.20| |
|====================================================================|
page #3


======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A.33 1.25 1.05|SKX4 0.70|A.36 0.80|
|A.34 H1.25 1.30|SampuZ4 0.95|A.37 0.80|
|PANIV 1.50 1.20|SampuZ4v2 1.80|CDK 0.85|
|A.35 0.70|Chevron 0.90|CDKv2 1.25|
|====================================================================|
page #4


======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|CDKv3 1.75 2.10|A.38 1.45|A.39v3 1.75 3.10|
|SampuZ5 1.05|Black-HoleX E1.5 1.55|A.40 0.95|
|NON-CON 1.00 |A.39 0.85|A.40v2 1.25 1.35|
|NameThatAlbumX 2.35|A.39v2 2.0 (t&e)4.65| |
|====================================================================|
page #5


======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A.41 0.75|A.42v2 2.0 (t&E)3.10|A.44v1.5 1.55|
|A.41v2 E2.0 2.40|A.43 1.15|A.44v2 1.55|
|Para's X 1.50 1.50|A.43v0 E1.25 0.95| |
|A.42 0.95|A.44 0.75| |
|====================================================================|
page #6


======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A.45 1.00|A.46Lite 0.95|A.48Hevvie 2.50 3.75|
|A.45EEggsv2 1.90|A.47 1.20| |
|A.45EEggsv3 1.65|A.47v1.5 0.85| |
|A.46 1.10|A.48 1.05| |
|====================================================================|
page #7


======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A.48Lite 0.95|A.50v2 3.0(t&E)2.85| |
|A.49 1.20|A.50v0.2 0.65| |
|A.49v2 H1.25 1.35| | |
|A.50 1.75 2.25| | |
|====================================================================|
page #8
Old scores from SSv3.3.0:
Killer rating table      
Rounded Score from SSv3.3.0
! = 0.10 change from previous version of score
pg# on this thread
(E) = Easy (H) = Hard
======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A..1 0.75 0.65|A..5 0.75 0.70|A.12 0.75|
|A..1v2 1.25 1.05|A..6 !1.00|A.13 0.70|
|A..2 0.75 0.75|A..7 0.80|Uluru 1.50 1.25|
|A..2X 1.50 1.65|A..8 0.70|A.14 0.75 0.70|
|A2X-Lite H1.00 !1.25|A..9 0.75 0.70|A.15 0.75 !0.80|
|A..3 0.85|A.10 0.75 0.75| |
|A..4 0.75|A.11 0.75| |
|====================================================================|
page #1


======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A.16 1.25 1.00|SKX1 !1.20|A.22 0.80|
|UTA H1.50 !2.25|A.19 1.00 0.80|SKX2 1.75 !2.95|
|UTAv2 H1.50 !1.60|A.20 1.00 0.80|A.23 0.75|
|A.17 1.00 0.70|A.20v2 1.25 1.15|A.24 H1.25 1.25|
|A.17v2 E1.50 !1.30|A.21 0.70| |
|A.18 1.25 !1.15|A.21v2 H1.50 1.55| |
|====================================================================|
page #2


======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A.25 0.80|SKX3 !0.90|Last06 H1.25 !1.10|
|A.25v2 H1.00 !2.40|A.30 0.75|A.32 !1.00|
|A.26 H1.25 1.40|Bullseye3 2.0 !3.80|A.32v2 !1.05|
|A.27 !1.05|A New One H1.5 !3.00|A.32v3 !1.05|
|A.28 0.80|A New Onev2 H1.75 2.05| |
|A.29 0.95|A.31 H1.0 0.95| |
|====================================================================|
page #3


======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A.33 1.25 1.10|SKX4 0.70|A.36 0.75|
|A.34 H1.25 !1.40|SampuZ4 1.00|A.37 0.85|
|PANIV 1.50 1.25|SampuZ4v2 1.80 !2.70|CDK 0.80|
|A.35 !0.85|Chevron !0.70|CDKv2 !1.10|
|====================================================================|
page #4


======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|CDKv3 1.75 !2.05|A.38 !1.20|A.39v3 1.75 !4.05|
|SampuZ5 1.00|Black-HoleX E1.5 !1.30|A.40 0.85|
|NON-CON 1.00 0.75|A.39 !1.05|A.40v2 1.25 !1.25|
|AlbumX 1.75 !3.05|A.39v2 2.0 !(t&e)6.00| |
|====================================================================|
page #5


======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A.41 0.80|A.42v2 2.0 (t&E)!4.10|A.44v1.5 1.5 !1.75|
|A.41v2 E2.0 !4.60|A.43 1.20|A.44v2 H1.5 !1.70|
|Para's X 1.50 !1.95|A.43v0 E1.25 !1.10| |
|A.42 0.95|A.44 0.80| |
|====================================================================|
page #6


======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A.45 0.95|A.46Lite 0.95|A.48Hevvie 2.50 !2.95|
|A.45 Eggsv2 1.75 !2.05|A.47 !0.90| |
|A.45 Eggsv3 H1.25!1.95|A.47v1.5 0.85| |
|A.46 1.25 !1.20|A.48 !1.20| |
|====================================================================|
page #7


======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A.48Lite !1.35|A.50v2 3.0(t&E)!5.00| |
|A.49 1.15|A.50v0.2 0.70| |
|A.49v2 H1.25 !1.50| | |
|A.50 1.75 !2.60| | |
|====================================================================|
page #8
Killer rating table
SudokuSolver Target range v3.6.3
Rating.....Score
0.50 = 0.85
0.75 = 0.90-0.95
1.00 = 1.00-1.20
1.25 = 1.25-1.45
1.50 = 1.50-1.70 (E) = Easy (H) = Hard

===========================================================================================
|A ## by Rate Score|A ## by Rate Score|A ## by Rate Score|
|-----------------------------+-----------------------------+-----------------------------|
|A..1 Ruud 0.75 0.85|A..5 Ruud 0.75 0.90|A.12 Ruud 0.85|
|A..1v2 Ed 1.25 1.30|A..6 Ruud 1.00|A.13 Ruud 0.85|
|A..2 Ruud 0.75 0.90|A..7 Ruud 0.90|Uluru Ed 1.50 1.35|
|A..2X mhp 1.50 1.60|A..8 Ruud 0.85|A.14 Ruud 0.75 0.85|
|A2-Lite mhp H1.00 1.20|A..9 Ruud 0.75 0.85|A.15 Ruud 0.75 0.90|
|A..3 Ruud 0.95|A.10 Ruud 0.75 0.85| |
|A..4 Ruud 0.90|A.11 Ruud 0.90| |
|=========================================================================================|
page #1


===========================================================================================
|A ## by Rate Score|A ## by Rate Score|A ## by Rate Score|
|-----------------------------+-----------------------------+-----------------------------|
|A.16 Ruud 1.25 1.05|SKX1 Ruud 1.05|A.22 Ruud 0.95|
|UTA Ed H1.50 1.85|A.19 Ruud 1.00 0.95|SKX2 Ruud 1.75 2.35|
|UTAv2 Ed H1.50 1.45|A.20 Ruud 1.00 0.90|A.23 Ruud 0.90|
|A.17 Ruud 1.00 0.85|A.20v2 Ed 1.25 1.00|A.24 Ruud H1.25 1.35|
|A.17v2 Ed E1.50 1.25|A.21 Ruud 0.85| |
|A.18 Ruud 1.25 1.05|A.21v2 Ed H1.50 1.60| |
|=========================================================================================|
page #2



===========================================================================================
|A ## by Rate Score|A ## by Rate Score|A ## by Rate Score|
|-----------------------------+-----------------------------+-----------------------------|
|A.25 Ruud 0.90|SKX3 Ruud 1.10|Last06 Ruud H1.25 1.25|
|A.25v2 Ed H1.00 1.85|A.30 Ruud 0.85|A.32 Ruud 1.00|
|A.26 Ruud H1.25 1.25|Bulls3 Ed 2.0 2.55|A.32v2 frank 1.00|
|A.27 Ruud 1.00|A NewOne nd H1.5 2.30|A.32v3 Ed 0.95|
|A.28 Ruud 0.90|ANOv2 nd H1.75 1.70| |
|A.29 Ruud 1.05|A.31 Ruud H1.0 1.20| |
|=========================================================================================|
page #3



===========================================================================================
|A ## by Rate Score|A ## by Rate Score|A ## by Rate Score|
|-----------------------------+-----------------------------+-----------------------------|
|A.33 Ruud 1.25 1.25|SKX4 Ruud 0.85|A.36 Ruud 1.15|
|A.34 Ruud H1.25 1.35|SampuZ4 Ed 1.05|A.37 Ruud 0.95|
|PANIV Ed 1.50 1.35|SampZ4v2Ed 1.80 2.25|CDK Nasen 0.95|
|A.35 Ruud 1.00|Chevron Ruud 1.15|CDKv2 Para 1.00|
|=========================================================================================|
page #4



===========================================================================================
|A ## by Rate Score|A ## by Rate Score|A ## by Rate Score|
|-----------------------------+-----------------------------+-----------------------------|
|CDKv3 Ed 1.75 1.75|A.38 Ruud 1.35|A.39v3 Ruud 1.75 3.05|
|SampuZ5 Ed 1.00|BlackX Ed E1.5 1.25|A.40 Ruud 0.95|
|NON-CON Nasen 1.00 0.90|A.39 Ruud 0.95|A.40v2 Ed 1.25 1.10|
|AlbumX Ruud 1.75 2.45|A.39v2 Ruud 2.0 5.15| |
|=========================================================================================|
page #5



===========================================================================================
|A ## by Rate Score|A ## by Rate Score|A ## by Rate Score|
|-----------------------------+-----------------------------+-----------------------------|
|A.41 Ruud 0.90|A.42v2 Ruud 2.0 (t&E)3.20|A.44v15 Para 1.5 1.55|
|A.41v2 Ed E2.0(t&E)4.40|A.43 Ruud 1.25|A.44v2 Para H1.5 1.70|
|Para'sX Para 1.50 1.60|A.43v0 Ruud E1.25 1.10| |
|A.42 Ruud 0.95|A.44 Ruud 1.00| |
|=========================================================================================|
page #6



===========================================================================================
|A ## by Rate Score|A ## by Rate Score|A ## by Rate Score|
|-----------------------------+-----------------------------+-----------------------------|
|A.45 Ruud 1.15|A46Lite Ruud 1.05|A48Hev Ruud 2.50 3.75|
|EEggsv2 Ruud 1.75 1.90|A.47 Ruud 0.95| |
|EEggsv3 Ruud H1.25 1.75|A.47v15 Ruud 1.00| |
|A.46 Ruud 1.25 1.20|A.48 Ruud 1.15| |
|=========================================================================================|
page #7



===========================================================================================
|A ## by Rate Score|A ## by Rate Score|A ## by Rate Score|
|-----------------------------+-----------------------------+-----------------------------|
|A48Lite Ruud 1.10|A.50v2 Ruud 3.0 5.20| |
|A.49 Ruud 1.10|A50v0.2 Ruud 0.85| |
|A.49v2 JC H1.25 1.45| | |
|A.50 Ruud 1.75 2.05| | |
|=========================================================================================|
page #8


Last edited by Ed on Sun Apr 11, 2010 8:16 am, edited 27 times in total.

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PostPosted: Mon Jun 02, 2008 11:20 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Assassin 1 by Ruud (June 06)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:4609:4609:2562:6915:6915:6915:1798:2833:2833:4609:2314:2562:6915:3597:6915:1798:4368:2833:3858:2314:1556:1556:3597:4375:4375:4368:1050:3858:2314:3869:3869:3597:2592:2592:4368:1050:2852:2852:2852:3367:3367:3367:5419:5419:5419:2349:4654:2096:2096:4657:3122:3122:3380:3381:2349:4654:1848:1848:4657:2363:2363:3380:3381:4159:4654:2634:6210:4657:6210:1349:3380:4687:4159:4159:2634:6210:6210:6210:1349:4687:4687:
Solution:
+-------+-------+-------+
| 8 9 7 | 5 4 3 | 2 1 6 |
| 1 2 3 | 9 7 6 | 5 8 4 |
| 6 4 5 | 1 2 8 | 9 7 3 |
+-------+-------+-------+
| 9 3 8 | 7 5 4 | 6 2 1 |
| 4 1 6 | 8 3 2 | 7 5 9 |
| 7 5 2 | 6 1 9 | 3 4 8 |
+-------+-------+-------+
| 2 7 4 | 3 9 1 | 8 6 5 |
| 5 6 9 | 4 8 7 | 1 3 2 |
| 3 8 1 | 2 6 5 | 4 9 7 |
+-------+-------+-------+
Quote:
Ruud: As if your brain cells were not battered enough already by this website, here is the latest addition
Henry: I managed to solve it in about an hour
Pete: I got it
mhparker:(rating) 0.75: Easy Assassin, like some of the very early ones, such as A1
Para, in A1v2 thread: Managed to solve it without pencilmarks. Seems we've come a long way since number 1. Couldn't think of going without pencilmarks these days
Caida: I found A5 easier than this one...I would rate this as 0.75
Walkthrough by Caida:
I had been going under the assumption that since A1 had a rating it must have a walkthrough and I was just unable to find it. For what it is worth I found A5 easier than this one - perhaps b/c I didn't see step 6 until the end. Here is my walkthrough for Assassin 1. I would rate this as 0.75.

Assassin 1 Walkthrough

Preliminaries
a. 10(2)n1 and n56 and n7 = {19/28/37/46} (no 5)
b. 9(3)n14 = {126/135/234} (no 7,8,9)
c. 15(2)n14 and n47 = {69/78} (no 1..5)
d. 6(2)n12 = {15/24} (no 3,6..9)
e. 17(2)n23 = {89} (no 1..7) -> 8,9 locked for r3
f. 7(2)n3 and n78 = {16/25/34} (no 7..9)
g. 4(2)n36 = {13} (no 2,4..9) -> 1,3 locked for c9
h. 11(3)n3 and n4 = {128/137/146/236/245} (no 9)
i. 9(2)n47 and n89 = {18/27/36/45} (no 9)
j. 8(2)n45 = {17/26/35} (no 4,8,9)
k. 12(2)n56 = {39/48/57} (no 1,2,6)
l. 21(3)n6 = {489/579/678} (no 1,2,3)
m. 13(2)n69 = {49/58/67} (no 2)
n. 5(2)n9 = {14/23} (no 5..9)

1. Innies Outies n3: r3c7 – r4c89 = 6
1a. -> r3c7 = 9; r4c8 = 2; r4c9 = 1
1b. -> r3c6 = 8
1c. -> r3c9 = 3
1d. -> r23c8 = [87]
1e. -> r34c1 = [69]
1f. -> r67c1 no 3
1g. -> r6c6 no 3
1h. -> r6c7 no 4
1i. -> r12c7 no 4
1j. -> r7c7 no 1

2. r4c34 = {78} -> locked for r4
2a. -> r4c67 = {46} -> locked for r4

3. Innie and Outie n1: r3c3 – r4c2 = 2
3a. -> r3c3 = 5; r4c2 = 3
3b. -> r3c4 = 1
3c. -> r4c5 = 5
3d. -> r23c2 = {24} -> locked for n1 and c2
3e. -> r1c3 no 8
3f. -> r6c3 no 7
3g. -> r6c4 no 3
3h. -> r6c7 no 7
3i. -> r23c5 = [72]
3j. -> r1c3 no 3
3k. -> r23c2 = [24]
3l. -> r1c7 no 5
3m. -> r7c3 no 6
3n. -> r7c4 no 2

4. killer pair {12} in c7 in 7(2)n3 and 5(2)n9
4a. -> r7c7 no 2
4b. -> r7c6 no 7

5. Innies and Outie n8: r7c46 – r6c5 = 3
5a. -> max r7c45 = 11 -> max r6c5 = 8 (no 9)

should have seen this much much earlier
6. Outies c12: r5c3 = 6
6a. -> r5c12 = [41]
6b. -> r5c34 = [26]
6c. -> r4c67 = [46]
6d. -> r6c5 = 1
6e. -> r7c46 = [31] (step 5a)
6f. -> r7c3 = 4
6g. -> r7c7 = 8
6h. -> r6c9 no 5,9
6i. -> r7c9 no 7
6j. -> r12c7 = [25]
6k. -> r56c7 = [73]
6l. -> r6c6 = 9
6m. -> r1c8 = 1
6n. -> r67c9 = [85] (4 blocked by r12c9)
singles and cage sums left
Assassin 1 V2 by sudokuEd (June 07)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:4865:4865:2562:6915:6915:6915:1542:3089:3089:4865:2058:2562:6915:3341:6915:1542:4112:3089:3858:2058:1812:1812:3341:6935:6935:4112:1306:3858:2058:3869:3869:3341:6935:6935:4112:1306:1572:1572:6439:6439:6439:6439:6439:3627:3627:2093:4654:3632:3632:4913:3122:3122:3380:3381:2093:4654:3632:3632:4913:2619:2619:3380:3381:4159:4654:2890:5954:4913:5954:1605:3380:4431:4159:4159:2890:5954:5954:5954:1605:4431:4431:
Solution:
+-------+-------+-------+
| 8 9 7 | 5 4 3 | 1 2 6 |
| 2 1 3 | 9 7 6 | 5 8 4 |
| 6 4 5 | 2 1 8 | 9 7 3 |
+-------+-------+-------+
| 9 3 8 | 7 5 4 | 6 1 2 |
| 4 2 6 | 8 3 1 | 7 5 9 |
| 7 5 1 | 6 2 9 | 3 4 8 |
+-------+-------+-------+
| 1 7 4 | 3 9 2 | 8 6 5 |
| 5 6 9 | 4 8 7 | 2 3 1 |
| 3 8 2 | 1 6 5 | 4 9 7 |
+-------+-------+-------+
Quote:
sudokuEd: Rating? About average Assassin one year on - an early placement, then steady progress with that extra trick to finally break it
Andrew: I'll rate A1V2 as a solid 1.25..two improvements..would make it a slightly easier 1.25
Para: Seems we've come a long way since number 1
First Post Walkthrough by udosuk:
Greetings everyone,

This is my very first post here. :sunny: Been stalking even before the opening of this section (more than a whole year! :oops:) and finally drag myself to actually register. 8-[

As I can see this community has prospered a lot over all this time, compared to the other forums I frequent, some of which are getting more and more quiet. :|

So great job Ruud! :thumright: Although I don't have too much online time in the near future due to work commitments I hope I can contribute a little bit here or there. :mrgreen:

Enough babbling. Here is my first contribution: a complete walkthrough & solution to this puzzle (including a text puzzle grid):
Code:
.-----.--.--------.--.-----.
|19   |10|27      |6 |12   |
|  .--:  |  .--.  |  :--.  |
|  |8 |  |  |13|  |  |16|  |
:--:  :--'--:  :--'--:  :--:
|15|  |7    |  |27   |  |5 |
|  |  :-----:  |     |  |  |
|  |  |15   |  |     |  |  |
:--'--+-----'--'-----+--'--:
|6    |25            |14   |
:--.--+-----.--.-----+--.--:
|8 |18|14   |19|12   |13|13|
|  |  |     |  :-----:  |  |
|  |  |     |  |10   |  |  |
:--:  :--.--:  :--.--:  :--:
|16|  |11|23|  |  |6 |  |17|
|  '--:  |  '--'  |  :--'  |
|     |  |        |  |     |
'-----'--'--------'--'-----'

6/2 @ r12c7,r89c7={15|24} (NQ @ c7)
Innie-outies @ n3: r3c7-r4c89=6
=> r3c7=9, r4c89={12} (NP @ r4,n6) => r4c6<>9, r3c9=3|4
=> 16/3 @ r234c8: r23c8=14|15={68|78} (8 @ c8,n2 locked)
=> 14/2 @ r5c89 can't have 4 => 4 @ r6,c6 locked @ r6c89
=> 12/2 @ r6c67=[57|93], 10/2 @ r7c67=[28|37|46|73]
=> Innie-outies @ n9: r6c89=r7c7+4={34|46|47|48}
=> HP @ r6,n6: r5c89={59} => 6/2 @ r5c12={24} (NP @ r5,n4)

15/2 @ r34c1=[69|78|87], 15/2 @ r4c34={69|78}
r3c6+r4c67=27-9=18 must include at least 2 values from {678}
(Otherwise r3c6+r4c67 can't exceed 4+5+8=17)
r4c134 all from {6789} => Only one of r4c67 can be 6|7|8
=> r3c6=6|7|8 => r3c168={678} (NT @ r3)
=> Innie-outies @ n2: r4c5=r3c6-3=3|4|5
=> 13/3 @ r234c5: r2c5 must be from {6789}
(Otherwise r234c5 can't exceed 3+4+5=12)

7/2 @ r3c34={25} ({34} clashes r3c9) (NP @ r3)
Innie-outies @ n1: r3c3=r4c12-7 must be at least 7+3-7=3
=> r3c34=[52] => HS @ r6,n5: r6c5=2
=> r78c5=19-2=17={89} (NP @ c5,n8 )
Innies @ n8: r7c46=[14|32] => r7c67=[28|46] => r6c89={46|48}
=> 13/3 @ r678c8: r78c8=7|9 can't have 9, also can't have 7
(Otherwise r78c8={27} clashes r234c8={178|268})
=> Innies @ c8: r159c8=16 with 9 @ c8 locked
=> r159c8={259|349} ({169} clashes r234c8={178|268})
=> 7 @ c8 locked @ r23c8={78} (NP @ n3), r4c89=[12], r3c9=3

Innies @ n2: r23c5+r3c6=16 => r3c6=8, r234c5=[715], r3c2=4
=> r23c8=[87], r34c1=[69], r5c12=[42], r24c2=8-4=4=[13]
=> r4c67=27-8-9=10=[46] => r7c46=[32], r7c7=8, r6c89=[48]
=> r7c9=13-8=5 => r5c9=9, r15789c8=[25639], r12c7=[15]
=> r78c5=[98], r7c2=7 => 11/2 @ r89c3=[92]

All naked singles from here.



:bball: My fav sport
Alternate ending to udosuk's Walkthrough by sudokuEd:
Thanks for the walk-through udosuk. You cram in the info and really made me think hard!

Some very clever moves that I missed. The main one is a hidden killer quad (paragraph 2 line 4). It led a nice naked triple (para.2 ln 5) that ultimately led to the final powerful innie move in n2 (para. 4).

Another way to unlock the puzzle at the end is to notice that the 1's in c3 in r567 means 1 cannot be in r7c4.(ie: 1 in r5c3 -> 1 in n5 in r6c4 -> no 1 r7c4.
1 in r67c3 -> no 1 in r7c4 (same cage)
Para wrote:
Seems we've come a long way since number 1.
We've taught Ruud too well :wink: .
Walkthrough by Andrew:
After finishing A2X I decided to have a go at A1V2, which I hadn't tried when Ed first posted it.

udosuk found a shorter solving route with a better version of step 4 and Ed's message gives a neat alternative finish.

I'll rate A1V2 as a solid 1.25. The two improvements mentioned above would make it a slightly easier 1.25.

Here is my walkthrough for A1V2.

Prelims

a) R12C3 = {19/28/37/46}, no 5
b) R12C7 = {15/24}
c) R3C34 = {16/25/34}, no 7,8,9
d) R34C1 = {69/78}
e) R34C9 = {14/23}
f) R4C34 = {69/78}
g) R5C12 = {15/24}
h) R5C89 = {59/68}
i) R67C1 = {17/26/35}, no 4,8,9
j) R6C67 = {39/48/57}, no 1,2,6
k) R67C9 = {49/58/67}, no 1,2,3
l) R7C67 = {19/28/37/46}, no 5
m) R89C3 = {29/38/47/56}, no 1
n) R89C7 = {15/24}
o) 19(3) cage in N1 = {289/379/469/478/568}, no 1
p) R234C2 = 1{25/34}, 1 locked for C2, clean-up: no 5 in R5C1
q) R678C5 = {289/379/469/478/568}, no 1
r) 27(4) cage at R3C6 = {3789/4689/5679}
s) 14(4) cage at R6C3 = {1238/1247/1256/1346/2345}, no 9

1. Naked quad {1245} in R1289C7, locked for C7, clean-up: no 7,8 in R6C6, no 6,8,9 in R7C7

2. 45 rule on C2 3 innies R159C2 = 19 = {289/469/478/568} (cannot be {379} because no 3,7,9 in R5C2), no 3
2a. R5C2 = {245} -> no 2,4,5 in R19C2

3. R678C2 = {279/369/378/567} (cannot be {459} which clashes with R234C2, cannot be {468} which clashes with R159C2), no 4

4. 45 rule on N3 2 innies R3C79 = 1 outie R4C8 + 11, max R3C79 = 13 -> max R4C8 = 2
4a. R3C79 = 12,13 = [84/93/94], clean-up: no 3,4 in R4C9
4b. R3C34 = {16/25} (cannot be {34} which clashes with R3C9)
[udosuk gave the better version 1 innie R3C7 = 2 outies R4C89 + 6 -> R3C7 = 9, R4C89 = {12}, locked for R4 and N6.]

5. Naked pair {12} in R4C89, locked for R4 and N6

6. 1 in 8(3) cage locked in R23C2, locked for C2, clean-up: no 9 in R12C3, no 6 in R3C4
6a. R234C2 = 1{25/34}
6b. 5 of {125} must be in R4C2 -> no 5 in R23C2

7. 4 in N6 locked in R6C89, locked for R6, clean-up: no 8 in R6C7

8. R234C8 = {69}1/{78}1/{59}2/{68}2, no 1,2,3,4 in R23C8
8a. Killer pair 8,9 in R3C7 and R23C8, locked for N3

9. 12(3) cage in N3 = {156/237/246} (cannot be {147} which clashes with R12C7, cannot be {345} which clashes with R3C9)

10. 27(4) cage at R3C6 = {3789/4689/5679}
10a. R4C67 cannot both be {6789} which would clash with R4C134 -> no 3,4,5 in R3C6
10b. 4,5 of {4689/5679} must be in R4C6 -> no 6 in R4C6
10c. Killer quad 6,7,8,9 in R4C134 and R4C67, locked for R4

11. Hidden killer quad 1,2,3,4 in R3C2, R3C34, R3C5 and R3C67 for R3 -> R3C5 = {1234}

12. R234C5 = {139/148/157/238/247/256/346}
12a. 6,7,8,9 only in R2C5 -> R2C5 = {6789}

13. 45 rule on N7 2 innies R7C13 = 1 outie R6C2, min R7C13 = 3 -> min R6C2 = 3

14. 45 rule on N9 2 innies R7C79 = 1 outie R6C8 + 9, max R7C79 = 17 -> max R6C8 = 8

15. 45 rule on N2 2 innies R3C46 = 1 outie R4C5 + 5, max R4C5 = 5 -> max R3C46 = 10, no 5 in R3C4, clean-up: no 2 in R3C3
15a. R89C3 = {29/38/47} (cannot be {56} which clashes with R3C3), no 5,6

16. 19(3) cage in N1 = {289/379/469/478} (cannot be {568} which clashes with R3C3), no 5

17. R3C3 = 5 (hidden single in N1), R3C4 = 2

18. 45 rule on N1 2 outies R4C12 = 12, no 6 in R4C1, clean-up: no 9 in R3C1
18a. 45 rule on R4, R4C12 = 12, R4C34 = 15, R4C89 = 3 -> R4C567 = 15 = {348/357/456}, no 9
18b. 9 in 27(4) cage locked in R3C67, locked for R3

19. R234C8 (step 8) = {78}1/{68}2/[961] (cannot be {59}2 because 5,9 only in R2C8), no 5

20. 45 rule on R12 3 innies R2C258 = 16, min R2C58 = 13 -> max R2C2 = 3

21. 45 rule on N2 3 remaining innies R2C5 + R3C56 = 16, min R2C5 + R3C6 = 13
-> max R3C5 = 3

22. 45 rule on C5 3 innies R159C5 = 13 = {148/157/238/247/256/346} (cannot be {139} which clashes with R3C5), no 9

23. 4 in N6 locked in R6C89
23a. 45 rule on N9 3 outies R7C6 + R6C89 = 14
23b. No 5 in R7C6 -> R6C89 cannot be 9, no 5 in R6C89, clean-up: no 8 in R7C9

24. 5 in N6 locked in R5C89 -> R5C89 = {59}, locked for R5 and N6, clean-up: no 1 in R5C1, no 3 in R6C6, no 4 in R7C9
24a. Naked pair {24} in R5C12 , locked for R5 and N4, clean-up: no 6 in R7C1
24b. No 9 in R6C9 -> max R6C89 = 12, no 1 in R7C6 (step 23a), clean-up: no 9 in R7C7

25. R234C2 (step 6a) = 1{25/34}
25a. 4 of {134} must be in R3C2 -> no 3 in R3C2

26. Killer pair 2,4 in R234C2 and R5C2, locked for C2

27. R3C7 = 9 (hidden single in C7)

28. R234C8 (step 19) = {78}1/{68}2, 8 locked for C8

29. R6C5 = 2 (hidden single in R6), R78C5 = 17 = {89}, locked for C5 and N8

30. R234C5 (step 12) = {157/346}
30a. 4 of {346} must be in R4C5 -> no 3 in R4C5

31. 4,5,9 in N2 locked in 27(5) cage = {14589/34569}, no 7

32. 45 rule on N8, 4 innies R7C456 + R8C5 = 22, R78C5 = 17 -> R7C46 = 5 = [14/32], clean-up: no 3,7 in R7C7

33. 3,7 in C7 locked in R456C7, locked for N6, clean-up: no 6 in R7C9

34. 14(4) cage at R6C3 = {1238/1256/1346} (cannot be cannot be {1247/2345} because 2,4 only in R7C3), no 7
34a. 2,4 only in R7C3 -> R7C3 = {24}

35. Naked pair {24} in R7C36, locked for R7, clean-up: no 6 in R6C1

36. Killer triple 2,3,4 in R12C3, R7C3 and R89C3, locked for C3

37. R678C8 = [436/463/472/634/652], no 1,9, no 5,7 in R8C8

38. Killer pair 6,7 in R23C8 and R678C8, locked for C8

39. 45 rule on C8 3 innies R159C8 = 16 = {259/349}, no 1

40. R4C8 = 1 (hidden single in C8), R4C9 = 2, R3C9 = 3, R3C5 = 1, R3C2 = 4, R24C2 = [13] (step 6a), R5C12 = [42], R24C5 = [75] (step 30), R6C67 = [93], clean-up: no 3 in R1C3, no 6 in R12C3, no 5 in R1C7, no 6 in R4C3, no 5 in R7C1

41. R4C6 = 4 (hidden single in R4), R7C67 = [28], R7C3 = 4, R7C4 = 3 (step 32), R78C5 = [98], clean-up: no 5 in R6C1, no 7 in R89C3, no 3 in R9C3

42. R6C34 = {16} (step 34), locked for R6 -> R67C1 = [71], R6C8 = 4, R6C9 = 8, R7C9 = 5, R5C89 = [59], R1C8 = 2, R9C8 = 9 (step 39), R6C2 = 5, clean-up: no 8 in R2C3, no 4 in R12C7 = [15], no 8 in R34C1 = [69], R4C3 = 8, R4C4 = 7, R4C7 = 6, R5C7 = 7, R3C6 = 8 (cage sum), R3C8 = 7, R78C8 = [63], R2C8 = 8, R7C2 = 7, R8C2 = 6 (cage sum)

and the rest is naked and hidden singles


Last edited by Ed on Fri Jun 13, 2008 12:00 pm, edited 2 times in total.

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PostPosted: Mon Jun 02, 2008 11:39 am 
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Posts: 1040
Location: Sydney, Australia
Assassin 2 by Ruud (June 06)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:4096:4096:3842:3842:4356:5381:5381:4359:4359:4096:3850:3850:3842:4356:5381:2831:2831:4359:2322:3850:5140:5140:4356:2327:2327:2831:3866:2322:2322:5140:4382:4382:3104:2327:3866:3866:2852:2852:2852:4382:3104:4137:3114:3114:3114:5165:5165:4143:3104:4137:4137:3891:3636:3636:5165:3383:4143:4143:2874:3891:3891:4157:3636:3903:3383:3383:5186:2874:5188:4157:4157:3143:3903:3903:5186:5186:2874:5188:5188:3143:3143:
Solution:
+-------+-------+-------+
| 9 4 5 | 2 3 6 | 8 1 7 |
| 3 1 6 | 8 5 7 | 4 2 9 |
| 2 8 7 | 4 9 1 | 3 5 6 |
+-------+-------+-------+
| 1 6 9 | 3 8 4 | 5 7 2 |
| 4 5 2 | 6 7 9 | 1 3 8 |
| 8 7 3 | 1 2 5 | 6 9 4 |
+-------+-------+-------+
| 5 3 4 | 9 6 2 | 7 8 1 |
| 7 9 1 | 5 4 8 | 2 6 3 |
| 6 2 8 | 7 1 3 | 9 4 5 |
+-------+-------+-------+
Quote:
mhparker:The question is: Was this the puzzle where Ruud developed his love of 3-cell cages? Estimated rating: 0.75
(non-optimal) Walkthrough by mhparker:
Hi folks,

Hey, I'm the first to post a WT for this one! \:D/ Come on guys, where are you all? :lol:

The question is: Was this the puzzle where Ruud developed his love of 3-cell cages?

Estimated rating: 0.75. Unfortunately, I messed it up a bit and strayed from the optimum route near the start. Clearly, I can't do 0.75-rated puzzles properly any more... :roll: Anyhow, here's my (non-optimal) WT:


Assassin 2 Walkthrough

Prelims:

a) 21(3) at R1C6 = {489/579/678} (no 1..3)
b) 11(3) at R2C7, R5C1 and R7C5 = {128/137/146/236/245} (no 9)
c) 9(3) at R3C1, R3C6 and R7C5 = {126/135/234} (no 7..9)
d) 20(3) at R3C3, R6C1, R8C4 and R8C6 = {389/479/569/578} (no 1,2)

1. Innie/Outie (I/O) diff. C789: R19C7 = R37C6 + 14
1a. -> R37C6 = {12}, locked for C6; R19C7 = {89}, locked for C7

2. Outies C89: R258C7 = 7(3) = {124}, locked for C7

3. 9(3) at R3C6 = {135} (last combo)
3a. -> R3C6 = 1; R34C7 = {35}, locked for C7

4. Naked single (NS) at R7C6 = 2

5. Outies R12: R3C258 = 22(3) = {589/679} (no 1..4)
5a. 9 locked for R3

6. Innies N3: R13C7+R3C9 = 17(3) = [836/854/935/953]
6a. -> R3C9 = {3..6} (no 2,7,8)

7. Hidden single (HS) in R3 at R3C1 = 2
7a. -> split 7(2) at R4C12 = {16/34} (no 5)

8. Outies N12: R1C7+R4C3 = 17(2) = {89} (no 3..7)
8a. no 8,9 in R1C3 (CPE)

9. Innies N1: R13C3 = 12(2) = [48]/{57} (no 1,3,6; no 4 in R3C3)

10. 11(3) at R5C1 = {128/245} (no 3,6,7)
(Note: {137/146/236} all blocked by R4C12 (step 7a))
10a. 2 locked for R5 and N4

11. 12(3) at R5C7 = {138/345} (no 6,7,9)
(Note: {147/156} both blocked by 11(3) at R5C1 (step 10))
11a. 3 locked for R5 and N6
11b. can only have 1 of {14}, which must go in R5C7
11c. -> no 1,4 in R5C89

12. R34C7 = [35]
12a. -> no 4 in R3C9 (step 6)

13. HS in R3 at R3C4 = 4
13a. -> R34C3 = [79] (last permutation)
13b. -> R1C3 = 5 (step 9)

14. 12(3) at R5C7 = {138} (last combo)
14a. -> R5C7 = 1; R5C89 = {38}, 8 locked for R5 and N6

15. 11(3) at R5C1 (step 10) = {245} (last combo), locked for R5 and N4
15a. cleanup: no 3 in R4C12 (step 7a)

16. Naked pair (NP) at R4C12 = {16}, locked for R4 and N4

17. 15(3) at R3C9 = {267} (no 4,5) (last combo)
17a. -> R3C9 = 6; R4C89 = {27}, locked for R4 and N6
17b. -> R1C7 = 8 (step 6)

18. R679 = [679]

19. NS at R3C8 = 5
19a. -> split 6(2) at R2C78 = {24}, locked for R2 and N3

20. NP at R6C89 = {49}, locked for R6
20a. -> R7C9 = 1 (cage sum)

21. HS in C4 at R6C4 = 1
21a. -> split 11(2) at R4C6+R5C5 = [47] (last combo/permutation)

22. HS in C4 at R1C4 = 2
22a. -> R2C4 = 8 (cage sum)

23. R3C25 = [89]
23a. split 7(2) at R2C23 = {16} (last combo), locked for R2 and N1
23b. split 8(2) at R12C5 = [35]

24. R4C45 = [38]
24a. -> R5C4 = 6 (cage sum)

25. 16(3) at R5C6 = [925]

26. R12C6 = [67]

27. 17(3) at R1C8 = [179] (last combo/permutation)

28. NS at R2C1 = 3

29. 20(3) = {389/578} (no 4,6)
29a. 7 of {578} must go in R6C2
29b. -> R6C1 = 8

Now all singles and simple cage sums to end
Assassin 2X by mhparker (Dec 07)
Puzzle pic: 1-9 cannot repeat on the diagonals:
Image
Code: Select, Copy & Paste into solver:
3x3:d:k:4352:4352:3842:3842:4612:3589:3589:3335:3335:4352:4618:4618:3842:4612:3589:4367:4367:3335:4626:4618:3860:3860:4612:3095:3095:4367:3354:4626:4626:3860:3614:3614:2592:3095:3354:3354:2596:2596:2596:3614:2592:5417:3626:3626:3626:3373:3373:4143:2592:5417:5417:4403:3380:3380:3373:4151:4143:4143:3130:4403:4403:6205:3380:4415:4151:4151:3906:3130:2628:6205:6205:3399:4415:4415:3906:3906:3130:2628:2628:3399:3399:
Solution:
+-------+-------+-------+
| 8 6 7 | 3 9 2 | 5 1 4 |
| 3 4 9 | 5 1 7 | 6 2 8 |
| 2 5 1 | 6 8 4 | 7 9 3 |
+-------+-------+-------+
| 7 9 8 | 2 5 3 | 1 4 6 |
| 5 1 4 | 7 6 8 | 2 3 9 |
| 6 3 2 | 1 4 9 | 8 5 7 |
+-------+-------+-------+
| 4 2 5 | 9 7 6 | 3 8 1 |
| 1 8 6 | 4 3 5 | 9 7 2 |
| 9 7 3 | 8 2 1 | 4 6 5 |
+-------+-------+-------+
Quote:
Note: Forum thread on this puzzle here.
mhparker: Est. rating: 1.75..Yeah, looks pretty straightforward, I know... Wink..this is more like a traditional V2, which (whilst having easier sections) generally involves more of a fight to dig away at the candidates
Caida: After several false starts I have finally managed to finish A2X. I don't know that I would rate this as a 1.75 (I managed to finish it through perseverance) but I could see rating it as 1.5
Afmob: Rating: 1.5, had some difficult moves but not too many of them
Andrew: There seems to be a very narrow solving path (to begin). It certainly took a lot more work after that. I'll agree with both of them and rate A2X as 1.5
Walkthrough by Caida with key moves close to the beginning:
After several false starts I have finally managed to finish A2X.
Most of my earlier problems came from faulty math and eliminating combos prematurely.

I don't know that I would rate this as a 1.75 (I managed to finish it through perseverance) but I could see rating it as 1.5.

Interested to see other approaches.

Here's my walkthough - after several restarts I have put what I found were the key moves (my steps 6,7,8) as close to the beginning as I could.

Any comments/suggestions/corrections appreciated!
Edited for typos - thanks Andrew!!

Assassin 2X walkthrough

Prelims:

a. 10(3)n4 and n5 and n89 = {127/136/145/235} (no 8,9)
b. 21(3)n5 = {489/579/678} (no 1,2,3)
c. 24(3)n9 = {789} (no 1..6) -> 7,8,9 locked for n9

1. Innies r1234: r4c456 = 10(3) = {127/136/145/235} (no 8,9)
1a. overlapping cages: r5c4 – r4c6 = 4
1c. -> r5c4 no 1,2,3,4
1d. -> r4c6 no 6,7

2. Innies r6789: r6c456 = 14(3)
2a. overlapping cages: r5c6 – r6c4 = 7
2b.-> r5c6 = 8,9 (no 4,5,6,7)
2c. -> r6c4 = 1,2 (no 3,4,5,6,7)

3. Innies c1234: r456c4 = 10(3) = {127/136/145/235} (no 8,9)
3a. overlapping cages: r4c5 – r6c4 = 4
3b. -> r4c5 = {56} (no 1,2,3,4,7)
3c. -> r4c6 no 4,5 (step 1a)

4. Innies c6789: r456c6 = 20(3) = [3]{89} -> 3 locked for diagonal -> no 3 elsewhere in diagonal top right (tr) -> bottom left (bl)
4a. -> {89} locked for c6 and n5
4b. r5c4 = 7 (step 1a)
4c. -> r6c5 = 4 (cage 21(3))
4d. h10(3)c4 (step 3) = {1[7]2}
4e. -> {12} locked for c4 in n5
4f. -> {56} locked for c5 in n5

5. 10(3)n4 = {136/145/235} {1 | 2} {5 | 6}
5a. killer pair {56} in r5 in 10(3)n4 and r5c5 -> no 5,6 elsewhere in r5

6. Innies n478: r4c123+r789c6 = 36
6a. -> max r4c123 = 24 -> min r789c6 = 12
6b. -> max r89c6 = 9 + max r7c6 = 7
6c. -> max r789c6 = 16 -> min r4c123 = 20 (no 1,2)

7. since 10(3)n4 must contain either 1 or 2 (but not both) and r4c123 doesn’t have either than
7a. -> r6c123 must have the other 1 or 2 for n4
7b. -> killer pair {12} in r6c123 and r6c4 -> no 1,2 elsewhere in r6
7c. -> killer pairs of {12} are also in r5c123 + r6c123 and in r5c123 and r5c789

I don’t think this next bit is t&e – but don’t know how to write it without making it look t&eish

8. if r6c4 = 1 -> r5c6 = 8 and 10(3)n4 = {1..} -> 14(3)n6 must have a 2 and 9 but no 1 or 8 (239)
8b. if r6c4 = 2 -> r5c6 = 9 and 10(3)n4 = {1..} -> 14(3)n6 must have a 1 and 8 but no 9 (158) -> no 5 available
8c. -> 14(3)n6 = 239 -> locked for r5 and n6
8d. -> h10(3)r4 = [253]
Andrew pointed out that I forgot to note the hidden single in r4c4
8e. -> 10(3)n5 = [361]
8f. -> 21(3)n5 = [849]
8g. -> 10(3)n4 = {145} -> locked for n4
8h. -> 2,6,9 locked for diagonal from top left (tl) -> bottom right (br)
8i. -> 1,6,3 locked for diagonal from top right (tr) -> bottom left (bl)

9. Outies r12: r3c258 = 22(3) = {589/679} (no 1..4) -> 9 locked for r3

10. Outies c12: r258c3 = 19(3) = [649/946/748/847/658/856] (no 1,2,3)
10a. -> r28c3 no 4,5

11. 17(3)n3 = {269/278/359/368/458/467} (no 1)
Note: combo {179} blocked by 24(3)n9
11a. Outies c89: r258c7 = 17(3) = [827/728/629/638/539]
11b. -> r2c7 no 2,3,4,9
11c. -> r5c7 no 9
11d. -> 17(3)n3: r2c8 no 5,7,8,9

12. Innies n1: r1c3+r3c13 = 10(3) = {127/136/145/235} (no 8,9)

13. Innies n9: r7c89+r9c7 = 8(3) = {125/134} (no 6) -> 1 locked for n9

14. 13(3)n69 = [571/751/562/652]
14a. -> 5 locked in n6 in r6c89 -> no 5 elsewhere in n6
14b. -> r6c89 no 8
14c. -> r7c9 no 3,4,5

15. {14} locked in n6 in r4c789
15a. -> r4c89 must contain at least 1 of {14} (could contain both)
15b. -> 13(3)n36 = [148/184/418/481/814/841/517/571/247/274/346/364]
15c. -> r3c9 no 6,7

16. {23} locked in n4 in r6c123
16a. -> r6c12 must contain at least 1 of {23} (could contain both)
15b. -> 13(3)n47 = [238/283/328/382/823/832/274/724/265/625/364/634]
15c. -> r7c1 no 1679

16. 17(3)n689 = [674/764/863/845/854] (no 1,2)
16a. -> 1 in diagonal tl-> br locked in n1 -> no 1 elsewhere in n1

17. h8(3)n9 (step 13) = [314/413/512/521]
17a. -> r9c7 no 5

18. 18(3)n14 = [567/576/468/486/369/396/378/387/279/297]
18a. -> r3c1 no 6,7
18b. 18(3)n1: min r2c3+r3c2 = 11 -> r2c2 no 8


19. Innies n7: r7c13+r9c3 = 12(3) = {129/138/147/237/246/345}
19a. -> r7c1 no 8
19b. -> r9c3 no 8, 9

20. 12(3)n236 = {147/246} (no 5,8)
Note combo [651] blocked by h22(3)r3; combo [156] blocked by h17(3)c7 and r6c7

21. Innies n3: r1c7+r3c79 = 15(3) = {258/348/357/456}
21a. -> r1c7 and r3c9 no 1,2,4,7,9
21b. -> single: r8c7 = 9
21c. -> pair {78} locked in n9 for c8
21d. -> h17(3)c7 = [539/629]
21e. -> r2c7 no 7,8
21f. -> 17(3)n3 = [629] -> 2 locked for diagonal
21g. -> r5c789 = [239]

22. h22(3)r3 = [679/589]
22a. -> r3c2 no 7,8

23. 9 locked for diagonal in n7 -> no 9 elsewhere in n7

24. 18(3)n1 = [495/396/486/576]
24a. -> r2c2 no 1,7
24b. triple {345} locked for diagonal in r2c2, r7c7, r9c9 -> no 3,4,5 elsewhere in diagonal (not in r1c1 or r3c3)

25. 15(3)n124 = [159/168/186]
25a. -> r3c3 = 1
25b. -> r3c4 no 3,4
25c. -> r4c3 no 7

26. Innies n7: r7c3 no 8, 9
26a. single: r9c1 = 9
26b. 17(3)n7: r8c1 and r9c2 = {17/26/35} (no 4,8)
26c. 8 in r9 locked in n8 -> no 8 elsewhere in n8

27. 12(3)n236 = {47}[1]
27a. -> {47} locked in r3
27b. -> h22(3)r3 = [589]
27c. -> 15(3)n124 = [168]
27d. -> 13(3)n36 = [3]{46} -> {46} locked for n6 and r4

singles and cages sums left

Cheers,

Caida
Walkthrough by Afmob with Killer XY-Wing:
Seems my key moves are not much different from Caida's ones. I wonder if my step 8c can be considered a Killer XY-Wing?

A2X Walkthrough:

1. N5
a) Innies+Outies R6789: 7 = R5C6 - R6C4
-> R5C6 = (89), R6C4 = (12)
b) Innies R5 = 21(3) <> 1,2,3
c) Innies C6789 = 20(3) <> 1,2
d) 10(3) <> 7 because 1,2 only possible @ R6C4
e) Innies R5 = 21(3) must have 4,5 xor 6 and R5C5 = (456) -> R5C4 <> 4,5,6
f) Innies C1234 = 10(3) = {127} -> R5C4 = 7, (12) locked for C4+N5

2. N5+R5
a) 21(3) = {489} locked for N5
b) Innies C5 = 15(3) = {456} -> R6C5 = 4, (56) locked for C5+N5
c) Innies C6789 = 20(3) = {389} -> R4C6 = 3, (89) locked for C6
d) Killer pair (56) locked in 10(3) + R5C5 for R5

3. N9
a) Innies = 8(3) = 1{25/34} -> 1 locked
b) 6 locked in 13(3) = 6{25/34}

4. C123
a) Outies C12 = 19(3) <> 1
b) Outies C12 = 19(3): R28C3 <> 2,3 because R5C3 <= 6
c) Innies N1 = 10(3) <> 8,9
d) 15(3) @ R8C4: R9C3 <> 9 because R89C4 >= 7
e) 13(3): R7C1 <> 9 because {139} blocked by Killer pair (13) of 10(3)

5. R123
a) Outies R12 = 22(3) = 9{58/67} -> 9 locked for R3
b) 12(3) <> 8

6. C789
a) 17(3) @ N9: R6C7+R7C6 <> 1,2 because R7C7 <= 5
b) 17(3) @ N9: R6C7 <> 3,5 because R7C67 <> 8,9

7. N12+C6 !
a) ! R789C6 <= 16 because R89C6 <= 9 -> R123C6 >= 9 (step 1c)
b) ! Innies+Outies N12: 11 = R4C123 - R123C6
-> R4C123 >= 20 <> 1,2

8. R456 !
a) R6C123 must have 1 xor 2 @ N4 because 10(3) <> {127}
b) Killer pair (12) locked in R6C123+R6C4 for R6
c) ! Consider placement of 6 in R5 -> R6C123 <> 1
- i) 6 in 10(3) @ N4 = {136} -> R6C123 <> 1
- ii) 6 in 10(3) @ N5 = {136} -> R6C4 = 1 -> R6C123 <> 1
d) Hidden Single: R6C4 = 1 @ R6 -> R5C5 = 6
e) R4C4 = 2, R4C5 = 5
f) Innies R6789 = 14(3) = {149} -> R6C6 = 9 -> R5C6 = 8
g) 1 locked in 10(3) @ N4 = {145} locked for R5+N4
h) 14(3) @ N6 = {239} locked for N6
i) 5 locked in 13(3) @ R6 (N6) -> 13(3) = 5{17/26}, R7C9 <> 5

9. N1
a) 17(3) @ N9 <> 1
b) 1 locked in D\ for N1
c) Innies N1 = 10(3): R3C3 <> 4,7 because R1C3+R3C1 <> 1
d) 18(3) @ R3C1: R3C1 <> 6,7 because R4C12 >= 13

10. C123
a) Outies C12 = 19(3) must have 4 xor 5 because R5C3 = (45) -> R28C3 <> 4,5
b) 13(3): R7C1 <> 1,6,7 because R6C12 <> 4,5

11. N9+D\
a) 10(3): R9C7 <> 2 because R89C6 <> 3 and Killer pair (17) of 12(3) @ N8 blocks {127}
b) Innies = 8(3): R9C7 <> 5 because R7C79 >= 4
c) 13(3) @ R8C9: R8C9+R9C8 <> 5 because R9C9 <> 2,6
d) 5 locked in R7C7+R9C9 for D\
e) 15(3) @ D\ must have 1 xor 3 because R3C3 = (13) -> R3C4 <> 3

12. C89 !
a) ! Innies+Outies C9: 7 = R1469C8 - R5C9
-> R5C9 <> 2,3 because R6C8 >= 5
b) R5C9 = 9

13. N12 !
a) ! Innies+Outies N1: 23 = R4C123+R3C4 - R1C3
-> R4C123 >= 22 because 9 locked there @ N4
-> R1C3 <> 2
b) 15(3) @ R1C3 <> 9
c) 9 locked in 18(3) @ N2 = 9{18/27} -> 9 locked for C5
d) 3 locked in 15(3) @ R1C3 = 3{48/57} for C4; R1C3 <> 3
e) 15(3) @ R1C3: R1C3 <> 5 because R12C4 <> 7
f) Innies N1 = 10(3) = 1{27/45} because R1C3 = (47) -> R3C3 = 1, R3C1 = (25)

14. C789
a) Hidden Single: R3C9 = 3 @ R3
b) 13(3) @ R3C9 = {346} -> (46) locked for R4+N6
c) Innies N3 = 15(3) = 3{48/57}, R1C7 <> 4
d) Hidden Single: R2C7 = 6 @ C7, R8C7 = 9 @ C7
e) 24(3) = {789} -> (78) locked for C8
f) 17(3) @ N3 = {269} -> R2C8 = 2, R3C8 = 9
g) 13(3) @ R6C8 = {157} -> R7C9 = 1, R6C8 = 5, R6C9 = 7
h) Innies N9 = 8(3) = {134} -> (34) locked for C7+N9
i) Innies N3 = {357} locked for N3
j) 17(3) @ R6C7 = 8[54/63] -> R6C7 = 8
k) 10(3) <> 7 because R9C7 = (34)

15. N12
a) 15(3) @ R3C3 = 1[59/68]
b) 18(3) @ R3C1 = {279} -> R3C1 = 2, (79) locked for N4
c) 15(3) @ R3C3 = {168} -> R4C3 = 8, R3C4 = 6

16. R123
a) 14(3) = {257} -> R1C6 = 2
b) 18(3) @ N2 = {189} locked for C5+N5
c) 15(3) = {357} -> R1C3 = 7, (35) locked for C4+N2
d) 18(3) @ N1 = {459} -> R2C2 = 4, R2C3 = 9, R3C2 = 5

17. N7
a) 16(3) = 6[28/37]
b) Hidden Single: R9C1 = 9 @ D/, R6C1 = 6 @ C1
c) 15(3) = {348} -> R9C3 = 3
d) 16(3) @ R6C3 = {259} -> R6C3 = 2, R7C3 = 5, R7C4 = 9

18. Rest is singles (without considering the diagonals).

Rating: 1.5, had some difficult moves but not too many of them
Walkthrough by Andrew:
I finished A2X on Christmas Eve but only managed to go through Caida's and Afmob's walkthroughs yesterday evening.

Afmob wrote:
Seems my key moves are not much different from Caida's ones.

There seems to be a very narrow solving path around Caida's step 8, Afmob's step 8 and my step 21.

Mike wrote:
Yes, it's a toughie. Unlike several recent Assassin V1's, which consist of finding one (or at most, two) key move(s), apart from which the rest is plain sailing, this is more like a traditional V2, which (whilst having easier sections) generally involves more of a fight to dig away at the candidates. This puzzle does contain at least one key move, however, that will make your life easier if you find it.

I assume Mike was referring to the narrow solving path mentioned above. It certainly took a lot more work after that. I've a feeling that my later stages were longer than those of Caida and Afmob although I haven't tried to compare them to see where they were quicker.

I'll agree with both of them and rate A2X as 1.5.

Here is my walkthrough.

Prelims

a) R5C123 = {127/136/145/235}, no 8,9
b) 10(3) cage in N5 = {127/136/145/235}, no 8,9
c) 21(3) cage in N5 = {489/579/678}, no 1,2,3
d) 10(3) cage at R8C6 = {127/136/145/235}, no 8,9
e) 24(3) cage in N9 = {789}, locked for N9

1. 45 rule on N1 3 innies R1C3 + R3C13 = 10 = {127/136/145/235}, no 8,9
1a. Max R3C1 = 7 -> min R4C12 = 11, no 1

2. 45 rule on N9 3 innies R7C79 + R9C7 = 8 = 1{25/34}, no 6, 1 locked for N9

3. 45 rule on R5 3 innies R5C456 = 21 = {489/579/678}, no 1,2,3

4. 45 rule on R1234 3 innies R4C456 = 10 = {127/136/145/235}, no 8,9

5. 45 rule on C1234 3 innies R456C4 = 10 = {127/136/145/235}, no 8,9

6. 45 rule on C6789 3 innies R456C6 = 20 = {389/479/569/578}, no 1,2

7. 45 rule on C1234 1 outie R4C5 = 1 innie R6C4 + 4, R4C5 = {567}, R6C4 = {123}

8. 45 rule on C6789 1 outie R6C5 = 1 innie R4C6 + 1, no 9 in R6C5

9. 45 rule on R1234 1 outie R5C4 = 1 innie R4C6 + 4 -> R5C4 = 7, R4C6 = 3, locked for D/, R6C5 = 4 (step 8)

10. Naked pair {56} in R45C5, locked for C5 and N5
10a. Naked pair {12} in R46C4, locked for C4
10b. Naked pair {89} in R56C6, locked for C6

11. Killer pair 5,6 in R5C123 and R5C5, locked for R5

12. 45 rule on R12 3 outies R3C258 = 22 = 9{58/67}, 9 locked for R3

13. 45 rule on C12 3 outies R258C3 = 19 = {289/379/469/478/568}, no 1
13a. 2,3 of {289/379} must be in R5C3 -> no 2,3 in R28C3

14. 45 rule on C9 4 outies R1469C8 = 1 innie R5C9 + 7
14a. Min R1469C8 = 10 -> min R5C9 = 3

15. 17(3) cage at R6C7 = {179/269/278/359/368/458/467}
15a. 8,9 of {179/269/278/359/368/458} must be in R6C7-> no 1,2,3,5 in R6C7
15b. 1,2 of {179/269/278} must be in R7C7 -> no 1,2 in R7C6

16. 45 rule on C89 3 outies R258C7 = 17 = {179/269/278/359/368/458/467}
16a. 3,4 of {359/368/458/467} must be in R5C7 -> no 3,4 in R2C7

17. 17(3) cage in N3 = {179/269/278/458/467}
17a. 4 of {458} must be in R2C8 -> no 5 in R2C8

18. 45 rule on R89 3 outies R7C258 = 17 = {179/269/278/359/368} (cannot be {458/467} because 4,5,6 only in R7C2), no 4
18a. 3 of {359/368} must be in R7C5 -> no 3 in R7C2

19. 45 rule on N478 6 innies R4C123 + R789C6 = 36
19a. Max R89C6 = 9 (because of 10(3) cage at R8C6), max R7C6 = 7 -> max R789C6 = 16 -> min R4C123 = 20, no 1,2

20. R5C123 = {136/145/235} [1/2]
20a. Hidden killer pair 1,2 in R5C123 and R6C123 for N4 -> R6C123 must contain 1/2
20b. Killer pair 1,2 in R6C123 and R6C4, locked for R6

21. Chaining steps 20a and 20b, R5C123 and R6C4 must contain the same value of 1/2
21a. 45 rule on R6789, 1 outie R5C6 = 1 innie R6C4 + 7 -> R5C6 + R6C4 = [81/92]
21b. -> R5C123 + R5C6 must contain 1,8 or 2,9
21c. R5C789 = {239} (only remaining combination, cannot be {149/248} which clash with R5C123 + R5C6), locked for R5 and N6 -> R56C6 = [89], 9 locked for D\

22. R1469C8 = R5C9 + 7 (step 14)
22a. Min R1469C8 = 11 -> no 3 in R5C9 -> R5C9 = 9

23. R5C123 = {145} (only remaining combination), locked for R5 and N4 -> R5C5 = 6, locked for both diagonals, R4C5 = 5, R4C4 = 2 (step 4), locked for D\, R6C4 = 1, locked for D/
23a. R12C9 cannot be {13} -> no 9 in R1C8

24. 17(3) cage at R6C7 (step 15) = {368/458/467}, no 1
24a. 1 on D\ locked locked in R1C1 + R2C2 + R3C3, locked for N1

25. R7C79 + R9C7 (step 2) = 1{25/34}
25a. 5 of {125} must be in R7C7 -> no 5 in R7C9 + R9C7

26. 5 in R6 locked in R6C89 for 13(3) cage at R6C8 = 5{17/26}, no 3,4,8

27. Min R4C12 = 13 -> max R3C1 = 5

28. R1C3 + R3C13 (step 1) = {127/136/145/235}
28a. 1 of {127/145} must be in R3C3 -> no 4,7 in R3C3

29. 2,3 in R6 locked in R6C123 -> at least one of 2,3 must be in R6C12
29a. 13(3) cage at R6C1 = {238/247/256/346} (cannot be {139} because 1,9 only in R7C1), no 1,9
29b. 4 of {247} must be in R7C1 -> no 7 in R7C1
29c. 6 of {256/346} must be in R6C12 -> no 6 in R7C1

30. 1,4 in R4 locked in R4C789 -> at least one of 1,4 must be in R4C89
30a. 13(3) cage at R3C9 = {148/157/247/346}
30b. 2,3,5 of {157/247/346} must be in R3C9 -> no 6,7 in R3C9

31. 45 rule on N3 3 innies R1C7 + R3C79 = 15 = {159/168/249/258/267/348/357/456}
31a. 9 of {159} must be in R1C7
31b. 8 of {168} must be in R3C7
31c. -> no 1 in R1C7

32. R258C3 (step 13) = {469/478/568}
32a. R5C3 = {45} -> no 4,5 in R28C3

33. 18(3) cage in N1 = {189/369/378/459/468/567}
33a. 1,3,4 of {189/378/468} must be in R2C2 -> no 8 in R2C2
33b. 8 on D\ locked in R1C1 + R8C8 -> no 8 in R1C8 + R8C1

34. R258C7 (step 16) = {179/269/278/359/368}
34a. 9 of {269} must be in R8C7 -> 2 of {269/278} must be in R5C7 -> no 2 in R2C7
34b. 1 of {179} must be in R2C7
34c. 9 of {269/359} must be in R8C7
34d. -> no 9 in R2C7

35. 17(3) cage in N3 (step 17) = {179/269/278/458/467}
35a. 2,4 of {278/458} must be in R2C8 -> no 8 in R2C8

36. 14(3) cage at R1C6 = {149/158/167/248/257/347/356} (cannot be {239} because 3,9 only in R1C7)
36a. 3,8,9 of {149/248/347} must be in R1C7 -> no 4 in R1C7

37. 45 rule on N7 3 innies R7C13 + R9C3 = 12 = {129/138/147/237/246/345} (cannot be {156} because 1,6 only in R9C3)
37a. 1 of {129/138} must be in R9C3 -> no 8,9 in R9C3
37b. 3 of {138} must be in R7C1 -> no 8 in R7C1

38. 2,3 in R6 locked in R6C123
38a. R6C12 cannot be {23} because max R7C1 = 5 -> R6C3 = {23}

39. 16(3) cage at R6C3 = {259/268/349/358/367} (cannot be {457} because R6C3 only contains 2,3)
39a. R6C3 = {23} -> no 2,3 in R7C34

40. 2,3 in R6 locked in R6C123 = {236/237/238}
40a. 45 rule on N7 6 outies R6C123 + R789C4 = 32
40b. R6C123 = 11,12,13 -> R789C4 = 19,20,21 = {389/469/489/568/569}
40c. Max R89C4 = 14 (because of 15(3) cage at R8C4) -> min R7C4 = 5

41. 12(3) cage at R3C6 = {147/156/246}, no 8
41a. 5 of {156} must be in R3C7 -> no 5 in R3C6

42. 9 in C8 locked in R237C8
42a. 45 rule on C89 4 innies R2378C8 = 1 outie R5C7 + 24 -> R2378C8 = 26,27
42b. R2378C8 = {2789/4589/4679/4689} (cannot be {5679} because 5,6 only in R3C8)
42c. 2,4 must be in R2C8 -> no 7,9 in R2C8

43. 17(3) cage in N3 (step 17) = {269/278/458/467} (cannot be {179} because R2C8 only contains 2,4), no 1

44. 9 on D/ locked in R7C3 + R8C2 + R9C1, locked for N7

45. 16(3) cage in N7 = {169/268/457} (cannot be {178} because R8C23 = {78} clashes with R8C8, cannot be {259} because R8C3 only contains 6,7,8)
45a. {457} must be [547]
45b. -> no 7 in R7C2, no 5,7 in R8C2

46. R7C258 (step 18) = {179/269/278/359/368}
46a. 1 of {179} must be in R7C2 -> no 1 in R7C5

47. R1C7 + R3C79 (step 29) = {159/348/357} (cannot be {168} because no 1,6,8 in R3C7, cannot be {249} which clashes with R2C8, cannot be {258/267/456} because there’s no place for 9 in N3), no 2,6
47a. 4 of {348} must be in R3C7 -> no 4 in R3C9

48. 12(3) cage at R3C6 (step 39) = {147/156/246}
48a. 6 of {156} must be in R4C7 (cannot be [651] which clashes with R3C258)
48b. 2 of {246} must be in R3C6
48c. -> no 6 in R3C6

49. R4C123 + R789C6 = 36 (step 19)
49a. R4C123 = 22,23,24 -> R789C6 = 12,13,14
49b. R789C6 = {147/156/246/157/247/256/167/257} [1/2]
49c. R789C5 = {129/138/237}
49d. Killer triple 1,2,3 in R789C56, locked for N8
49e. Min R89C4 = 9 -> max R9C3 = 6

50. 3 in N8 locked in R789C5, locked for C5
50a. R789C5 = {138/237}, no 9
50b. 9 in N8 locked in R789C4, locked for C4

51. R789C6 = 12,13,14 (step 47a) -> R789C4 = 19/20/21
51a. R789C4 = {469/569/489} [4/5]
51b. Hidden killer pair 4,5 in N8 -> R789C6 must contain 4/5 -> R789C6 not {167}

52. 45 rule on R89 4 innies R8C2378 = 1 outie R7C5 + 23
52a. Max R8C2378 = 30 -> no 8 in R7C5

53. R89C6 must contain 1/2 (step 49b)
53a. 10(3) cage at R8C6 = {127/136/145/235}
53b. 4 of {145} must be in R9C7 -> no 4 in R89C6

54. R7C258 (step 18) = {179/269/278/359/368} [8/9]
54a. Hidden killer pair 8,9 in R7 -> R7C34 must contain 8/9
54b. 16(3) cage at R6C3 (step 39) = {259/268/349/358} (cannot be {367}), no 7

55. R7C13 + R9C3 (step 37) = {129/138/246/345}
55a. 1,6 of {129/246} must be in R9C3 -> no 2 in R9C3
55b. R7C13 + R9C3 cannot be {246} because [246] clashes with R258C3 = {568}
55c. -> R7C13 + R9C3 = {129/138/345}, no 6
55d. 3 of {345} must be in R9C3 (cannot be in R7C1 because R79C3 = {45} clashes with R5C3) -> no 4,5 in R9C3
55e. {345} must be [453] (if [543] cannot make combination for 16(3) cage at R6C3) -> no 5 in R7C1, no 4 in R7C3
55f. R9C67 cannot be {13} -> no 6 in R8C6

56. R789C4 = {469/569/489}
56a. R9C3 = {13} -> R89C4 = {159/348} (cannot be {168} which clashes with R789C4), no 6
56b. R789C4 = {569/489} (cannot be {469} which clashes with R89C4) -> R7C4 = {69}

57. 16(3) cage at R6C3 (step 54b) = {259/268} (cannot be {358} because R7C4 only contains 6,9) -> R6C3 = 2, R7C34 = [59/86], no 9 in R7C3

58. 3 in N4 locked in R6C12, locked for 13(3) cage -> no 3 in R7C1

59. R7C13 + R9C3 = [453] (only remaining permutation), 5 locked for D/, R7C4 = 9 (step 57), R3C3 = 1, R5C3 = 4, R7C7 = 3, locked for D\, R5C78 = [23]

60. R7C79 + R9C7 (step 2) = [314] (only remaining permutation), R9C9 = 5, locked for D\

61. R2C2 = 4 (hidden single on D\), R2C8 = 2, locked for D/, R9C8 = 6, R8C9 = 2

62. Naked pair {78} in R78C8, locked for C8 and N9 -> R6C8 = 5, R8C7 = 9, R8C2 = 8, locked for D/, R8C8 = 7, locked for D\

and the rest is naked singles and cage sums, possibly only one cage sum if the right one is selected
Assassin 2X-Lite (A2X-Lite) by mhparker(Dec 07)
Puzzle pic: 1-9 cannot repeat on the diagonals:
Image
Code: Select, Copy & Paste into solver:
3x3:d:k:4096:4096:2050:2050:3588:4613:4613:3591:3591:4096:5130:5130:2050:3588:4613:4879:4879:3591:2066:5130:4884:4884:3588:4631:4631:4879:4634:2066:2066:4884:2590:2590:3616:4631:4634:4634:3620:3620:3620:2590:3616:5417:3114:3114:3114:4397:4397:4655:3616:5417:5417:1587:3892:3892:4397:3127:4655:4655:3898:1587:1587:4925:3892:4927:3127:3127:4674:3898:3908:4925:4925:2119:4927:4927:4674:4674:3898:3908:3908:2119:2119:
Solution:
+-------+-------+-------+
| 6 8 3 | 4 2 5 | 7 1 9 |
| 2 9 7 | 1 3 6 | 5 8 4 |
| 1 4 5 | 8 9 7 | 2 6 3 |
+-------+-------+-------+
| 4 3 6 | 2 5 1 | 9 7 8 |
| 5 1 8 | 3 7 9 | 4 2 6 |
| 7 2 9 | 6 4 8 | 1 3 5 |
+-------+-------+-------+
| 8 6 4 | 5 1 2 | 3 9 7 |
| 9 5 1 | 7 8 3 | 6 4 2 |
| 3 7 2 | 9 6 4 | 8 5 1 |
+-------+-------+-------+
Quote:
mhparker, lead-in: Est. rating: 1.25
Caida:much easier (than A2X) - nicer for my first attempt at a "Killer-X". I would consider rating A2XLite a 1.0
Nasenbaer:Yes, A2X-Lite is much easier
Andrew: I'd originally been thinking of rating it as an easier 1.25 but ..I'll make it a high 1.0
Reworked Walkthrough by Caida:
mhparker wrote:
In the meantime, maybe this is more like the puzzle you're looking for?:
This was much easier - nicer for my first attempt at a "Killer-X". Thanks!!

Here's my walkthrough for A2XLite. Any comments/suggestions/corrections are always appreciated!

I would consider rating A2XLite a 1.0 (but would like to hear what others have to say).

Thanks Andrew!!
Preliminaries:

a. 8(3)n12 and n14 and n9 = {125/134} (no 6..9)
a1. -> 1 locked in n9 -> no 1 elsewhere in n9
a2. -> r4c4 no 1 (CPE with 8(3)n12 and 8(3)n24)
Andrew pointed out that I missed the obvious CPEs of r1c56 and r56c1 oops!!
b. 20(3)n1 = {389/479/569/578} (no 1,2)
c. 19(3)n124 and n3 and n7 and n9 = {289/379/469/478/568} (no 1)
d. 10(3)n5 = {127/136/145/235} (no 8,9)
e. 21(3)n5 = {489/579/678} (no 1,2,3)
f. 6(3)n698 = {123} (no 4..9)
f1. -> killer pair {23} locked in n9 in r7c7 and 8(3)n9 -> no 2,3 elsewhere in n9

1. Innies n1: r1c3+r3c13 = 9(3) = {126/135/234} (no 7..9)
1a. -> 19(3)n124: r3c4 and r4c3 no 2,3 (requires 89 or 79)

2. Innies n9: r7c79+r9c7 = 18(3) = [2]{79}/[3]{69/78}
2a. -> r7c9 and r9c7 no 4,5

3. Innies r1234: r4c456 = 8(3) = {125/134} (no 6..9) -> 1 locked in r4c56 for r4 and n5
3a. cage overlap: r5c4 – r4c6 = 2
3b. -> r5c4 no 2

4. Innies r5: r5c456 = 19(3) ={379/469/478/568} (no 2)
Note: {289} blocked by r5c4

5. Innies r6789: r6c456 = 18(3)
5a. cage overlap: r5c6 – r6c4 = 3
5b. -> r5c6 no 4; r6c4 no 7,8,9

6. Innies c1234: r456c4 = 11(3) = {236/245} (no 7) -> 2 locked for c4 and n5
6a. -> r5c4 no 4 (step 3a)
Andrew noticed that I missed eliminating 5 from r4c6 also b/c of step 3a
6b. cage overlap: r6c4 – r4c5 = 1
6c. -> r6c4 no 3
6d. -> r5c6 no 6 (step 5a)
6e. r4c4 no 5 (from h8(3) step 3)
6f. h11(3)c4 = [236/362]
Note: [254] blocked from h11(3) by h8(3) and 10(3) and [452] blocked by step 5
You can't have 254 b/c this would put a 2 in the h8(3)r4 - but if 8(3) has a 2 then it must also have a 5 - but it can't have a 5 b/c it is in the h11(3)c4.
452 won’t work because this puts a 2 in r6c4 so then you need a 5 in r5c6 (step 5a) but the 5 is already placed in r5c4.

6g. 2,3,6 locked for n5 in c4
6h. -> r4c6 no 5 (step 3a)
6i. -> r5c6 no 7, 8 (step 5a)
6j. 21(3)n5 = [9]{48}/[5]{79}/[9]{57} -> 9 locked in 21(3) for n5

7. 14(3)n5 = [176/482]
7a. -> r5c5 no 4,5

8. Innies c6789: r456c6 = 18(3) = [198/459/495]
8a -> r6c6 no 4,7
8b. -> r6c5 no 5,8,9
8c. -> 7 locked in n5 in c5 -> no 7 elsewhere in c5
8d. -> 9 locked in n5 in c6 -> no 9 elsewhere in c6
8e. -> 8 locked in n5 in diagonal top left to bottom right - > no 8 elsewhere on that diagonal

9. 8(3)n14: r3c1 = 1
9a. -> killer quadruple {2345} locked for r4 8(3)n14 and h8(3)n5 -> no 2,3,4,5 elsewhere in r4

10. 8(3)n12 = [2]{15}/[3]{14}
10a. -> r1c3 no 4,5
10b. -> 1 locked in r12c4 for c4 and n2 -> no 1 elsewhere in c4 and n2

Changing walkthrough b/c of faulty early elimination to original step 11 (I had said that Innies c5: r456c5 = 16(3) = [574] Andrew pointed out that I missed [187] which is still valid. This was a BIG mistake on my part).

new11. hidden single: r9c9 = 1 (only 1 on \d)
new11a. hidden single: r2c4 = 1
new11b. innies n1 (step 1): r3c3 no 2,3,4

new12. 19(3)n124 = {469/568} (no 7) -> 6 locked in r34c3 -> no 6 elsewhere in c6
new12a. -> r3c4 no 9
new12b. -> 9 locked in n2 in c5 -> no 9 elsewhere in c5
new12c. -> 7 locked in n2 in c6 -> no 7 elsewhere in c6
new12d. 14(3)n2 = {239} -> locked for n2 and c5
new12e. -> {23} locked in n8 in r789c6
new12f. -> r89c6 <> {23} -> r7c6 = {23} (no 1) -> pair {23} locked in r7 in c67
new12g. -> r6c7 = 1 (only 1 in 6(3))
new12h. single: r1c8 = 1
new12i. -> r8c6 no 1 (not possible to have {12/13} in 15(3))
new12j. -> hidden single r4c6 = 1
new12k. -> r5c4 = 3 (step 3a)
new12l. -> r4c45 = [25]

Now the rest of my steps are valid

11. Innies c5: r456c5 = 16(3) = [574]
11a. -> r4c456 = [251]
11b. -> r5c456 = [379]
11c. -> r6c456 = [648]
11d. -> 278 locked for diagonal l->r
11e. -> 167 locked for diagonal r->l

12. 6(3)n689 = [123]
12a. -> 3 locked for diagonal l->r
12b. -> 8(3)n9 = {125} -> locked for n9

13. pair {34} locked in r4c12 for n4
13a. 14(3)n4 = {158} -> locked for n4 and r5
13b. hidden single: r4c3 = 6
13c. triple {279} locked in r6c123 for r6

14. 15(3)n69 = {35}[7]
14a. -> r7c9 = 7
14b. -> r9c7 = 8 (step 2)

15. 15(3)n89 = {34}[8]
15a. -> {34} locked for n8 and c6 -> no 3,4 elsewhere in n8 and c6
Made some changes here – based on my new steps #11 and 12
new15b. -> triple {567} locked in r123c6 -> no 5,6,7 elsewhere in n2
new 15c. -> 8(3)n12 = [341]


16. this is now step new15b
16a. this is now step new12d
16b. single: r3c4 = 8
16c. 19(3)n124 = [586] -> 5 locked for diagonal l->r
16d. this is now step new11
16e. r9c5 = 6
16f. this is now step new12h
16g. this is now step new15c

17. 18(3)n23 = {567} no 2,9
17a. 18(3)n478 = [945]
17b. -> 4 locked for diagonal r->l
17c. 18(3)n234 = [729]
17d. -> 2 locked for diagonal r->l

Everything left is cage sums and singles

I'll have to give the original A2X another go in a bit.
But would really love if someone else did a walkthrough so I could take a peek :wink:

Cheers,

Caida
Walkthrough by Nasenbaer with lots of jumping around:
Beaten again. Oh well. :wink:

Yes, A2X-Lite is much easier. And here is my walkthrough. It's the way I solved it so no nice shortcuts and a lot of jumping around. Don't know about the rating, haven't looked into that.

A2X Lite

1. n12: 8(3) = 1{25|34} -> no 6,7,8,9 -> 1 locked for 8(3) -> no 1 in r1c56

2. n1: 20(3) = {389|479|569|578} -> no 1,2

3. n3: 19(3) = {289|279|469|478|568} -> no 1

4. n14: 8(3) = 1{25|34} -> no 6,7,8,9 -> 1 locked for 8(3) -> no 1 in r56c1

5. n124: 19(3) = {289|279|469|478|568} -> no 1

6. n5: 10(3) = {127|136|145|235} -> no 8,9

7. n5: 21(3) = {489|579|678} -> no 1,2,3

8. n689: 6(3) = {123} -> no 4,5,6,7,8,9 -> 1,2,3 locked for 6(3)

9. n9: 19(3) = {289|279|469|478|568} -> no 1

10. n7: 19(3) = {289|279|469|478|568} -> no 1

11. n9: 8(3) = 1{25|34} -> no 6,7,8,9 -> 1 locked for 8(3) and n9

12. n9: {23} locked in 8(3) and r7c7 for n9

13. n9: 19(3) = {469|478|568}
13a. -> {45} locked in 19(3) and 8(3) for n9

14. r7c79 + r9c7 = h18(3) = {279|369|378} -> no 1,2,3,4,5 in r7c9 and r9c7

15. n1: r1c3 + r3c13 = h9(3) = {126|135|234} -> no 7,8,9 in r3c3

16. n124: 19(3): cleanup -> no 2,3 in r3c4 and r4c3

17. 45 on r12: r3c258 = h19(3) = {289|279|469|478|568} -> no 1

18. 45 on r1234: r4c456 = 8(3) = 1{25|34} -> no 6,7,8,9 -> 1 locked for 8(3), r4 and n5

19. (step 4) -> r3c1 = 1

20. (step 1) -> 1 locked in r12c4 for c4 and n2

21. r9c9 = 1 (single for D\)

22. r2c4 = 1 (single for r2)

23. {12345} locked in r4c12456 for r4

24. n36: 18(3) = {279|369|378|468|567} -> r3c9 = {2345}

25. n5: 10(3): cleanup -> no 4 in r4c5

26. 45 on r6789: r6c456 = 18(3) = {279|369|378|468|567} ({459} blocked by h8(3))
26a. -> cleanup -> no 7,8,9 in r6c4 (r6c56 must be at least 12 from the 21(3) cage)

27. n5: 14(3): cleanup -> no 2,4 in r5c5

28. n1: h9(3): cleanup -> no 4 in r1c3, no 2,4 in r3c3

29. n12: 8(3): cleanup -> no 3 in r1c4

30. n124: 19(3) = {379|469|568}

31. 45 on c1234: r456c4 = h11(3) = 2{36|45} -> 2 locked for h11(3), c4 and n5

32. n12: 8(3): cleanup -> no 5 in r1c3

33. n1: h9(3): cleanup -> no 3 in r3c3

34. n124: 19(3) = 6{49|58} -> no 7 in r4c3, no 7,9 in r3c4

35. r4: 7 locked in r4c789 for r4 and n6

36. n1: 20(3): {569} blocked by r3c3 -> no 6 in 20(3)

37. n1: 16(3) = {268|349|358|457} ({259|367} blocked by h9(3))

38. n5: 10(3): {145} blocked by r1c4 -> 10(3) = 3{16|25} -> no 4 in r45c4 -> 3 locked for 10(3) and n5

39. n5: 14(3): cleanup -> no 5,6 in r5c5

40. n5: h8(3): cleanup -> no 5 in r4c4, no 3 in r4c5

41. n5: 10(3): cleanup -> no 5 in r5c4 -> 3 locked in r45c4 for c4 and n5

42. {23} locked in r4c4 and r7c7 for D\ -> no 2,3 in r1c1 and r2c2

43. 45 on c6789: r456c6 = h18(3) = {189|459|468|567}

44. n5: h8(3) and 10(3): no 5 in r4c6 (would mean r4c45 = [21], r5c4 = 7 -> not possible)
44a. 14(3): {257} not possible
44b. h18(3) at r4c6: {567} not possible -> no 7 in r56c6
44c. 21(3): no 5,6 at r6c5
44d. h18(3) at r4c6: {468} not possible (would force 6 in r5c4) -> no 4,6 in r56c6
44e. -> 9 locked in r56c6 for 21(3), c6 and n5
44f. no 8 in r6c5
44g. 14(3): {158} not possible, blocked by h18(3) at r4c6 -> no 4,5 in r6c4
44h. combination check: no 5 in r6c6, no 8 in r5c6, no 2 in r5c4 (h18(3) at r6c4 = [675] clashes with 14(3) = [176])

45. n5: h11(3) = {236} -> 2,3,6 locked for c4 and n5

46. n5: 7 locked in r56c5 for n5 and c5

47. n8: 7,9 locked in r789c4 for n8 and c4

48. n2: 9 locked in 14(3) -> 14(3) = {239} -> 2,3,9 locked for c5 and n2

49. n8: 15(3) = 6{18|45} -> 6 locked for c5 and n8

50. n23: 18(3) = {378|468|567} (no 1,2,9}

51. -> r1c8 = 1

52. n3: 14(3) = 1{49|58|67} -> no 2,3

53. 45 on r5: r5c456 = h19(3) = {379|568}

54. n4: 14(3) = {149|158|347} (other combinations blocked by h19(3) and r4c12)
54a. -> {45} locked in 14(3) and r4c12 for n4

55. n6: 2 locked in 12(3) for r5 and c6
55a. n6: 12(3) = 2{19|46} (other combinations blocked by h19(3)) -> no 9 at r5c7

56. r7: 2 locked in r7c67 for 6(3) and r7

57. r5: 14(3): {149} blocked by h19(3) and 12(3) -> no 9

58. 8 locked in r5c5 and r6c6 for n5 and D\

59. n6: 5 locked in r6c89 for n6, r6 and 15(3)
59a. 15(3) = 5{37|46} -> no 6 in r6c89

60. n9: h18(3): no 6,7 in r9c7

61. n89: 15(3) = {159|249|258|348} -> no 8 in r89c6

62. n6: 8 locked in r4c789 for n6 and r4

63. n124: 19(3): 6 locked in r34c3 for 19(3) and c3
63a. no 5 in r3c4

64. n3: 14(3): {167} blocked by r7c9 -> no 6,7

65. n3: 19(3): {289|478} blocked by 14(3) -> no 2
65a. {89} locked in 14(3) and 19(3) -> no 8,9 in r13c7

66. n7: 19(3): no 2 in r8c1 (blocked by r9c7)


67. 45 on n3: r1c7 + r3c79 = h12(3) = 2{37|46} -> 2 locked in r3c79 for h12(3), r3 and n3

68. n6: 3 locked in r6c789 for n6 and r6

69. n47: 17(3): {458|359} not possible -> no 5

70. 45 on c89: r258c7 = h15(3) = 5{19|28|46} -> no 3,7

71. from step 17: r3: h19(3) = 9{37|46} -> no 5,8 -> no 4 in r3c8

72. 45 on r89: r7c258 = h16(3) = {169|178|349|358|367|457}

73. 45 on c12: r258c3 = h16(3) = {178|349|358|457}

74. n78: 18(3) = {279|378|459} -> no 7,8,9 in r9c3

75. n8: 4 or 5 in r89c6 (15(3)) -> 15(3) = {168}

76. r456c5 = [574], r456c6 = [198], r456c4 = [236], r7c67 = [23], r6c7 = 1, r7c9 = 7

77. n6: 12(3) = {246}

78. r4c3 = 6, r3c34 = [58]

79. r1c34 = [34]

80. n1: 20(3) = {479}

81. r1c167 = [657], r23c6 = [67], r34c7 = [29], r4c89 = [78], r123c9 = [943], r123c5 = [239]


Edit: Thanks for your comments, Andrew. They are included in blue.
Cheers,
Nasenbaer
Reworked Walkthrough by Andrew:
I finished A2X-Lite (I prefer Light) yesterday evening and went through Caida's and Nasenbaer's walkthroughs today. Since neither of them had my breakthrough move, I'm posting my walkthrough now. Must admit I didn't initially spot step 21 but when I did I reworked it to put it in the right place.

I'd originally been thinking of rating it as an easier 1.25 but after I found step 21 I'll make it a high 1.0.

Here is my walkthrough for A2X-Lite.

Prelims

a) 8(3) cage at R1C3 = 1{25/34}, CPE no 1 in R1C56
b) 20(3) cage in N1 = {389/479/569/578}, no 1,2
c) 19(3) cage in N3 = {289/379/469/478/568}, no 1
d) 8(3) cage at R3C1 = 1{25/34}, CPE no 1 in R56C1
e) 19(3) cage at R3C3 = {289/379/469/478/568}, no 1
f) 10(3) cage in N5 = {127/136/145/235}, no 8,9
g) 21(3) cage in N5 = {489/579/678}, no 1,2,3
h) 6(3) cage at R6C7 = {123}
i) 19(3) cage in N9 = {289/379/469/478/568}, no 1
j) 19(3) cage in N7 = {289/379/469/478/568}, no 1
k) 8(3) cage in N9 = 1{25/34}, 1 locked for N9

1. Killer pair 2,3 in R7C7 and 8(3) cage, locked for N9

2. 19(3) cage in N9 = {469/478/568}
2a. Killer pair 4,5 in 8(3) cage and 19(3) cage, locked for N9
2b. Min R7C9 = 6 -> max R6C89 = 9, no 9
2c. Min R9C7 = 6 -> max R89C6 = 9, no 9

3. 45 rule on N1 3 innies R1C3 + R3C13 = 9 = {126/135/234}, no 7,8,9

4. 45 rule on R12 3 outies R3C258 = 19 = {289/379/469/478/568}, no 1

5. 45 rule on R5 3 innies R5C456 = 19 = {289/379/469/478/568}, no 1
5a. 2 of {289} must be in R5C4 -> no 2 in R5C5

6. 45 rule on R1234 3 innies R4C456 = 8 = 1{25/34}, 1 locked for R4 and N5
6a. R3C1 = 1 (only remaining position for 1 in 8(3) cage), R4C12 = {25/34}
6b. Naked quint {12345} in R4C12456, locked for R4
6c. R13C3 = 8 (step 3) = [26/35], no 4, no 2 in R3C3

7. 8(3) cage at R1C3 = 1{25/34}, 1 locked in R12C4, locked for C4 and N2
7a. 3 of {134} must be in R1C3 -> no 3 in R12C4

8. R9C9 = 1 (hidden single in D\), R8C9 + R9C8 = {25/34}
8a. 1 in N3 locked in R1C78, locked for R1
8b. R2C4 = 1 (hidden single in C4), R1C34 = {25}/[34]
[Hidden single in R2 would have been slightly quicker but that’s not what I spotted.]

9. 45 rule on R1234 1 outie R5C4 = 1 innie R4C6 + 2, no 2 in R5C4

10. 45 rule on R6789 1 outie R5C6 = 1 innie R6C4 + 3, no 4 in R5C6, no 7,8,9 in R6C4

11. 10(3) cage in N5 = {127/136/145/235}
11a. 1 of {145} must be in R4C5 -> no 4 in R4C5

12. 45 rule on C1234 3 innies R456C4 = 11 = {236} (cannot be {245} which clashes with R1C4), locked for C4 and N5, clean-up: no 5 in R1C3 (step 8b), no 3 in R3C3 (step 6c), no 5 in R4C6 (step 9), no 7,8 in R5C6, no 3 in R6C4 (both step 10)

13. Naked pair {23} in R4C4 + R7C7, locked for D\

14. 21(3) cage in N5 = {489/579}, 9 locked for N5

15. 14(3) cage in N5 = {167/248} (cannot be {158} because 5,8 only in R5C5, cannot be {257} because R4C6 only contains 1,4), no 5
15a. 4 of {248} must be in R4C6 -> no 4 in R5C5

16. 45 rule on C5 3 innies R456C5 = 16 = {178/457}, no 9, 7 locked for C5 and N5
16a. 5 of {457} must be in R4C5 -> no 5 in R6C5

17. 9 in N5 locked in R56C6, locked for C6
17a. 45 rule on N5 3 remaining innies R456C6 = 18 = {189/459}
17b. 4 of {459} must be in R4C6 -> no 4 in R6C6

18. 21(3) cage in N5 (step 14) = {489/579}
18a. 4 of {489} must be in R6C5 -> no 8 in R6C5
[At this stage I missed 8 locked in R5C5 + R6C6 for D\, fortunately it didn’t matter.]

19. 19(3) cage at R3C3 = {469/568} (cannot be {478} because R3C3 only contains 5,6), no 7, 6 locked in R34C3, locked for C3
19a. 4 of {469} must be in R3C4 -> no 9 in R3C4
19b. 7 in R4 locked in R4C789, locked for N6
19c. 7,9 in C4 locked in R789C4, locked for N8

20. 9 in N2 locked in R123C5 = {239} (only remaining combination), locked for C5 and N2
20a. 6 in C5 locked in R789C5, locked for N8

21. 2,3 in N8 locked in R789C6, R89C6 cannot be {23} -> R7C6 = {23}
21a. Naked pair {23} in R7C67, locked for R7
21b. R6C7 = 1 (only remaining position for 1 in 6(3) cage)

22. R1C8 = 1 (hidden single in R1), R12C9 = 13 = {49/58/67}, no 2,3

23. R5C456 (step 5) = {379/568}
23a. R5C789 = {246} (only remaining combination, cannot be {345} which clashes with R5C456), locked for R5 and N6 -> R5C4 = 3, R4C4 = 2, R4C5 = 5, R5C6 = 9, R6C4 = 6, R6C6 = 8, R5C5 = 7, R6C5 = 4, R4C6 = 1, 1,6,7 locked for D/, 2,7,8 locked for D\ -> R7C7 = 3, R7C6 = 2, clean-up: no 6,7 in R2C9 (step 22), no 4 in R8C9 + R9C8 (step 8)
23b. Naked pair {25} in R8C9 + R9C8, locked for N9

24. R4C3 = 6 (hidden single in R4), R3C3 = 5, R3C4 = 8 (step 19)

25. Naked pair {35} in R6C89, locked for R6, R7C9 = 7
25a. 45 rule on N9 1 remaining innie R9C7 = 8, R9C5 = 6
25b. R9C7 = 8 -> R89C6 = 7 = {34}, locked for C6 and N8

26. R1C4 = 4 (hidden single in C4), R1C3 = 3 (step 8b), clean-up: no 9 in R2C9 (step 22)

27. 18(3) cage at R1C3 = {567} (only remaining combination), no 2,9 in R1C7
27a. 5 in C6 locked in R12C6 -> no 5 in R1C7

28. R2C7 = 5 (hidden single in C7), clean-up: no 8 in R12C9 (step 22)

and the rest is naked singles, including eliminations along the diagonals, and cage sums

Maybe some of the steps I used here may be helpful for A2X, when I've got time to look at it.


Last edited by Ed on Fri Jun 13, 2008 12:21 pm, edited 2 times in total.

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Location: Sydney, Australia
Assassin 3 (16 June 2006) by Ruud
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:3072:3072:4866:4866:4866:4869:4869:1031:1031:2057:3850:3850:3850:4866:3342:4869:3856:3856:2057:2835:2835:4629:4629:3342:3342:3856:4122:3867:3867:2835:2835:4629:5152:5152:5152:4122:3867:4389:4389:3111:3111:3111:4138:4138:4138:3867:4142:4142:4912:4913:4913:4913:4148:4138:5174:4142:4142:4912:4912:2619:2619:4148:4148:5174:5184:4417:4417:4417:2619:4677:4677:1863:5174:5184:5184:5184:3404:3404:3404:4677:1863:
Solution:
+-------+-------+-------+
| 8 4 6 | 5 7 2 | 9 3 1 |
| 7 2 9 | 4 1 3 | 8 5 6 |
| 1 3 5 | 6 9 8 | 2 4 7 |
+-------+-------+-------+
| 4 6 1 | 2 3 7 | 5 8 9 |
| 3 9 8 | 1 5 6 | 7 2 4 |
| 2 5 7 | 8 4 9 | 6 1 3 |
+-------+-------+-------+
| 6 1 3 | 9 2 5 | 4 7 8 |
| 5 8 4 | 7 6 1 | 3 9 2 |
| 9 7 2 | 3 8 4 | 1 6 5 |
+-------+-------+-------+
Quote:
sudokuEd: couldn't resist the prospect of using 'overlap' on r5 and c1. Didn't end up needing it - but still very challenging. Had to redo it a few times before getting it out - when the sum chart comes out, the mistakes multiply!
sudokuEd: (nd) definately made it easier than the way(s!) I took
nd: re: combinations: I never use charts -- not all that reliable. I usually just work out combinations for myself on paper if needed
no extensive use of combo chart Walkthrough by nd:
Ed--here's my version--tell me if this is clear/if I've made any typos. No extensive use of combination charts &c.

Step 1. R1C89 = {13}, R34C9 = {79}, R1C12 = {48|57}, R5C23 = {89}, 11(4) cage beginning in N1 = {1235}.

Step 2. 45 rule on C1 -> R14C2 = 10, so R1C2 = {478}, R4C2 = {236}. 45 rule on R1234 -> R4C12 = 10 -> R56C1 = 5 = {14|23}. 45 rule on R5 -> R6C9 = R5C1 = {1234}.

Step 3. 20(3) cage in R4 = {389}, {569} or {578}, i.e. must contain {79} -> complex pair with {79} in R4C9 -> {79} eliminated in the rest of R4. So R4C12 = [46], R1C12 = [84], R56C1 = R6C9 = {23}, R23C1 = {17}, R789C1 = {569}, R4C3 = {15}, R6C23 = {(1|5)7}.

[Step 4 deleted]

Step 5. In R4 the 2 can't go in R4C5 because this would make R3C45 = {79}, contradicting R3C9. Only place left is R4C4 = 2 -> R4C3 = 1, R7C23 = [13], R3C23 = [35], R6C23 = [57].

Step 6. The 20(3) cage in R4 has now been narrowed down to {389} or {578}, i.e. it must contain an 8. So R4C5 = {35}, and the only remaining combos for the 12(3) cage in N5 = {147} or {156}. So 1 is locked in R5 in N5 and R6C8 = 1 (can't be in 19(3) cage obviously because this would make the remaining two cells > 17) -> R1C89= [31]. Subtraction combo on remaining cells in R6 ({4689}) -> R6C4 = 8, R6C567 = {469}.

Step 7. 45 on R7 -> R8C6 = R7C1 - 5, i.e. R7C1 = {69}, R8C6 = {14}. R7C89 = [78] or [96]. R7C45 = {29|47|56}. So we have a complex triple on {679} in R7! So R7C67 = {45}, R8C6 = 1, R7C45 = [92], R7C1 = 6, R7C89 = [78], R9C7 = 1.
[Footnote: I'll leave this step as it is but I see that it's far more complex than necessary: the simplest thing is to note that in R7 the 8 must go in R7C89. So R7C89 = [78]; in turn R7C67 must have the 4 in them, so the 10(3) cage has {145} in it. No innie-outie differences or complex triples required!]

Step 8. 45 on N9 -> R7C67 = [54], R9C56 = {48}, R89C9 = {25}, R6C9 = R5C1 = 3, R6C1 = 2, R8C7 = R9C4 = 3, R8C45 = {67}, R8C3 = 4, R89C8 = [96], R89C1 = [59], R89C9 = [25], R8C2 = 8, R9C23 = [72], R5C23 = [98], R2C2 = 2.

Step 9. In N6 the 2 and 4 must be in 16(4). So the remaining cell of the 16(4) = 7, which goes in R5C7. R4C9 = 9, R4C6 = 7, R4C78 = {58}, R4C5 = 3, R5C6 = 6, R5C89 = [24], R2C9 = 6, R23C8 = [54]. 45 rule on R1 -> R2C57 = 9 = [18]. And you carry on....
Assassin 4 (aka June 23 2006) by Ruud
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:7936:3073:3073:3075:3588:3588:3588:7943:7943:7936:7936:3075:3075:2829:2829:7943:7943:4369:2834:7936:7936:3349:2829:7943:7943:2841:4369:2834:6172:7936:3349:6431:2336:2336:2841:2841:2834:6172:6172:6431:6431:6431:3370:3370:4396:3117:3117:815:815:6431:2866:7475:3370:4396:1590:3117:7992:7992:4666:2866:7475:7475:4396:1590:7992:7992:4666:4666:3396:3396:7475:7475:7992:7992:3658:3658:3658:3396:4430:4430:7475:
Solution:
+-------+-------+-------+
| 9 7 5 | 6 8 2 | 4 1 3 |
| 8 6 2 | 4 3 1 | 5 7 9 |
| 3 1 4 | 5 7 9 | 6 2 8 |
+-------+-------+-------+
| 6 9 3 | 8 1 7 | 2 4 5 |
| 2 8 7 | 9 4 5 | 1 3 6 |
| 4 5 1 | 2 6 3 | 8 9 7 |
+-------+-------+-------+
| 5 3 9 | 1 2 8 | 7 6 4 |
| 1 4 8 | 7 9 6 | 3 5 2 |
| 7 2 6 | 3 5 4 | 9 8 1 |
+-------+-------+-------+
Quote:
sudokuEd: This puzzle seemed a lot easier than last week
non-cryptic Walkthrough by sudokuEd:
Trying to learn to write non-cryptic walkthru's. How did I go? Any feedback welcomed. This puzzle seemed a lot easier than last week.

Assassin Killer 23 June 06 Walkthru by SudokuEd

Step 1.
24(3) cage in N4 is {789} only -> no 789 elsewhere in N4.

Every combination for 31(6) in N1 uses at least two out of 7, 8 or 9. Since no 7, 8 or 9 in r4c3 -> 7, 8 or 9 used in 31(6) must be in N1. Also, since 12(2) in N1 must use a 7, 8 or 9 -> no 7, 8 or 9 can be in r2c3 or r3c1.

Step 2.
“45” on c1 -> innies = (hidden) h28(4) -> no 1, 2 or 3 in those 4 cells ->1, 2 and 3 locked in 11(3) or 6(2) in c1.
Since 6(2) uses 1 or 2 -> 11(3) must have two out of 1, 2 or 3 -> only combination in 11(3) is {236}
->6(2) in c1 is {15}
->r6c1= 4,

Step 3a.
17(2) cage in r9 is {89} only -> no 8 or 9 elsewhere in r9 or N9.
Since the 29(6) cage in N9 must use 8 or 9 -> r6c7 can only be {89}
Can also now see that r9c1= 7
->{89} in r12c1
->{57} in 12(2) in N1

Step 3b.
3(2) cage in r6 is {12} only -> no 1 or 2 elsewhere in r6. Also, now have an 8(2) cage in r67c2 ->no 3 in r6c2 since no 5 in r7c2.

In N7, 31(6) + 8(2) + 6(2) + r9c3 – 2 outies = 45 ie. 45 + r9c3 – 2 outies = 45
-> r6c2 + r7c4 = r9c3.
Since maximum digit in r9c3 = 6 and since minimum digit in r6c2 = 5 -> r7c4 =1, r6c2=5, r9c3=6.
->r7c2=3, r6c34=[12], r78c1=[51], r1c23=[75]
->{89} naked pair in r45c2 -> r5c3=7
->{24} naked pair in r89c2
->{16} naked pair in r23c2

Step 4.
In N1, 31(6) + 12(2) – 1 outie + 2 innies = 45 ie. 43 – r4c3 + 2 innies = 45
-> r3c1 + r2c3 – r4c3 = 2
Since r4c3={23} -> 2 innies = 4 or 5. But only option is {23} which = 5 -> [3] in r4c3.
-> r2c3 [2], r3c1 [3], r3c3 [4]

Step 5.
“45” on r9 -> innies = h7(3) ie {124} only in r9c269
->{24} naked pair in r9c26 -> r9c9=1

Step 6.
“45” on N8 -> 2 outies = 6 -> r6c6 =3, r8c7 = 3, r7c6 = 8, r78c3 = [98], r89c6 = [64], r89c2 = [42]

Step 7.
“45” on N5 -> 2 innies = 15 -> r4c46 = [87], r3c4 = 5, r4c7 = [2], r45c2 = [98], etc, all singles
Assassin 5 by Ruud (June 06)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:1792:5889:5889:3075:3075:5381:5381:775:775:1792:5889:5889:3075:4877:4877:5381:3600:3600:4370:4627:4627:4627:4877:4877:2328:2328:2586:4370:4370:3613:3613:5919:2336:2336:2336:2586:3876:3876:3876:5919:5919:5919:3626:3626:3626:2349:3630:3630:3630:5919:4402:4402:2868:2868:2349:2359:2359:5689:5689:4411:4411:4411:2868:831:831:3137:5689:5689:4164:5189:5189:2631:4424:4424:3137:3137:4164:4164:5189:5189:2631:
Solution:
+-------+-------+-------+
| 3 9 8 | 4 6 5 | 7 2 1 |
| 4 5 1 | 2 7 3 | 9 6 8 |
| 6 7 2 | 9 8 1 | 4 5 3 |
+-------+-------+-------+
| 8 3 9 | 5 4 2 | 6 1 7 |
| 5 4 6 | 8 1 7 | 2 3 9 |
| 2 1 7 | 6 3 9 | 8 4 5 |
+-------+-------+-------+
| 7 6 3 | 1 9 4 | 5 8 2 |
| 1 2 4 | 7 5 8 | 3 9 6 |
| 9 8 5 | 3 2 6 | 1 7 4 |
+-------+-------+-------+
Quote:
Caida: I found A5 easier than (Assassin 1)
Caida: I always figured that no walkthrough meant that the assassin was impossible to do (or at least well out of my range of skills). Looking at this one I think perhaps I could have tried it earlier :) . I'd rate it a 0.75 at the most - the whole thing can be solved with cage combinations and some easy 45 rules
Andrew: You probably found Assassin 5 slightly easier than I did because you were using elimination solving. I solved as least the first 18 Assassins by insertion solving before I started using elimination solving
Walkthrough by Caida:
I've been doing an inventory of the walkthroughs available and noticed that Assassin 5 didn't have a walkthrough. I learned to do killers by going step by step through the walkthroughs I found on this forum and I always figured that no walkthrough meant that the assassin was impossible to do (or at least well out of my range of skills). Looking at this one I think perhaps I could have tried it earlier :-)

I'd rate it a 0.75 at the most - the whole thing can be solved with cage combinations and some easy 45 rules.

Cheers

Caida


Here's the walkthrough


Assassin 5 walkthrough

Preliminaries:

a. 7(2)n1 = {16/25/34} (no 7..9)
b. 21(3)n23 = {xx} (no 1..3)
c. 3(2)n3 and n7 = {12} (no 3..9) -> 1, 2 locked for n3 and n7 and r1 and r8
d. 14(2)n3 and n45 = {59/68} (no 1..4, 7)
e. 9(2)n3 and n47 and n7 = {18/27/36/45} (no 9)
f. 10(2)n36 and n9 = {19/28/37/46} (no 5)
g. 9(3)n56 = {xxx} (no 7..9)
h. 17(2)n56 and n7 = {89} (no 1..7) -> 8, 9 locked for r6 and n7 and r9
i. 11(3)n69 = {xx} (no 9)

cleanup:
j. r2c1 no 5,6
k. r3c78 no 7,8
l. r4c9 no 8,9
m. r6c1 no 1, 7
n. r7c23 no 7
o. 3 locked in n3 in r3 -> no 3 elsewhere in r3

1. Outies n3: r1c6+r4c9 = 12(2) = [93/84/66/57]
1a. -> r1c6 no 4,7
1b. -> r4c9 no 1,2
1c. cleanup: r3c9 no 8,9

2. Outies n7: r6c1+r9c4 = 5(2) = [23/32/41]
2a. -> r6c1 no 5,6
2b. -> r9c4 no 4,5,6,7
2c. cleanup: r7c1 no 3,4

3. Innies n8: r7c6+r9c4 = 7(2) = [61/52/43]
3a. -> r7c6 no 1,2,3,7,8,9

4. Innies n789: r7c19 = 9(2) = [54/63/72]
4a. -> r7c9 no 1,5,6,7,8

5. Innie and Outie n1: r3c4-r3c1 = 3
5a. -> r3c4 no 1,2,6
5b. -> r3c1 no 7,8,9

6. Innies n2: r1c6+r3c4 = 14(2) = [59/68/95]
6a. -> r1c6 no 8
6b. -> r3c4 no 4,7
6c. cleanup: r3c1 no 1,4 (step 5)
6d. r4c9 no 4 (step 1)
6e. r3c9 no 6

7. Innies r12: r2c56 = 10(2) = {19/28/37/46} (no 5)
7a. -> split 19(4)n2: r3c56 = 9(2) = {18/27/45} (no 6,9)

8. Innies r89: r8c34 = 12(2) = {39/48/57} (no 6)
8a. -> split 22(4)n8: r7c34 = 10(2) = {19/28/37/46} (no 5)

9. Innie r1234: r4c5 = 4
9a. Innie r6789: r6c5 = 3
9b. cleanup: r2c6 no 6,7
9c. r3c6 no 5
9d. r7c4 no 6,7
9e. r8c4 no 8,9
9f. r7c1 no 6
9g. r9c4 no 2
9h. r7c6 no 5
9i. r7c9 no 3

10. 12(3)n78 = {47}[1]/{45}[3]
Note: combo {56}[1] blocked by 9(2)n7
10a. -> r89c3 no 3,6
10b. -> 4 locked in r89c3 for n8 and c3
10c. -> 9(2)n8 = {36} -> locked for n8 and r7
10d. single: r7c6 = 4
10e. -> r7c9 = 2
10f. r67c1 = [27]
10g. r8c12 = [12]
10h. r1c89 = [21]
10i. 12(3)n78 = {45}[3] -> 5 locked for c3

11. 22(4)n8 = {19}{57} -> locked for n8
11a. -> {19} locked for r7
11b. -> {57} locked for r8
11c. -> r89c3 = [45]
11d. single; r8c6 = 8


cage sums and singles to the end


Last edited by Ed on Fri Jun 13, 2008 12:28 pm, edited 1 time in total.

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PostPosted: Thu Jun 05, 2008 4:34 am 
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Posts: 1040
Location: Sydney, Australia
Assassin 6 (aka July 7 2006) by Ruud (July 06)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:2816:2816:3586:3586:5124:5124:4102:4102:4872:5385:2816:3586:4108:2061:5124:4102:4872:4872:5385:5385:4108:4108:2061:2061:5400:1561:1561:3099:3099:4125:5662:1823:1823:5400:5400:1561:3099:4125:4125:5662:5662:5662:3114:3114:4140:3629:4910:4910:4144:4144:5662:3114:4140:4140:3629:3629:4910:2873:2873:4923:4923:3901:3901:4415:4415:3137:2626:2873:4923:4933:4166:3901:4415:3137:3137:2626:2626:4933:4933:4166:4166:
Solution:
+-------+-------+-------+
| 2 1 4 | 7 9 5 | 8 3 6 |
| 7 8 3 | 2 1 6 | 5 9 4 |
| 5 9 6 | 8 3 4 | 7 1 2 |
+-------+-------+-------+
| 1 7 9 | 4 5 2 | 6 8 3 |
| 4 5 2 | 6 8 3 | 1 7 9 |
| 3 6 8 | 9 7 1 | 4 2 5 |
+-------+-------+-------+
| 9 2 5 | 1 4 7 | 3 6 8 |
| 8 3 7 | 5 6 9 | 2 4 1 |
| 6 4 1 | 3 2 8 | 9 5 7 |
+-------+-------+-------+
Quote:
sudokuEd: I had to do some combo hunting.. - any simpler way to have done that?
nd:a fairly tricky one! No combination charts needed, but it does take some finesse!
Walkthrough by sudokuEd:
Am finally over the shock - ND doesn't use a combo chart!!! You've inspired me ND - so trying to relearn my bad habits. This weeks assassin forced me to use min/max to avoid the combo chart. Much better. Too many 'elbows' (Ruud is a tennis fan??) to use 'subtraction combo'. I had to do some combo hunting in Step 4 - any simpler way to have done that?

Thanks for a great puzzle Ruud. What about a cycling theme??

Assassin 7 July

Step 1.
“45” on N9->outies at r789c6=24-> {789} only -> no 789 elsewhere in N8 or c6
->20(3) cage in N2, r12c6 Maximum = 6+5=11 -> minimum r1c5 = 9 -> r1c5 = 9, r12c6 {56} only
-> no 56 elsewhere in N2 or c6
->8(3) in N2 {134} only ->not elsewhere in N2
->r123c4 {278} only -> not elsewhere in c4
->r6c45=[97]
also r5c5=8 (hidden single N5)

Step 2.
“45” on r12 -> 3 innies=10
->no 7 or 8 possible in r2c4 since r2c1=>4
->r2c4=2, r3c34=[68], r1c4=7

Step 3.
now 2 innies left from step 2 means that r2c15= 8 -> r2c5 {13}, r2c1 {57}
->4 in N2 only in r 3 -> no 4 elsewhere in r3
also 2 in r3 locked in 6(3) cage in N3 -> no 2 elsewhere in N3 or r4c9
also 9 in N1 only in r3 ->no 9 in r3c7
also 21(3) cage in N1 {579} only -> no 579 elsewhere in N1
->11(3) cage in N1 = {128} only -> no 128 elsewhere in N1
->r12c3 now 7(2) -> {34} only -> no 3 or 4 elsewhere in c3

Step 4.
“45” on N7 ->
a. innies r7c123 = h16(3)
b. outies r6c123 = h17(3)
c. r6c1 – r7c3 = -2 (or r7c3 – 2= r6c1) -> minimum r7c3 = 3, maximum r6c1 = 7
->r7c3 = {578} (no 9 since no 7 in r6c1); r6c1 = {356}
-> 19(3) cage at r6c23r7c3 = [487/658/685] ->r6c2 = {46}, r6c3={58}, r7c3={578}
->h17(3) cage in N4 = [368/548] only
-> r6c3 = 8

Step 5.
8 in N6 now locked in r4c78 in 21(3) cage-> {678} only
->r3c7=7, r2c1=7, r4c9 = 3 (outie on N3)
Also r4c78 {68} only -> no 6 or 8 elsewhere in N6 or r4
->r4c56 = [52], r5c4 = 6 (hidden single N5), r6c2 = 6 (hidden single N4), r7c3= 5, r6c1 =3, r5c6 = 3

Step 6.
r3c89 ={12} -> no 1 or2 elsewhere in N3 or r3
->r3c56 = [34], r2c5 and r6c6 = 1, r4c4 = 4, r2c2 = 8

Step 7.
r4c123 = triple on {179} -> no 179 elsewhere in N4
->r5c3=2, r4c3 = 9, r5c2 = 5, r45c1=[14], r4c2=7, r3c12=[59], r1c12=[21]

Step 8.
r7c12 now 11(2) -> [92]
r89c3 = {17} = 8 -> r89c2 = [34]

Step 9.
In N8, 5 is now only in 10(3) cage -> {235} only
->r89c4=[53], r9c5=2, r7c4=1

Step 10.
"45" on r89 -> innies = h16(3) at r8c569
Minimum r8c56 sum=11 -> max. R8c9 =5
->h16(3) can only be [682/691]
->r8c5=6, r7c5=4, r89c1=[86]

Step 11
"45" on N9 ->r7c7 - r9c6= -5.
->r7c7=3, r9c6=8
.....etc
Walkthrough by nd:
Here's my walkthrough.

1. R3C89 + R4C9 = {123}. 45 on N8 -> R789C6 = {789}, R7C7 = {234}. R1C5 = 9, R12C6 = {56}, R2C5 + R3C56 = {134}, R123C4 = {278}, R6C45 = [97], R5C5 = 8.

2. Naked quad in R3 blocks {1234} from R4C1234; 4 in N2 is locked in R3C56, 2 in N3 is locked in R3C89. The 16(3) cage in N2 cannot have {78} in it (since this would make R3C3 = 1), so the only solution is R123 = [728], R3C3 = 6, R3C127 = {579}.

3. 45 on N3 -> R3C7 = R4C9 + 4 = {57}, so R4C9 = {13}, 9 in N1 is locked in R3C12, and R2C1 = {57}. R12C3 = {34}, R1C12 + R2C2 = {128} (with the 2 locked in R1).

4. 45 on R6 -> R6C6789 = 12 = {12(36|45)}. 45 on N7 -> R6C1 = {356}, R7C3 = {578}. But 8 is now locked in R6 in R6C23, so R6C1 = {35}, R7C3 = {57}. The 19(3) cage must be {478} or {568}, so R6C2 = {46}, R6C3 = 8, R4C78 = {68}, R3C7 = R2C1 = 7, R3C12 = {59}.

5. 45 rule on R12 -> R2C5 = 1 -> R3C89 = {12}, R4C9 = 3, R4C56 = [52]. R4C4 = {14} and we have a naked triplet in N5 so R5C4 = 6, R6C12 = [36], R7C3 = 5, R5C6 = 3, R3C56 = [34], R6C6 = 1, R4C4 = 4.

The puzzle from this point on is easy sailing
Assassin 7 (aka July 14 2006) by Ruud (July 06)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:1536:1536:1794:6915:6915:6915:2054:4359:4359:5385:2314:1794:6915:7181:6915:2054:2832:4113:5385:2314:4884:7181:7181:7181:2840:2832:4113:5385:3612:4884:4884:7181:2840:2840:3106:4113:3620:3612:3612:7719:7181:7719:3106:3106:3628:3620:3620:5167:7719:7719:7719:5683:3628:3628:2358:3639:5167:5167:7719:5683:5683:2621:2366:2358:3639:5167:5954:5954:5954:5683:2621:2366:2358:4937:4937:4937:5954:3917:3917:3917:2366:
Solution:
+-------+-------+-------+
| 5 1 3 | 6 2 4 | 7 9 8 |
| 6 2 4 | 7 9 8 | 1 5 3 |
| 8 7 9 | 3 5 1 | 2 6 4 |
+-------+-------+-------+
| 7 3 2 | 8 6 5 | 4 1 9 |
| 1 6 5 | 2 4 9 | 3 8 7 |
| 9 4 8 | 1 3 7 | 6 2 5 |
+-------+-------+-------+
| 2 9 1 | 4 8 3 | 5 7 6 |
| 4 5 7 | 9 1 6 | 8 3 2 |
| 3 8 6 | 5 7 2 | 9 4 1 |
+-------+-------+-------+
Quote:
nd: Despite Ruud's warning, this one requires no combination tables, either. But it.. takes a little finesse after the straightforward start
Walkthrough by nd:
Despite Ruud's warning, this one requires no combination tables, either. But it's a nice puzzle that takes a little finesse after the straightforward start (the lefthand nonets crack easily at the beginning).

1. R1C12 = {(15)|(24)} -> R12C3 = {(16)|(34)} -> R23C2 = {(18)|(27)}. Hidden killer pair on {12} in the 6(2) and 9(2) cages, so R12C3 = {34}, R1C12 = {15}, R23C2 = {27}.

2. 45 rule on C1 -> R6C2 = 4, R1C12 = [51], R789C1 = {234}, R56C1 = {19}, R4C1 = 7, R23C1 = {68}, R3C3 = 9. 45 rule on N4 -> R46C3 = 10 = {28}. R5C3 = {56}, R45C2 = {356}, R9C2 = {89}, R4C4 = {28}.

3. In N7 the 1 is locked in the 20(4) cage (since it cannot go in a 19(3) cage). In turn this means R6C3 cannot be 2 (because 20 - 2 - 1 = 17 which is too high for the remaining 2 cells since one contains {567}). So R6C3 = 8, R4C34 = [28].

4. 45 rule on N3 -> R4C9 = 9, R3C7 = 2, R23C2 = [27], R1C89 = [98]. The 8 in N6 must be in the 12(3) cage so that cage = {138}. 45 rule on N6 -> R46C7 = 10 = {46}. So R6C7 = 6, R4C67 = [54]. 45 rule on N789 -> R7C5 = 8.

5. R23C8 = {(47)|(56)}. R23C9 = {(16)|(34)}, which eliminates {135} in R789C9. So R789C9 = {2(16)|(34)}, locking 2 in C9 within N9. So R78C8 = {37} ({46} is blocked by the 11(2) cage in C8), R45C8 = [18], R5C7 = 3, R12C7 = [71], R23C8 = {56}, R23C9 = {34}, R789C9 = {126}, R56C9 = {57}, R6C8 = 2, R9C8 = 4.

6. 45 rule on N369 -> R79C6 = {23}. 45 rule on N7 -> R79C4 = 9 = [45]. R9C23 = [86], R78C2 = {59}, R45C2 = [36], R5C3 = 5, R56C9 = [75] R4C5 = 6. 45 rule on N2 -> R5C5 = 4. R9C67 = [29], R7C6 = 3, R78C7 = [58], R78C8 = [73], R9C1 = 3, R9C9 = 1, R9C5 = 7.

7. In N2 the 27(5) cage in N2 must contain {46}; it must also have {27} in it (because they are blocked from the 28(5) cage). The remaining 5th cell is 27 - 2 - 4 - 6 - 7 = 8. So the cage = {24678}, R2C6 = 8, R2C4 = 7.... and the puzzle more or less finished itself from this point on
even less combo-work Walkthrough by sudokuEd:
Here's a different solving path - even less combo chart.

Step 1
“45” on N1 -> 3 innies = 23 = {689} -> no 6,8 or 9 elsewhere in N1
7 now locked in 9(2) cage in N1 -> {27} only -> no 2 or 7 elsewhere in N1 or c2
->6(2) cage in N1 {15} only -> no 1 or 5 elsewhere in N1 or r1
->7(2) cage in N1 {34} only -> no 3 or 4 elsewhere in N1 or c3

“45” on N1 ->r3c3- r4c1=2
->r4c1= {467}

Step 2
“45” on c1-> 2outies = 5 -> no 5 possible in r1c2 -> r1c12=[51], r6c2=4
4 in N7 now locked in 9(3) cage ->{234} only -> no 2,3 or 4 elsewhere in N7 or c1
->r56c1= {19} only -> no 1 or 9 elsewhere in c1 or N4
->r3c3=9, r4c1=7
->14(3) cage in N2 {356} only -> no 3, 5 or 6 elsewhere in N4
->r4c34 ={28} only -> no 2 or 8 elsewhere in r4

Step 3.
r46c3 is now {28} only -> no 2 or 8 elsewhere in c3
Since 1 is locked in r78c3 in 20(4) cage -> maximum possible in r78c3+r7c4={179}=17 ->min r6c3 =3
->r6c3=8, r4c34= [28]

Step 4.
17(2) = {89} -> no 8 or 9 elsewhere in r1 or N3
“45” on N3 -> 3 innies = 9 -> no 7 in r3c7 or r23c9
->16(3) cage at r2c9 = {169\259\349} = 9{16/25/34} ->r4c9 =9, r1c89=[98]
“45” on c9 ->r6c8=2
“45” on N3 ->r3c7=2, r23c2=[27]

Step 5.
In N6, r56c9 = {57} only -> no 5 or 7 elsewhere in N6 or c9
12(3) cage now {138} only ->no 1,3 or 8 elsewhere in N6
->r46c7 = [46], r4c6=5

Step 6.
In N9, 10(2) cage = {37\64} -> 9(3) cage = {126} only (no{234} since 3 or 4 needed in 10(2) cage)
-> no 1,2 or 6 elsewhere in N9 or c9
-> r23c9 = {34} only -> r12c7=[71]
->r23c8 = {56} only
->r78c8 = {37} only -> r45c8 = [18], r5c7=3, r4c2=3, r9c8=4, r4c5=6
“45” on N2 -> r5c5=4
“45” on N5 -> r7c5=8
also r5c23 = {56} only ->r56c9 = [75]

Step 7.
“45” on c789 -> r79c5=5(2) = {23} only ->r5c4=2(hidden single N5), r1c5=2
->23(4) cage in N8= {1679} only -> r79c4 = [45][/size]
etc


Last edited by Ed on Fri Jun 13, 2008 12:30 pm, edited 1 time in total.

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PostPosted: Thu Jun 05, 2008 4:38 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Assassin 8 (aka July 21) by Ruud (July 06)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:2816:4865:6402:6402:2820:4357:4357:3847:1544:2816:4865:4865:6402:2820:4357:3847:3847:1544:3858:1299:1299:6402:5398:4357:4120:4120:3098:3858:3858:11549:5398:5398:5398:11549:3098:3098:1572:1572:11549:11549:11549:11549:11549:2603:2603:5421:5421:11549:3632:3632:3632:11549:5684:5684:5421:1335:1335:5433:3632:5947:3644:3644:5684:1343:5696:5696:5433:2115:5947:3141:3141:1095:1343:5696:5433:5433:2115:5947:5947:3141:1095:
Solution:
+-------+-------+-------+
| 6 7 9 | 5 2 1 | 3 8 4 |
| 5 4 8 | 3 9 7 | 1 6 2 |
| 1 3 2 | 8 4 6 | 9 7 5 |
+-------+-------+-------+
| 9 5 3 | 7 8 2 | 4 1 6 |
| 4 2 1 | 6 5 9 | 8 3 7 |
| 8 6 7 | 1 3 4 | 2 5 9 |
+-------+-------+-------+
| 7 1 4 | 2 6 3 | 5 9 8 |
| 3 9 5 | 4 7 8 | 6 2 1 |
| 2 8 6 | 9 1 5 | 7 4 3 |
+-------+-------+-------+
Quote:
Your quote to go here
walkthrough by nd:
Here's my walkthrough.

1. R89C9 = {13}, R12C9 = {24}, R3C78 = {79}. 45 rule on N3 -> R1C7 + R3C9 = 8 -> R3C9 = 5, R1C7 = 3, R4C89 = [16], R2C7 = 1, R12C8 = {68}.

2. In N6 the 22(3) cage = {589} (since the only other combo, {679}, is blocked) so R6C8 = 5, R7C78 = [59] (because {568} are blocked from R7C8), R5C89 = [37], R67C9 = [98].

3. 45 rule on N9 -> R9C7 = 7, R3C78 = [97], R8C7 = 6, R89C8 = {24}. 45 rule on N78 -> R7C15 = 13 = {67}. 45 rule on N7 -> R7C1 + R9C3 = 13 -> R9C3 = 6, R7C15 = [76], R6C12 = {68}.

4. 45 rule on R6789 -> R6C37 = 9 = [72]. 45 rule on R5 -> R4C37 = 7 = [34], R5C12 = {24}, R5C3 = 1, R4C12 = {59}, R3C1 = 1. R3C5 = 21 - (2 + 7 + 8) = 4, R3C23 = [32], R89C1 = {23}. 45 rule on N1 -> R1C3 = 9.

& you carry on....
Assassin 9 (aka July 28) by Ruud (July 06)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:5888:5888:1794:1794:6916:2309:2309:8967:8967:5888:5888:5888:5888:6916:8967:8967:8967:8967:3346:3346:3348:2581:6916:2583:3864:1817:1817:2843:5660:3348:2581:6916:2583:3864:4642:4643:2843:5660:5660:3367:3367:3367:4642:4642:4643:2843:5660:2607:1072:3633:3122:2099:4642:4643:3382:3382:2607:1072:3633:3122:2099:2877:2877:9279:9279:9279:9279:3633:5700:5700:5700:5700:9279:9279:2890:2890:3633:3405:3405:5700:5700:
Solution:
+-------+-------+-------+
| 4 8 5 | 2 7 6 | 3 9 1 |
| 2 3 1 | 5 9 8 | 4 6 7 |
| 6 7 9 | 4 3 1 | 8 2 5 |
+-------+-------+-------+
| 1 2 4 | 6 8 9 | 7 5 3 |
| 3 5 6 | 7 4 2 | 1 8 9 |
| 7 9 8 | 3 1 5 | 2 4 6 |
+-------+-------+-------+
| 9 4 2 | 1 5 7 | 6 3 8 |
| 8 6 7 | 9 2 3 | 5 1 4 |
| 5 1 3 | 8 6 4 | 9 7 2 |
+-------+-------+-------+
Quote:
sudokuEd: Seems like this one needs T&E at the end unless I'm missing something
Ruud: You must have missed something. This is not a RUUDICULOUS killer
Andrew: Having reached a stage similar to that shown by SudokuEd I realised that in the....cage.... must be (odd number) since .... must be an odd number and .... an even number
Andrew, on 11 Aug: I only found the Weekly Assassins at the beginning of this month and am gradually working my way through them
Caida in Dec 07: I'd rate it 0.75
Walkthrough by Caida:
Hello,

I just noticed that although this one has a thread there isn't actually a full walkthrough.

Here's my walkthrough:

I'd rate it 0.75

Assassin 9 walkthrough

Preliminaries

a. 7(2)n12 and n3 = {16/25/34} (no 7..9)
b. 13(2)n1 and n14 and n7 and n89 = {49/58/67} (no 1..3)
c. 10(2)n25(x2) and n47 = {19/28/37/46} (no 5)
d. 9(2)n23 = {18/27/36/45} (no 9)
e. 15(2)n36 = {69/78} (no 1..5)
f. 11(3)n4 = {128/137/146/236/245} (no 9)
g. 4(2)n58 = {13} -> locked for c4
h. 12(2)n58 = {39/48/57} (no 1,2,6)
i. 8(2)n69 = {17/26/35} (no 4,8,9)
j. 11(2)n78 and n9 = {29/38/47/56} (no 1)
k. 23(6)n12 = {123458/123467} (no 9) -> 9 locked in n1 in r3 -> no 9 elsewhere in r3
l. 22(6)n89 = {123457} (no 6,8,9)
m. 14(4)n58 = {1238/1247/1256/1346/2356} (no 9)

cleanup:
o. r1c3 no 4,6
p. r34c4 no 7,9
q. r4c6 no 1
r. r4c7 no 6
s. r9c3 no 8


1. Innie c5: r5c5 = 4
1a. r5c47 = [27/63/72/81] no 5,9
1b. r5c7 no 6,8
1c. r3c46 no 6
1d. r7c6 no 8

2. 9 in c4 locked in n8 -> no 9 elsewhere in n8
2a. -> r6c6 no 3
2b. -> r9c7 no 4

3. Innies r12: r12c5 = 16(2) = {79} -> locked for c5 and n2
3a. -> r1c7 no 2
3b. -> r4c6 no 3
3c. split 11(2) r34c5 = {38/56} (no 1,2)

4. 1 in n2 locked in c6 -> no 1 elsewhere in c6
4a. 1 in n5 locked in r6 -> no 1 elsewhere in r6
4b. 1 in 22(6)n89 locked in n9 -> no 1 elsewhere in n9
4c. r5c4 no 8
4d. r7c3 no 9
4e. r67c7 no 7

5. Innies r89: r89c5 = 8(2) = {26/35} (no 1,8)
5a. split 6(2): r67c5 = 6(2) = {15} -> locked for c5
5b. -> r89c5 = {26} -> locked for c5 and n8
5c. r9c3 no 5,9
5d. r9c7 no 7

6. 2 in 22(6)n89 locked in n9 -> no 2 elsewhere in n9
6a. r6c7 no 6
6b. r7c89 no 9
6c. single: r9c7 = 9
6d. r9c6 = 4
6e. single: r8c4 = 9
6f. r9c34 no 2,7
6g. r6c6 no 8
6h. r4c6 no 6
6i. r3c7 no 6

7. hidden single r7: r7c3 = 2
7a. r6c3 = 8
7b. r34c3 no 5
7c. r1c4 no 5

8. Innie n4: r4c3 = 4
8a. r3c3 = 9
8b. r3c12 no 4
8c. r9c4 = 8
8d. r9c3 = 3
8e. r1c4 no 4

9. pair {78} in r34c7 -> no {78} elsewhere in c7
9a. pair {26} in r14c4 -> no {26} elsewhere in c4
9b. single r3c4 = 4
9c. r4c4 = 6
9d. r5c4 = 7
9e. r5c6 = 2
9f. r12c4 = [25]
9g. r1c3 = 5
9h. r3c12 = {67} no 8 -> {67} locked for r3 and n1
9i. r34c6 = [19]
9j. r2c3 = 1
9k. r67c6 = [57]
9l. r67c5 = [15]
9m. r67c4 = [31]
9n. r34c5 = [38]
9o. r34c7 = [87]
9p. r67c7 = [26]
9q. r5c3 = 6
9r. r6c12 = [79]
9s. r8c3 = 7
9t. r8c6 = 3
9u. r3c12 = [67]
9v. r7c12 = [94]

10. 11(3)n4 = {13}[7] -> 1,3 locked for n4 and c1
10a. r45c2 = [25]
10b. r89c1 = [85]
10c. r12c1 = [42]
10d. single c7: r8c7 = 5
10e. single c7: r2c7 = 4

11. 6 in n3 locked in 35(6)n23
11a. -> r2c6 = 8
11b. -> r1c67 = [63]
11c. r12c2 = [83]
11d. r5c7 = 1
11c. r45c1 = [13]

12. 18(3)n6 = [594/396]
12a. -> r5c9 = 9
12b. -> r5c8 = 8
12c. r7c89 = [38]
12c. r4c89 = [53]
12d. r6c89 = [46]
12e. r3c89 = [25]
12f. r1c89 = [91]
12g. r2c89 = [67]
12h. r8c89 = [14]
12i. r9c89 = [72]
12j. r89c2 = [61]
12k. r1289c5 = [7926]


Last edited by Ed on Fri Jun 13, 2008 12:35 pm, edited 1 time in total.

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PostPosted: Thu Jun 05, 2008 4:44 am 
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Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Assassin 10 (aka August 4) by Ruud (Aug 06)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:7168:2561:2561:6915:6915:6915:2566:2566:5896:7168:7168:2561:6915:6669:6915:2566:5896:5896:1298:7168:4116:6669:6669:6669:7704:5896:3354:1298:5916:4116:4116:6669:7704:7704:3618:3354:6692:5916:5916:4116:4136:7704:3618:3618:5676:6692:6692:5916:1328:4136:1586:3618:5676:5676:2358:6692:5176:1328:4136:1586:5948:5676:1598:2358:2358:5176:5176:3395:5948:5948:1598:1598:4424:4424:4424:5176:3395:5948:4430:4430:4430:
Solution:
+-------+-------+-------+
| 4 1 6 | 9 3 8 | 2 7 5 |
| 8 7 3 | 5 4 2 | 1 9 6 |
| 2 9 5 | 7 1 6 | 8 3 4 |
+-------+-------+-------+
| 3 2 1 | 4 8 7 | 6 5 9 |
| 7 4 8 | 6 5 9 | 3 2 1 |
| 6 5 9 | 3 2 1 | 4 8 7 |
+-------+-------+-------+
| 1 8 4 | 2 9 5 | 7 6 3 |
| 5 3 7 | 8 6 4 | 9 1 2 |
| 9 6 2 | 1 7 3 | 5 4 8 |
+-------+-------+-------+
Quote:
Caida: I found this one really easy - I'd rate it 0.75
Caida: Now I think all of the Assassins (except for the still "unsolveables") have walkthroughs
Walkthrough by Caida:
Below is my walkthrough for Assassin 10. Now I think all of the Assassins (except for the still "unsolveables") have walkthroughs.

I found this one really easy - I'd rate it 0.75

Assassin 10 walkthrough

Preliminaries

a. 28(4)n1 = {4789/5689} (no 1..3) -> 8,9 locked for n1
b. 5(2)n14 and n58 = {14/23} (no 5..9)
c. 10(3)n3 = {127/136/145/235} (no 8,9)
d. 30(4)n356 = {6789} (no 1..5)
e. 13(2)n36 and n8 = {49/58/67} (no 1..3)
f. 6(2)n58 = {15/24} (no 3, 6..9)
g. 14(4)n6 = {1238/1247/1256/1346/2345} (no 9)
h. 9(3)n7 = {126/135/234} (no 7..9)
i. 6(3)n9 = {123} -> 1,2,3 locked for n9

1. Innies n1: r3c13 = 7(2) = [16/25]/{34}
1a. -> r3c3 no 1,2,7

2. Innies n3: r3c79 = 12(2) = [75/84]
2a. -> r3c7 no 6,9
2b. -> r3c9 no 6,7,8,9
2c. -> r4c9 no 4,5,6,7
2d. -> r4c45 no 6,9 (CPE with 30(4)n356))

3. Innies n7: r7c23+r8c3 = 19(3) = {289/379/469/478/568} (no 1)

4. Innies n9: r7c78+r8c7 = 22(3) = {589/679}
4a. r7c78+r8c7 no 4
4b. 9 locked for n9 in r7c78+r8c7 -> no 9 elsewhere in n9
4c. 4 locked for n9 in r9 -> no 4 elsewhere in r9
4d. r8c5 no 9

5. Innies c1234: r123c4 = 21(3) = {489/579/678} (no 1,2,3)

6. Innies c6789: r123c6 = 16(3)
6a. -> r123c5 = 8(3) = {125/134} (no 6,7,8,9)
6b. -> 1 locked in c5 and n2

7. Innie c5: r4c5 = 8 (using step 6a for r123c5)
7a. r4c9 = 9
7b. r3c9 = 4
7c. r3c7 = 8 (step 2)
7d. r5c6 = 9 (hidden single within 30(4))
7e. pair {67} locked for r4 in r4c67
7f. r3c13 no 3 (step 1)
7g. r4c1 no 1,2
7h. r89c5 no 5
7i. r7c8 no 5 (step 4)

8. 28(4)n1 = {4789} -> locked for n1
Note: {5689} blocked by r3c3

9. Innie and Outie n6: r4c7 = r7c8
9a. -> r7c8 no 8,9
9b. -> r7c78+r8c7 = {679} (step 4)
9c. -> 17(3)n9 = {458} -> locked for n9 and r9

10. 23(4)n89
10a. -> r78c7 = {69/79}
10b. -> r89c6 = 8(2)/7(2) -> no 8
10c. -> single: r8c4 = 8
10d. -> r7c2 = 8

11. 17(3)n7 = {179/269}
11a. -> r9c123 no 3
11b. -> 9 locked in r9c123 for n7 and r9
11c. single: r7c5 = 9
11d. -> r8c7 = 9
11e. -> 13(2)n8 = {67} -> locked for n8 and c5

12. Innies n7 (step 3): r78c3 = 11(2) = {47/56} (no 2,3)
12a. -> r9c4 = 1
12b. 5(2)n58 = {23} -> locked for c4
12c. single: r6c6 = 1
12d. r7c6 = 5
12e. r7c6 = 4
12f. r7c7 = 7; r9c6 = 3 (cage sum)

Singles and cage sums are all that is left
Assassin 11 (aka August 11) by Ruud (Aug 06)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:2560:2560:5634:5634:3076:6661:6661:2567:2567:2560:5634:5634:6156:3076:6156:6661:6661:2567:2834:2834:5396:6156:6156:6156:4632:2329:2329:2587:2587:5396:5396:4383:4632:4632:3618:3618:2596:3877:3877:5396:4383:4632:3114:3114:1324:2596:3877:3119:3119:4383:3890:3890:3114:1324:2102:2102:3119:5689:5689:5689:3890:4157:4157:4415:5952:5952:5689:2371:5689:5957:5957:3655:4415:4415:5952:5952:2371:5957:5957:3655:3655:
Solution:
+-------+-------+-------+
| 6 1 8 | 2 3 7 | 9 4 5 |
| 3 7 5 | 6 9 4 | 2 8 1 |
| 2 9 4 | 8 1 5 | 7 3 6 |
+-------+-------+-------+
| 8 2 7 | 1 4 3 | 6 5 9 |
| 1 5 6 | 9 8 2 | 4 7 3 |
| 9 4 3 | 7 5 6 | 8 1 2 |
+-------+-------+-------+
| 5 3 2 | 4 6 8 | 1 9 7 |
| 7 8 9 | 3 2 1 | 5 6 4 |
| 4 6 1 | 5 7 9 | 3 2 8 |
+-------+-------+-------+
Quote:
nd: No-one posting walkthroughs anymore?
Oscar, in A12 thread: Assassin 11 took me too long to solve..
sudokuEd: nice walkthrough (by nd). I missed that ....step 3 - but ....... made big inroads at that point as well - so no real harm done
Walkthrough by nd:
No-one posting walkthroughs anymore? Here's one.

Step 1. R7C89 = {79}. Innie-outie difference on N9 -> R7C7 = 1, R9C6 = 9. 45 rule on N8 -> R9C4 = 5. 45 rule on N7 -> R7C3 = 2, R7C12 = {35}, R7C456 = {468}, R89C5 = {27}, R8C46 = {13}.

Step 2. In C5 the 1 is blocked from R12789C5. It also cannot go in the 17(3) cage as this would make it {179} (and 7 is already blocked). So R3C5 = 1; 45 rule on C5 -> R7C5 = 6, 5 is locked in N5 in the 17(3) cage. Since {59} is now blocked from R6C6, R6C67 = {68}. 45 rule on N6 -> R46C7 = 14 -> R4C7 = {68}, R4C89 = {59}, R6C34 = {19|37}. 45 rule on N4 -> R46C3 = [19] or {37}.

Step 3. In N3, the 8 cannot go in the 9(2) cage (because {18} is blocked) nor in the 10(3) cage of course, & it's blocked from R123C7, so R2C8 = 8. 45 rule on R12 -> R2C46 = 10 = {37|46}, producing a hidden {34} pair in N2 in conjunction with the 12(2) cage (which is {39|48}! 45 rule on N2 -> R1C46 = 9 = {27} (since {134} are blocked). R2C46 = {46}, R12C5 = {39}, R3C46 = [85], R1C3 = 8.

Step 4. 45 rule on N123 -> R3C37 = 11. So we have two 11(2) cages in R3, neither of which can contain a 6 (because {56} is blocked}, so R3C89 = {36}. The 1 in N3 must go in the 10(3) cage (can't go in a 26(4) cage). 45 rule on N3 -> R1C6 = R3C7 = {27}, so the 10(3) cage cannot contain {127} -> the only possibility is that the 10(3) cage contains {145} -> R2C7 = {27}, R1C7 = 9, R12C5 = [39]. 6 is locked in R1 in the 10(3) cage in N1 -> R1C12 = {16}, R2C1 = 3, R7C12 = [53], R1C89 = {45}, R2C9 = 1.

Step 5. Basically mopping up from here on in. R8C7 = 5 -> remaining two cells in the 23(4) cage = 9 = {36} -> R9C7 = 3, R8C8 = 6, R3C89 = [36], R5C7 = 4, R56C8 = {17}, R56C9 = {23}, R7C89 = [97], R4C89 = [59], R1C89 = [45], R9C8 = 2, R89C9 = {48}, R89C5 = [27]. In N7 the 1 cannot go in the 17(3) cage as this would create {179} and {79} is blocked from two of its cells -> R9C3 = 1, R46C3 = R6C4 = {37}, R56C8 = [71], R56C9 = [32], R8C23 = [89].... and you carry on.


Last edited by Ed on Fri Jun 13, 2008 12:51 pm, edited 3 times in total.

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PostPosted: Thu Jun 05, 2008 4:48 am 
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Posts: 1040
Location: Sydney, Australia
Assassin 12 (aka Aug 18) by Ruud (Aug 06)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:2560:2560:2050:2050:4612:3333:3333:3591:3591:2560:5642:5642:2050:4612:4612:2831:2831:3591:3858:5642:3348:3348:3606:4375:4375:2831:5914:3858:4892:3348:3606:3606:3104:4375:5914:5914:4892:4892:5670:5670:3606:3104:3104:1579:1579:1837:1837:4143:5670:5169:5169:2867:1579:2869:1837:2871:4143:4143:5169:2867:2867:4925:2869:3903:2871:2871:4418:4418:3652:4925:4925:4167:3903:3903:2890:2890:4418:3652:3652:4167:4167:
Solution:
+-------+-------+-------+
| 6 3 2 | 1 8 4 | 9 7 5 |
| 1 9 8 | 5 3 7 | 4 6 2 |
| 7 5 4 | 6 2 9 | 3 1 8 |
+-------+-------+-------+
| 8 4 3 | 7 1 2 | 5 9 6 |
| 9 6 5 | 8 4 3 | 7 2 1 |
| 2 1 7 | 9 5 6 | 8 3 4 |
+-------+-------+-------+
| 4 8 6 | 3 9 1 | 2 5 7 |
| 3 2 1 | 4 7 5 | 6 8 9 |
| 5 7 9 | 2 6 8 | 1 4 3 |
+-------+-------+-------+
Quote:
sudokuEd: Lots of sums to do on this one. Took a while to find the right "45" for each new part of the puzzle
sudokuEd: Please keep the lead-in Ruud
Ruud: These “elbow soup” killers have become one of my specialities. I even allowed a little imperfection in the symmetry to get this puzzle right
Oscar: A12 was easy enough to be solved in only two hours!
Walkthrough by sudokuEd:
Lots of sums to do on this one. Took a while to find the right "45" for each new part of the puzzle. So good to have SuMoCue to help out! Thanks Ruud.

BTW- I missed not having a lead-in introduction on the puzzle page. The lead-in gives a puzzle more personality. Please keep the lead-in Ruud. :)

A walkthru follows.

Step 1
“45” on r12 -> 2 outies = 6 -> r3c2=5, r3c8=1 -> r5c9=1

Step 2
r2c23={89}-> no 8 or 9 elsewhere in N1 or r2
-> r4c1 = {89}
-> naked triple on {689} in r4c189 -> no 6, 8 or 9 elsewhere in r4 with 6 locked in N6
-> no 6 elsewhere in N6 or in r3c9 .

Step 3
“45” on r6-9 -> 2 innies = 12
->r6c8=3, r6c4=9, r5c8=2

Step 4
“45” on c12 -> 2 outies = 9
->r2c3=8, r8c3=1, r2c2=9

Step 5
“45” on N7 -> 3 innies = 19
but 2 cannot be in r7c1 since that would require {89} in r79c3
-> r7c1 = 4
-> 2 innies in N7 at r79c3 = 15 = {69} only -> no 6 or 9 elsewhere in N7 or c3

Step 6
r6c12 = {12} -> no 1 or 2 elsewhere in N4
-> 2 in c3 only in N1 -> no 2 elsewhere in N1
-> 10(3) cage in N1 {136} only -> no 1, 3 or 6 elsewhere in N1
-> r34c1= [78]

Step 7
r4c3 = 3 (hidden single c3)
->19(3) cage in N4 = {469} only with r45c2 = [46] and r5c1 =9
-> r5c34 =[58], r67c3=[76], r7c4=3, r9c34=[92], r3c34=[46], r3c9=8, r67c9 =[47]
the rest is mostly singles
Assassin 13 by Ruud (06)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:6912:6912:3586:3586:3588:1797:1797:5639:5639:1545:6912:6912:2316:3588:2830:5639:5639:3345:1545:4371:6912:2316:3588:2830:5639:4889:3345:7195:4371:4371:4371:6687:4889:4889:4889:6691:7195:7195:7195:6687:6687:6687:6691:6691:6691:7195:3886:3886:3886:6687:6706:6706:6706:6691:2870:3886:6200:4153:4154:2363:6716:6706:1086:2870:6200:6200:4153:4154:2363:6716:6716:1086:6200:6200:2378:2378:4154:2637:2637:6716:6716:
Solution:
+-------+-------+-------+
| 7 8 9 | 5 4 6 | 1 3 2 |
| 1 6 2 | 8 3 9 | 4 5 7 |
| 5 3 4 | 1 7 2 | 8 9 6 |
+-------+-------+-------+
| 4 5 7 | 2 9 3 | 6 1 8 |
| 6 1 8 | 4 5 7 | 3 2 9 |
| 9 2 3 | 6 1 8 | 5 7 4 |
+-------+-------+-------+
| 8 4 1 | 9 2 5 | 7 6 3 |
| 3 9 5 | 7 6 4 | 2 8 1 |
| 2 7 6 | 3 8 1 | 9 4 5 |
+-------+-------+-------+
Quote:
Andrew: Very challenging, I found it the hardest Weekly Assassin so far
Oscar: this the most easy Assassin that I have solved! :) ....Solving time was slightly more than one hour
Oscar: I think this very good puzzle at a starting level
First ever posted walkthrough by Andrew:
Nice puzzle! Very challenging, I found it the hardest Weekly Assassin so far.

Here is my first ever attempt at a posted walkthrough.

1. R78C4 = {79}; R78C9 = {13}; 45 rule on C1234 -> R5C4 = 4; 45 rule on C6789 -> R5C6 = 7; 45 rule on N8 -> R9C46 = {13}; R78C6 = {45}; R789C5 = {268}

2. R1C34 = {59/68}; 45 rule on N2 -> R1C46 = 11; 45 rule on N1 -> R1C3 + R3C2 = 12; 45 rule on N3 -> R1C7 + R3C8 = 10; applying these four results together and eliminating identical digits in N1 and in N3 -> R1C46 = [56]; R1C3 = 9; R3C2 = 3; R1C7 = 1; R3C8 = 9; R23C4 = {18}; R23C6 = [92]; R123C5 = {347}; R456C5 = {159} with the 1 in R56C5 from 45 rule on R1234; R9C46 = [31]; R46C4 = {26}; R46C6 = [38] (cannot have both 8 and 9 in 19(4) cage); R9C3 = 6; 45 rule on N7 -> R7C2 = 4; R78C6 = [54]; R9C7 = 9; 45 rule on N9 -> R7C8 = 6; R6C78 = {57}; R4C78 = [61]; R8C5 = 6; R46C4 = [26]; R6C23 = [23]; R2C2 = 6; R5C1 = 6

3. In N3 6 must be in C9 and is blocked from R1C9 so R23C9 = [76]; 22(5) cage in N3 = {23458}; 26(5) cage in N9 = {24578}

4. In N7 3 must be in C1 and is blocked from R9C1 so R78C1 = {38}; 24(5) cage = {12579}

5. In N6 {49} must be in C9; R5C789 = {23} and either 8 or 9

In C1 9 must be in N4; R8C2 = 9; R78C4 = [97]; R9C8 = 4; R7C7 = 7; R6C78 = [57]; R2C8 = 5; R9C9 = 5; R8C78 = {28}; R78C1 = [83]; R78C9 = [31]; R9C12 = [27]; R78C3 = [15]; R79C5 = [28]; R23C1 = [15]; R23C4 = [81]; R2C3 = 2; R5C2 =1; R1C2 = 8; R3C7 = 8; R8C78 = [28]; R5C78 = [32]; R1C9 = 2; R1C8 = 3; R2C57 = [34]; R45C5 = {59}; R6C5 = 1; R5C359 = [859] ; R6C19 = [94]; R4C23 = [57] and so on

I expect that the more expert solvers will have found more concise approaches but hopefully this is worth posting


Last edited by Ed on Fri Jun 13, 2008 12:53 pm, edited 3 times in total.

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PostPosted: Thu Jun 05, 2008 5:01 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Uluru X - Ruudiculous tag by sudokuEd Aug '06
Puzzle pic: 1-9 cannot repeat on the diagonals:
Image
Code: Select, Copy & Paste into solver:
3x3:d:k:5376:5376:5378:5378:5378:5378:5378:5639:5639:5376:5642:4619:4619:5133:5133:5133:2320:5639:5376:5642:5642:4619:5133:3607:3607:2320:2320:5376:5916:2845:2845:5407:3607:8225:8225:2851:2852:5916:2845:6695:5407:3607:8225:2859:2851:2852:5916:5916:6695:5407:5407:8225:2859:2357:2852:6695:6695:6695:5434:3643:8225:8225:2357:4415:3648:3648:5434:5434:3643:3643:3643:4167:4415:4415:5450:5450:5450:5450:5450:4167:4167:
Solution:
+-------+-------+-------+
| 6 1 2 | 3 4 5 | 7 9 8 |
| 7 8 4 | 6 1 9 | 3 2 5 |
| 3 9 5 | 8 7 2 | 4 6 1 |
+-------+-------+-------+
| 4 7 3 | 2 6 1 | 5 8 9 |
| 8 5 6 | 9 3 7 | 1 4 2 |
| 1 2 9 | 5 8 4 | 6 7 3 |
+-------+-------+-------+
| 2 4 7 | 1 5 8 | 9 3 6 |
| 5 6 8 | 7 9 3 | 2 1 4 |
| 9 3 1 | 4 2 6 | 8 5 7 |
+-------+-------+-------+
Quote:
sudokuEd: a variation in solving a Killer - Tag Killer - the 'tag' being like in 'tag-team' wrestling - one person starts, then another takes over...a Killer... which is "Ruudiculous" - ie very hard and quite possibly is not solvable logically
nd: It's actually completely solvable by logic--try a more powerful solving program like JC Godart's
sudokuEd: The only thing I can find to make any progress is a short contradiction move. Has a whiff of T& E about it so not real happy – but...getting desperate!
Andrew: (solving killers) is clearly a matter of practice and I'll hopefully improve with experience
tag solution by Sumocue, sudokuEd & Andrew
Andrew, April '10: found a completely different way to solve it....I'll rate my walkthrough for Uluru at 1.5
Condensed Walkthrough by sudokuEd:
Here is the walk-through for this puzzle. It's the short-cut route - rather than just mirroring the way we actually went. SumoCue's hints about unplaceable candidates were not needed ( :D ).

Just a quick reminder - this is a diagonals puzzle! 1-9 cannot repeat on the diagonals
Step 1
22(3) cages [edited] in N1 and N3 must have 9
“45” on c1 -> two outies = 4 = {13}
->17(3) cage in N7 = {179/359/368} = {6/9, 8/9....}
14(2) cage in N7 = {59/68} = {6/9, 8/9} -> Killer pair on both 6 and 9, 8 and 9 with 17(3) cage
-> no 6, 8 or 9 elsewhere in N7.
“45” on N689 -> the difference between the one innie and one outie = 0 ->r7c4 = r9c3
-> r7c4 cannot have 6, 8 or 9 since these have been eliminated from r9c3.
“45” on N7 -> 4 innies = 14 = {1247}{2345} = 24{17/35}
ie, 2 & 4 are locked in these 4 cells.
-> 2 & 4 must also be in r7c1234 because r7c4 = r9c3! (If 2 or 4 are in r9c3, they must also be in r7c4)
->2 and 4 cannot be elsewhere in r7
“45” on r89 -> two outies = 13 -> r7c56 = {58/67}
-> 9 in r7 locked in r7c78 -> no 9 elsewhere in N9 or 32(6) cage in N89
but 9 cannot go in r7c8 because this would mean no 9's in N6 since 9 in N3 would have to be in c9
->r7c7=9 and r3c2 = 9

Step 2
A short contradiction move is required at this point. Feels a little like T&E – but can't see any other way to make any real progress....caught between a rock and a hard place (couldn't resist the pun!)

Complex innies/outies on r1 -> sum of cages + 2 innies (r1c12) – 1 outie (r2c9) = 45
-> 2 innies – 1 outie = 2
min 1 outie = 5 -> min 2 innies = 7
Since max r1c2 = 3 -> min r1c1 = 4
We already know that r19c2 = {13}
Now, when r1c2 = 1
-r1c1 can only be 6 or 8 ( not 4,5 or 7 since these are taken in the 21(5) cage in r1 which can only be {23457} when r1c2 = 1)
-3 must be in r9c2
-r89c1 can now only be {59} – not {68} because this would leave no 6 or 8 in r1c1 which would be a bit of a problem!
-> 6 & 8 can be eliminated from the 17(3) cage in N7
-> the 17(3) cage is only {179/359} = 9{17/35} with 9 only in r89c1.
“45” on r 9 -> two outies = 9 -> no 9 in r8c19
->r9c1=9, r6c3 = 9 (9 cannot go in 11(3) cage in N45 ->hidden single N4), 14(2) cage in N7 = {68}, r8c1 = {57}

Step 3
“45” on N6 -> 2 outies = 9 -> r7c89 = hidden 9(2) cage = {18/63} = {6/8...}
“45” on r9 -> 2 outies = 9 -> r8c9 = {24} -> r9c89 = {57/68}, but {68} conflicts with hidden 9(2) cage in N9
-> r9c89 = {57} ->r8c19 = [54], r19c2 = [13]
r8c45 now {79} -> r7c56 = [58], r9c7 = 8 (h single N9)
r7c89 = {36} -> r8c78 = {12} -> r8c6 = 3
r67c9 = {36} -> r45c9 = {29}, r3c9 = 1 (h single c9)

Step 4
In r1, the 21 (5) cage is now {23457} only
->r1c189 = [698], r2c9 = 5, r9c89 = [57], r8c23 = [68], r2c2 = 8, r3c3=5, r23c8 = [26], r8c78 = [21], r7c89 = [36], r6c9 = 3, r56c8 = {47}, r4c8 = 8

Step 5
“45” on c2 -> r7c2 = 4
r456c2 = {257}
r234c1 = {347} -> r7c1 = 2 (hidden single c1)
Naked triple on {234} on \diagonal in N5
the rest is basically naked and hidden singles with a few cage combination singles thrown in.
Thanks Andrew for your helpful suggestions to make some points clearer
Solo effort by Andrew April '10:
I took part in the "tag" solution although I only played a minor part with one significant contribution. That was only about 3 weeks after I joined this site and I was still a Newbie to solving Assassins level killers.

Since I've been working on puzzles in my Unfinished solver I decided to have another go at Uluru, this time as a solo effort.

This time I found a completely different way to solve it. I spotted the first two lines of step 13 fairly early but it took me a few steps before I was in a position to use it.

I'll rate my walkthrough for Uluru at 1.5 because of my permutation analysis in step 13c.

Here is my walkthrough for Uluru. I've included a comment for SudokuEd, who has already seen my walkthrough, plus a couple of comments after I looked at the SudokuSolver log which Ed kindly provided. Please see my next message for an interesting step from the SS log.

Prelims

a) R45C9 = {29/38/47/56}, no 1
b) R56C8 = {29/38/47/56}, no 1
c) R67C9 = {18/27/36/45}, no 9
d) R8C23 = {59/68}
e) 22(3) cage in N1 = {589/679}
f) 22(3) cage in N3 = {589/679}
g) 9(3) cage in N3 = {126/135/234}, no 7,8,9
h) 11(3) cage at R4C3 = {128/137/146/236/245}, no 9
i) 11(3) cage at R5C1 = {128/137/146/236/245}, no 9
j) 21(3) cage in N8 = {489/579/678}, no 1,2,3
k) 14(4) cage at R3C3 = {1238/1247/1256/1346/2345}, no 9
l) 14(4) cage at R7C6 = {1238/1247/1256/1346/2345}, no 9

Steps resulting from Prelims
1a. 22(3) cage in N1 = {589/679}, 9 locked for N1
1b. 22(3) cage in N3 = {589/679}, 9 locked for N3

2. 45 rule on C1 2 outies R19C2 = 4 = {13}, locked for C2
2a. 17(3) cage in N7 = {179/359/368} (only combinations which contain 1 or 3), no 2,4
2b. R9C2 = {13} -> no 1,3 in R89C1
2c. Killer pair 8,9 in 17(3) cage and R8C23, locked for N7
[There was also Killer pair 6,9 in 17(3) cage and R8C23, locked for N7 but I didn’t spot that.]

3. 21(5) cage at R1C3 = {12459/12468/12567/23457} (other combinations clash with R1C2), 2 locked for R1
3a. Killer pair 1,3 in R1C2 and 21(5) cage at R1C3, locked for R1
3b. 21(5) cage at R9C3 = {12459/12468/12567/23457} (other combinations clash with R9C2), 2 locked for R9
3c. Killer pair 1,3 in R9C2 and 21(5) cage at R9C3, locked for R9

4. 45 rule on R9 2 outies R8C19 = 9 = [54/63/72/81], no 9, no 5,6,7,8 in R8C9
4a. 17(3) cage in N7 (step 2a) = {179/359/368}
4b. 9 of {179/359} must be in R9C1 => no 5,7 in R9C1
4c. 16(3) cage in N9 = {169/178/259/268/349/358/367/457}

5. 45 rule on R89 2 outies R7C56 = 13 = {58/67}/[94], no 4 in R7C5, no 1,2,3 in R7C6

6. 45 rule on C9 2 outies R19C8 = 1 innie R3C9 + 13
6a. Min R19C8 = 14, no 4 in R9C8
6b. Max R19C8 = 17 -> max R3C9 = 4

7. 45 rule on C12 3 outies R368C3 = 1 innie R7C2 + 18
7a. Min R7C2 = 2 => min R368C3 = 20 -> no 1,2 in R6C3
7b. Max R368C3 = 24 -> max R7C2 = 6

8. 45 rule on N69 3 innies R8C78 + R9C7 = 11 = {128/137/146/236/245}, no 9
8a. 45 rule on N69 2 outies R78C6 = 1 innie R9C7 + 3
8b. Min R78C6 = 5 -> min R9C7 = 2
[At this stage I missed 9 in C7 only in R4567C7, locked for 32(6) cage, no 9 in R47C8. However I don’t think this made much difference to my solving path; these eliminations are made in steps 15 and 17.]

9. 45 rule on N7 4 innies R7C123 + R9C3 = 14 = {1247/2345} (cannot be {1256} which clashes with R8C23, cannot be {1346} which clashes with R9C2), no 6

10. 45 rule on N4 2(1+1) outies R4C4 + R7C1 = 1 innie R4C1
10a. Min R4C4 + R7C1 = 2 -> min R4C1 = 2
[Ed pointed out that R4C4 and R7C1 cannot both be 1, because there would be no place left for 1 in N4, so min R4C1 = 3. I got this result a different way in the next step.]

11. 45 rule on N1 2 innies R12C3 = 1 outie R4C1 + 2
11a. Min R12C3 = 5 (cannot be {12} because no 1 in R4C1, cannot be {13} which clashes with R1C2) -> min R4C1 = 3

12. 45 rule on R9 4 innies R9C1289 = 24 = {1689/3489/3579/3678} (other combinations don’t contain 1 or 3 for R9C2)
12a. 9 of {1689} must be in R9C1 (17(3) cage in N7 cannot be [881]), 4 of {3489} must be in R9C9, 9 of {3579} must be in R9C1 -> no 9 in R9C9

13. 45 rule on R19+C19 (counting corner cells twice) 5 innies R19C19 + R3C9 = 31
[Note than R19C19 "see" each other because this is a Killer-X so they must all be different.]
13a. R3C9 = {1234} -> R19C19 = 27,28,29,30 must contain 9 which is only in R1C9 + R9C1, locked for D/, clean-up: no 5 in R8C3
13b. R3C9 + R19C19 = 1{6789}/2{5789}/3{4789/5689}/4{4689/5679}
13c. 3{4789}/4{4689} must have the 4 for R19C19 in R1C1 (16(3) cage in N9 (step 4c) cannot be {349} when 3 in R3C9 and 4 of {457} must be in R8C9) -> no 4 in R9C9

14. R9C1289 (step 12) = {1689/3579/3678}
14a. 9 of {1689} must be in R9C1 (17(3) cage in N7 cannot be [881]), 9 of {3579} must be in R9C1 -> no 9 in R9C8

15. 9 in N9 only in R7C78, locked for R7 and 32(6) cage at R4C7, clean-up: no 4 in R7C6 (step 5)

16. 9 in N6 only in the two 11(2) cages -> one of the 11(2) cages must be {29}, locked for N6, clean-up: no 7 in R7C9

17. R7C7 = 9 (hidden single in C7), placed for D\
17a. R3C2 = 9 (hidden single in N1)

18. 45 rule on N6 2 remaining outies R7C89 = 9 = {18/36/45}/[72], no 2 in R7C8

19. 14(4) cage at R7C6 = {1238/1247/1256/1346/2345}
19a. 7,8 of {1238/1247} must be in R7C6 -> no 7,8 in R8C678

[Even though I used 45s on N69 in step 8, I’ve only now spotted ones which use larger groups of nonets.]
20. 45 rule on N689 1 outie R9C3 = 1 innie R7C4, no 6,8 in R7C4

21. 45 rule on N6789 2 outies R56C4 = 1 innie R7C1 + 12
21a. Min R56C4 = 13, no 1,2,3, no 4 in R5C4
21b. Max R56C4 = 17 -> max R7C1 = 5

22. 45 rule on N6789 4 innies R7C1234 = 14 = {1247/2345}, 2,4 locked for R7, clean-up: no 5,7 in R7C8 (step 18), no 5 in R7C9 (step 18), no 4,5,7 in R6C9
22a. 7 in N9 only in R9C789, locked for R9, clean-up: no 7 in R7C4 (step 20)

23. R45C9 = {29/47/56} (cannot be {38} which clashes with R67C9), no 3,8

24. Hidden killer quad 1,2,3,4 in R3C9, R45C9, R67C9 and R8C9 for C9, R3C9 = {1234}, R67C9 contains one of 1,3, R8C9 = {1234} -> R45C9 must contain one of 2,4
24a. R45C9 (step 23) = {29/47} (cannot be {56} which doesn’t contain 2 or 4), no 5,6

25. 16(3) cage in N9 = {178/358/367/457} (cannot be {268} which clashes with R7C89), no 2, clean-up: no 7 in R8C1 (step 4)

26. R7C3 = 7 (hidden single in N7), placed for D/, clean-up: no 6 in R7C56 (step 5)

27. Naked pair {58} in R7C56, locked for R7 and N8, clean-up: no 1 in R7C89 (step 18), no 1,8 in R6C9, no 5 in R9C3 (step 20)
27a. Naked pair {36} in R7C89, locked for R7 and N9, clean-up: no 6 in R8C1 (step 4), no 3 in R9C3 (step 20)
27b. Naked pair {36} in R67C9, locked for C9

28. 16(3) cage in N9 (step 25) = {178/457}, 7 locked for N9

29. 17(3) cage in N7 (step 2a) = {359/368} -> R9C2 = 3, R1C2 = 1
29a. R89C1 = [59/86], no 8 in R9C1

30. R8C6 = 3 (hidden single in N8)
30a. 14(4) cage at R7C6 (step 19) = {1238/2345}, 2 locked for N9
30b. R7C6 = {58} -> no 5 in R8C78
30c. Naked triple {124} in R8C789, locked for R8 and N9

31. 45 rule on N3 3 innies R123C7 = 14 = {167/248/347} (cannot be {158} which clashes with R9C7, cannot be {257/356} which clash with 22(3) cage), no 5

32. 21(5) cage at R1C3 (step 3) = {23457} (only remaining combination), locked for R1
32a. 22(3) cage in N3 = {589/679}
32b. 5,7 only in R2C9 -> R2C9 = {57}

33. Killer pair 6,8 in R1C1 and 22(3) cage, locked for N1

34. R89C1 (step 29a) = [59] (cannot be [86] which clashes with R1C1) -> R8C1 = 5, R9C1 = 9, placed for D/, R1C9 = 8, placed for D/, R1C1 = 6, placed for D\, R8C2 = 6, placed for D/, R8C3 = 8, R1C8 = 9, R2C9 = 5 (step 32b), R9C9 = 7, placed for D\, R2C2 = 8, R3C3 = 5, both placed for D\, clean-up: no 4 in R45C9
34a. Naked pair {29} in R45C9, locked for C9 and N6

35. R19C19 = [6897] = 30 -> R3C9 = 1 (step 13b), R8C9 = 4, R9C8 = 5 (step 28), R9C7 = 8, clean-up: no 6 in R56C8
35a. R3C9 = 1 -> R23C8 = 8 = {26} -> R2C8 = 2, placed for D/, R3C8 = 6, R7C8 = 3, R67C9 = [36], R8C8 = 1, placed for D\, R8C7 = 2, R7C6 = 8 (step 30a), R7C5 = 5, clean-up: no 8 in R56C8

36. Naked pair {47} in R56C8, locked for N6 -> R4C8 = 8

37. 1,8 in C1 only in 11(3) cage at R5C1 = {128} (only remaining combination), locked for C1

38. R6C3 = 9 (hidden single in C3), R456C2 = 14 = {257} (only remaining combination), locked for C2 and N4 -> R7C2 = 4, R6C4 = 5

39. R7C1 = 2 (hidden single in C1), R7C4 = 1, R5C4 = 9 (cage sum), R45C9 = [92], R8C45 = [79], R9C3 = 1

40. 11(3) cage at R4C3 = {236} (only remaining combination) -> R4C4 = 2, R45C3 = {36}, locked for C3 and N4, R2C3 = 4, R1C3 = 2, R4C1 = 4, R6C6 = 4, R5C5 = 3, placed for D/

and the rest is naked singles.
Interesting breakthough in SS by Andrew:
Thanks Ed for the SSv3.3 log for Uluru. It used an interesting breakthrough step. Here is the position after step 100.

Code:
.-------------------------------.-------------------------------.-------------------------------.
| 68        1         23457     | 23457     23457     2457      | 2347      689       89        |
| 234578    5678      234578    | 3456789   123456789 12456789  | 1234678   1234      57        |
| 234578    9         5678      | 12345678  12345678  1245678   | 12347     23456     124       |
:-------------------------------+-------------------------------+-------------------------------:
| 23456789  245678    12345678  | 1234      56789     1247      | 1345678   1345678   2479      |
| 1234678   245678    1245678   | 5689      1234      1245678   | 1345678   23456789  2479      |
| 1234678   245678    123456789 | 5689      56789     124       | 1345678   23456789  36        |
:-------------------------------+-------------------------------+-------------------------------:
| 12        247       1247      | 124       58        58        | 9         36        36        |
| 58        568       689       | 679       679       3         | 124       124       14        |
| 69        3         124       | 12469     12469     12469     | 58        578       578       |
'-------------------------------.-------------------------------.-------------------------------'



First SS found
101. Conjugate pair r2c9=5=r9c9 in c9
101a. Candidate 5 removed from r2c2
101b. Cage sum in cage 22(3) n1 - removed 8 from r3c3

which in my words is 5 in c9 only in r29c9 -> no 5 in r2c2 (using the diagonal), then no 8 in r3c3

Next SS found the interesting
102. X-Cycle on candidate 5 at r2c9=r3c8 - r3c3=r9c9
102a. Removed candidate 5 from r3c1456

A complicated step, possibly some sort of "Fish". In my words it seems to be
5 in c9 only in r29c9, 5 in n3 only in r2c9+r3c8, 5 in d\ only in r3c3+r9c9 -> 5 in r3 only in r3c38, locked for r3


Last edited by Ed on Fri Apr 09, 2010 10:15 pm, edited 3 times in total.

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PostPosted: Thu Jun 05, 2008 5:06 am 
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Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Assassin 14 by Ruud (Sep 06)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:2304:3841:3841:4867:4867:4867:3846:3846:2312:2304:3841:2571:2571:2317:2318:2318:3846:2312:6162:6162:6162:6162:2317:7703:7703:7703:7703:4123:3100:4381:6162:2317:7703:4129:3618:3875:4123:3100:4381:4647:4647:4647:4129:3618:3875:4123:3100:4381:5424:5169:6194:4129:3618:3875:5424:5424:5424:5424:5169:6194:6194:6194:6194:1599:5952:2113:2113:5169:3396:3396:4422:1607:1599:5952:5952:2635:2635:2635:4422:4422:1607:
Solution:
+-------+-------+-------+
| 8 4 6 | 7 9 3 | 1 5 2 |
| 1 5 2 | 8 4 6 | 3 9 7 |
| 9 3 7 | 1 2 5 | 8 4 6 |
+-------+-------+-------+
| 6 9 5 | 4 3 7 | 2 1 8 |
| 7 2 4 | 9 1 8 | 5 6 3 |
| 3 1 8 | 6 5 2 | 9 7 4 |
+-------+-------+-------+
| 5 7 1 | 2 8 4 | 6 3 9 |
| 2 6 3 | 5 7 9 | 4 8 1 |
| 4 8 9 | 3 6 1 | 7 2 5 |
+-------+-------+-------+
Quote:
Ruud, lead-in: Don’t you feel like you’re behind bars when you look at this killer? Try to escape from this prison
Andrew: Escaped. The prison needs stronger bars!
Oscar: Easy Assassin, just pick the right innies..done little less than one hour. I would rate it 0.50
Walkthrough by Andrew:
Escaped. The prison needs stronger bars!

Here is my walkthrough.

1. 45 rule on R12 -> R2C5 = 4, R34C5= {23}, 45 rule on R89 -> R8C5 = 7, R67C5 = {58}, R159C5 = {169} with R1C5 = {69}, R9C5 = {16}

2. 23(3) cage in N7 = {689}, 45 rule on C1 -> R37C1 = 14 = [95], R89C1 = {24}, R67C5 = [58], 7 in N7 locked in R7 in R7C23, 7 in N9 locked in R9 in R9C78, 17(3) cage in N9 cannot contain a 3, R8C34 = [35], R8C67 = {49}, R89C1 = [24], R89C9 = [15], R7C23 = {17}, R8C8 cannot be 6 so R8C28 = [68], R9C78 = {27}, 45 rule on C9 -> R37C9 = 15 = [69], R8C67 = [94], R7C6 = 4, R7C78 = {36}, R6C6 = 2, R34C5 = [23]

3. R12C9 = {27}, R456C9 = {348}, R67C4 = [62], R5C5 = {19} -> R5C456 = {189}, R4C46 = [47], R3C678 = {458} -> R3C8 = 4, R3C234 = {137}, 9 in N3 is locked in the 15(3) cage which must be {159}, R3C67 = [58], R2C67 = [63], R7C78 = [63], 16(3) cage in N6 = {259} -> R6C7 = 9, 14(3) cage in N6 = {167}, R9C78 = [72], R1C7 = 1

4. R12C1 = [81], R3C4 = 1, 16(3) cage in N4 = {367} -> R4C1 = 6, 45 rule on N1 -> R2C34 = [28], 15(3) cage in N1 = {456} -> R2C2 = 5, R1C23 = [46], R159C5 = [916], R1C46 = [73], R5C46 = [98], R9C46 = [31], 2 is locked in C2 in N4 so 12(3) cage = [921], 17(3) cage in N4 = {458} and carry on, the rest is simple elimination
Assassin 15 by Ruud (Sept 06)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:2816:2561:6146:6146:6146:6146:6146:3591:5384:2816:2561:2561:4620:4620:4620:3591:3591:5384:2816:5139:2836:2836:790:3863:3863:3865:5384:5139:5139:2333:10270:790:10270:3617:3865:3865:4388:4388:2333:10270:10270:10270:3617:1323:1323:2349:2349:2333:10270:1841:10270:3617:4404:4404:5174:2349:2360:2360:1841:3899:3899:4404:3134:5174:3648:3648:4418:4418:4418:4677:4677:3134:5174:3648:5194:5194:5194:5194:5194:4677:3134:
Solution:
+-------+-------+-------+
| 2 4 9 | 1 6 5 | 3 8 7 |
| 6 1 5 | 3 8 7 | 4 2 9 |
| 3 8 7 | 4 2 9 | 6 1 5 |
+-------+-------+-------+
| 5 7 4 | 9 1 3 | 2 6 8 |
| 8 9 3 | 6 7 2 | 5 4 1 |
| 1 6 2 | 5 4 8 | 7 9 3 |
+-------+-------+-------+
| 7 2 1 | 8 3 6 | 9 5 4 |
| 4 5 6 | 7 9 1 | 8 3 2 |
| 9 3 8 | 2 5 4 | 1 7 6 |
+-------+-------+-------+
Quote:
Ruud, lead-in: This Assassin is like a safe that requires the right combination to be opened
Andrew: hopefully found Ruud's combination to crack the safe
Oscar: very easy one...with some 40 minutes work I would rate it as 0.50
Walkthrough by Andrew:
Here is my walkthrough. I've edited it for clarity and added more notes of explanation based on comments received from sudokuEd. Thanks for those comments.

1. R34C5 = {12}, R67C5 = {34}, R5C12 = {89}, 7 in N4 locked in 20(3) cage which must have {49/58} in the other 2 cells with R3C2 = {89} to avoid clashing with R5C12, 45 rule on R123 3 innies R3C258 = 11 -> R3C2 = 8, R3C58 = {12}, 45 rule on N6 2 outies = 6 -> R7C8 = {45}, R5C12 = [89], R4C12 = {57}, 45 rule on R12 2 outies R3C19 = 8 -> R3C19 = [35] because the 21(3) cage in N3 cannot contain a 3, 45 rule on N4 2 outies = 10 -> R7C2 = 2

2. R3C34 = {47}, 45 rule on N1 2 innies = 16 -> R13C3 = [97], R3C4 = 4, 45 rule on N3 3 innies = 10 -> max 7 in each innie -> R3C67 = [96], 45 rule on N3 again 2 remaining innies = 4 -> R1C7 = 3, R37C8 = [15], R34C5 = [21], 2 in N4 locked in C3, 2 in N1 locked in C1 -> R12C1 = {26}, 10(3) cage in N1 = {145}, R12C9 = [79], 14(3) cage in N3 = {248}, R4C89 = {68}, R6C89 = [93], R5C89 = [41], R2C7 = 4, R12C8 = {28}, R1C2 = 4, R4C89 = [68], 14(3) cage in N6 = {257} with the 2 in R4C7, R67C5 = [43], R6C12 = [16], R456C3 = [432]

3. 45 rule on R89 2 outies = 11 -> R7C19 = [74], R7C67 = [69], R4C12 = [57], R89C1 = {49}, R7C34 = {18}, 45 rule on N7 3 innies = 11 -> R9C3 = {18}, 14(3) cage in N7 = {356} with the 6 in R8C3, R89C9 = [26], 45 rule on N9 3 innies = 15 -> R9C7 = 1, 18(3) cage in N9 = {378} with the 8 in R8C7, R79C3 = [18], R7C4 = 8

4. R1C456 = {156} so 6 in R1 locked in N2 -> R12C1 = [26], R12C8 = [82], R2C456 = {378}, 1 in N8 locked in R8 so R8C456 = {179}, R9C456 = [254] and carry on, the rest is simple elimination


Last edited by Ed on Fri Jun 13, 2008 12:59 pm, edited 1 time in total.

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