SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Tue Jun 02, 2020 1:00 am

All times are UTC




Post new topic Reply to topic  [ 3 posts ] 
Author Message
PostPosted: Wed Apr 03, 2019 9:26 pm 
Offline
Addict
Addict

Joined: Sat Jan 05, 2019 1:02 pm
Posts: 38
This one is a standard Jigsaw Killer (SS rating 1.2).

It demonstrates an improved version of my rendering program - some cage layouts only require 3 colors and this one is an example. The pattern selection in the printer friendly image has also been improved.

Attachment:
TJK-102.png
TJK-102.png [ 13.19 KiB | Viewed 1249 times ]


SS definition:

SumoCueV1=9J2+0J4+0J4=26J4+3J4=18J3=23J3+6J3=9J3=21J2+9J4+9J2+3J4+3J3+5J3+6J5+6J5+8J3=14J2+9J2=10J2+20J4=20J1+5J3+5J5=16J5+25J5+18J2=20J2+28J4+28J4+22J1+22J3+22J5+25J5=13J5=18J2+36J6+28J1=8J1+39J1+39J1=19J1+35J5+35J9+36J6=11J6=19J6+47J8+47J1+42J7+42J7+42J9=10J9+46J6+46J6=25J6+56J8+47J1=17J7+59J9=16J9+53J9=14J8=16J6+64J6+56J8=19J8+67J7+61J9+61J7+61J9+63J8+64J8+64J8+56J8+67J7+67J7=14J7+78J7+78J9


Top
 Profile  
Reply with quote  
PostPosted: Wed Apr 03, 2019 9:28 pm 
Offline
Addict
Addict

Joined: Sat Jan 05, 2019 1:02 pm
Posts: 38
TJK-102 Print-friendly:
Attachment:
TJK-102-PF.png
TJK-102-PF.png [ 17.95 KiB | Viewed 1248 times ]


Top
 Profile  
Reply with quote  
PostPosted: Fri May 15, 2020 5:29 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1715
Location: Lethbridge, Alberta, Canada
By far the hardest of Mathimagics' batch of Texas Jigsaw Killers because of its more complicated jigsaw pattern.

I'll agree with the SS score although at a human level it felt harder. I had a glance at how SS solved it; several hidden 4-cell cages were used, not an approach most people would use, I didn't.

Here is my walkthrough for Texas Jigsaw Killer 102:
Jigsaw nonets identified by their upper-left cells, for example NR3C5

Prelims

a) R12C9 = {18/27/36/45}, no 9
b) R34C1 = {59/68}
c) R3C34 = {19/28/37/46}, no 5
d) R67C9 = {19/28/37/46}, no 5
e) R7C67 = {89}
f) R89C1 = {59/68}
g 9(3) cage at R1C1 = {126/135/234}, no 7,8,9
h) 8(3) cage at R5C4 = {125/134}
i) 11(3) cage at R6C2 = {128/137/146/236/245}, no 9
j) 26(4) cage at R1C4 = {2789/3689/4589/4679/5678}, no 1

Steps resulting from Prelims
1a. 8(3) cage at R5C4 = {125/134}, 1 locked for R5 and NR3C5
1b. Naked pair {89} in R7C67, locked for R7, clean-up: no 1,2 in R6C1
1c. Naked pair {89} in R7C67, CPE no 8,9 in R69C7
1d. Naked quad {5689} in R3489C1, locked for C1

2a. 45 rule on R1234 1 outie R5C3 = 1 innie R4C9 + 6 -> R4C9 = {123}, R5C3 = {789}
2b. 18(3) cage at R5C1 = {279/378} (cannot be {189/369/459/468/567} because 5,6,8,9 only in R5C2) -> R56C1 = {27/37}, 7 locked for C1, R5C2 = {89}
2c. 45 rule on R6789 1 outie R5C7 = 1 innie R6C1 = {237}, R56C1 = {27/37} -> R5C17 = {27/37}, 7 locked for R5, clean-up: no 1 in R4C9
2d. Naked pair {89} in R5C23, locked for R5
2e. Killer triple 2,3 in R5C17 and 8(3) cage at R5C4, locked for R5
2f. 13(3) cage at R4C9 = {256/346}, CPE no 6 in R3C9 + R67C8
2g. 6 in NR3C5 only in R3467C5, locked for C5

3a. Naked pair {89} in R5C23, CPE no 8,9 in R4C2 + R68C3
3b. 8,9 in NR5C2 only in R568C2, locked for C2
3c. Hidden killer pair 8,9 in R34C1 and R23C3 for NR1C1, R34C1 contain one of 8,9 -> R23C3 must contain one of 8,9
3d. Killer pair 8,9 in R23C3 and R5C3, locked for C3

4a. Hidden killer pair 8,9 in R689C4 + R8C5 and R89C1 for NR6C4, R89C1 contain one of 8,9 -> R689C4 + R8C5 can only contain one of 8,9
4b. 25(4) cage at R7C3 = {3679/4579/4678} (cannot be {1789/2689/3589} which contain both of 8,9), no 1,2
4c. 25(4) cage at R7C3 = {3679/4579/4678}, CPE no 7 in R9C3
4d. Killer pair 8,9 in 25(4) cage and R89C1, locked for NR6C4
4e. 45 rule on R89 2 innies R89C4 = 1 outie R7C8 + 11
4f. Max R89C4 = 16 -> max R7C8 = 5
4g. Hidden killer pair 8,9 in R1234C4 and R89C4 for C4, R89C4 contain one of 8,9 -> R1234C4 must contain one of 8,9

5. 45 rule on R12 2 innies R12C6 = 1 outie R3C2 + 2, max R3C2 = 7 -> max R12C6 = 9, no 9 in R12C6

[Time to start using Law of Leftovers (LoL). For those not familiar with LoL, the outies and innies must contain exactly the same numbers.]
6. LoL for R1234 2 outies R5C18 = 2 innies R34C5, no 8,9 in R5C18 -> no 8,9 in R34C5
6a. R5C3 + R6C5 = {89} (hidden pair in NR3C5)

7. LoL for R6789 2 outies R5C29 = 2 innies R67C5, no 2,3,7 in R5C29 -> no 2,3,7 in R67C5
7a. Min R67C5 = 12 -> max R6C34 = 7, no 7 in R6C34
7b. 7 in NR3C5 only in R34C5 + R5C7, CPE no 7 in R4C7

8. LoL for C1234 2 outies R18C5 = 2 innies R5C34, no 7 in R5C34 -> no 7 in 2 R18C5
8a. R5C3 = {89} -> R1C5 = {89}
8b. Naked pair {89} in R16C5, locked for C5
8c. R1234C4 must contain one of 8,9 (step 4g), killer pair 8,9 in R1234C4 and R1C5, locked for NR1C2

9. 45 rule on R789 2 outies R6C29 = 1 innie R7C5 + 7, min R7C5 = 4 -> min R6C29 = 11, no 1 in R6C2

10. 45 rule on R123 2 outies R4C18 = 1 innie R3C5 + 11
10a. Max R4C18 = 17 -> max R3C5 = 6
10b. Min R3C5 = 2 -> min R4C18 = 13 -> min R4C8 = 4

11. 45 rule on R1234 4 innies R4C2349 = 14 = {1238/1247/1256/1346/2345}, no 9

[This step could be considered to be a forcing chain or combined cages.]
12. 13(3) cage at R4C9 = {256/346}, 8(3) cage at R5C4 = {125/134} -> combined cage R4C9 + R5C45689 = 2{134}{56}/3{125}{46} -> no 2,3 in R4C5

[The hardest part for me was spotting useful 45s on the jigsaw nonets; this one and the next one crack this puzzle.]
13. 45 rule on NR5C9+NR6C6 2 outies R5C7 + R8C5 = 1 innie R5C9 + 5
13a. Min R5C9 = 4 -> min R5C7 + R8C5 = 9, max R8C5 = 5 -> R5C7 = 7 -> R6C1 = 7 (step 2c), clean-up: no 3 in R7C9
13b. R5C9 = R8C5 + 2, R5C9 = {456} -> R8C5 = {234}
13c. LoL for R1234 (step 6) R5C18 = R34C5 -> R3C5 = {23}
13d. LoL for C1234 (step 8) R18C5 = R5C34 -> R5C4 = {234}

14. 45 rule on NR1C1+NR1C2 2 outies R2C5 + R5C3 = 1 innie R5C1 + 10
14a. R6C1 = 7 -> R5C12 = 11 = [29/38] -> R5C13 = [28/39]
14b. R5C3 6 more than R5C1 -> R2C5 = 4, clean-up: no 5 in R12C9
14c. R9C5 = 7 (hidden single in C5)
14d. 4 in NR3C5 only in 8(3) cage at R5C4 = {134}, 3,4 locked for R5, 3 locked for NR3C5 -> R3C5 = 2, R5C1 = 2, R5C2 = 9, R5C3 = 8, R5C58 = [13], R6C5= 9 -> R1C5 = 8, clean-up: no 1 in R2C9, no 1 in R7C9
14e. R8C5 = 3 -> R5C9 = 5 (step 13b)
14f. R5C89 = [65] -> R4C9 = 2 (cage sum), clean-up: no 7 in R12C9, no 8 in R6C9
14g. R12C9 = [18] (cannot be {36} which clashes with R67C9)
14h. LoL for C1234 (step 8) R18C5 = R5C34, R18C5 = [83] -> R5C34 = [83], R5C6 = 4, clean-up: no 7 in R3C3
14i. R89C5 = [37] = 10 -> R89C6 = 9 = {18}, locked for NR6C6 -> R7C67 = [98]
14j. R12C5 = [84] = 12 -> R12C4 = 14 = {59}, locked for C4, 5 locked for NR1C2, clean-up: no 1 in R3C3
14k. 9(3) cage at R1C1 = {234} (only remaining combination), locked for R1, 2 locked for NR1C2
14l. 25(4) cage at R7C3 = {4678} (only remaining combination), 7 locked for C4, 8 locked for NR6C4, clean-up: no 3 in R3C3, no 6 in R89C1
14m. Naked pair {59} in R89C1, locked for C1, 5 locked for NR6C4
14n. Naked pair {68} in R34C1, 6 locked for NR1C1, clean-up: no 4 in R3C4
14o. R6C4 = 2 (hidden single in C4), R6C5 = 9 -> R6C3 + R7C5 = 8 = [35], clean-up: no 7 in R7C9
14p. Naked pair {46} in R67C9, locked for C9 and NR5C9
14q. Naked pair {46} in R7C39, locked for R7 -> R7C4 = 7
14r. R7C12 = [12] -> R6C2 = 8 (cage sum)
14s. R2C1 = 3 -> 9(3) cage at R1C1 = [432]
14t. R2C1 = 3 -> 21(4) cage at R2C1 = {3567} (only remaining combination) -> R2C2 = 6, R2C3 + R3C2 = {57}, locked for N1, R4C2 = 1, R4C345 = [746], R34C1 = [68], R3C4 = 1 -> R3C3 = 9

and the rest is naked singles, using rows, columns and jigsaw nonets.

Solution:
4 3 2 5 8 7 6 9 1
3 6 5 9 4 2 1 7 8
6 7 9 1 2 5 4 8 3
8 1 7 4 6 3 9 5 2
2 9 8 3 1 4 7 6 5
7 8 3 2 9 6 5 1 4
1 2 4 7 5 9 8 3 6
9 5 6 8 3 1 2 4 7
5 4 1 6 7 8 3 2 9


Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 3 posts ] 

All times are UTC


Who is online

Users browsing this forum: No registered users and 4 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
Powered by phpBB® Forum Software © phpBB Group