SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Thu Mar 28, 2024 9:56 pm

All times are UTC




Post new topic Reply to topic  [ 2 posts ] 
Author Message
 Post subject: Old Lace Groups PDD 5
PostPosted: Tue Oct 28, 2014 12:34 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
Old Lace Groups Pair Directed Digitized 5

The cages are ordered increasing top left to bottom right (row first).
The cages are digital - the last digit of the sum is in one of the cells.
The first two cells are consecutive - the third one is non-consecutive.

For example [128] is the smallest valid combination.

Note the blue cell is in two groups.

Difficulty should be about paper solvable - interested in your views.

Image

Puzzle:

3x3:d:k:1:10:11:12:13:14:15:16:17:18:1:19:20:21:22:23:24:25:26:27:1:28:29:7:7:7:30:31:32:4:33:34:35:8:36:8:37:38:4:39:40:41:42:8:43:44:45:46:4:5:5:5:47:48:49:50:51:52:9:53:3:54:55:56:57:58:9:59:9:60:3:61:62:63:64:65:66:67:68:69:70:

remove 0(2) cage @ r7c7 then add 0(3) on the diagonal at r6c6

Old Lace Groups (enter puzzle then paste as extra groups):

3x3::k:11521:11521:11528:11528:11528:11528:11528:11522:11522:11521:11521:11521:11521:11528:11522:11522:11522:11522:11525:11521:11521:11528:11529:11528:11522:11522:11527:11525:11521:11525:11529:11528:11529:11527:11522:11527:11525:11525:11529:11525:11529:11527:11529:11527:11527:11525:11524:11525:11529:11526:11529:11527:11523:11527:11525:11524:11524:11526:11529:11526:11523:11523:11527:11524:11524:11524:11524:11526:11523:11523:11523:11523:11524:11524:11526:11526:11526:11526:11526:11523:11523:

solution:

164378952
723956841
958142376
841567293
372491685
695823714
286715439
417239568
539684127


Top
 Profile  
Reply with quote  
PostPosted: Wed Oct 29, 2014 3:14 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks HATMAN for a fun puzzle! :D

I agree that it's Paper Solvable:
A few of my steps are advanced ones, LoLs and a short contradiction, but they can be visualised just by looking at the diagrams; I actually used two diagrams, one for the cages and the other for the jigsaw houses.

Here is my walkthrough for Old Lace Groups PDD 5:
The cages are ordered increasing top left to bottom right (row first).
The cages are digital - the last digit of the sum is in one of the cells.
The first two cells are consecutive - the third one is non-consecutive.
Valid cage permutations [128], [129], [237], [238], [346] and [347]; cannot be [456] because the third digit has to be non-consecutive.

1. The two cages on D/ must start [12x] and [34y]
1a. R6C6 is the middle cell of the cage at R6C5 so cannot contain 1 -> R1C1 + R2C2 = [12], placed for D\, R6C6 + R7C7 = [34], placed for D/, R6C5 = 2

2. 3 already placed for Old Lace -> cage at R7C5 = [12x] -> R7C5 = 1, R8C4 = 2

3. R6C5 = 2 -> 2 in Old Lace must be in R5C37
3a. 2 in R5C7 would make R45C3 = [34] and R4C79 = [34] -> R5C3 = 2 -> R4C3 = 1

4. R4C3 = 1, placed for pale green house, R7C5 = 1, placed for Old Lace -> R5C6 = 1 (hidden single in N5)

5. Cage at R3C6 must be [23x] -> R3C67 = [23]

6. R4C3 = 1 -> cage at R4C7 must contain 3 -> R4C9 = 3, R4C7 = 2

7. Cages at R3C6 and R4C7 are both [23x] -> R35C8 must contain one of 7,8 -> [34y] diagonal cage at R6C6 must be [346] -> R8C8 = 6

8. R3C4 = 1 (hidden single for darker green house)
8a. R6C8 = 1 (hidden single in R6)
8b. R9C7 = 1 (hidden single in turquoise house)
8c. R8C2 = 1 (hidden single in R8), placed for D/
8d. R2C9 = 1 (hidden single in purple house)
8e. R7C1 = 2 (hidden single in pale green house)
8f. R9C8 = 2 (hidden single in R9) -> R1C9 = 2 (hidden single in R1)
8g. R7C8 = 3 (hidden single in C8)

9. Cage at R7C5 = [12x] -> R8C6 must contain one of 8,9, whichever value is in R8C6 must be in R7C9 and whichever value is in R7C9 must be in R6C2 (LoL for R789), cage at R4C3 = [12x] -> R6C4 must contain one of 8,9 -> R6C24 contain 8,9 for R6 -> cage at R6C5 must be [237] -> R6C7 = 7
9a. Cage at R4C7 must be [238] -> R5C8 = 8
9b. Cage at R3C6 must be [237] -> R3C8 = 7
9c. R7C9 must contain one of 8,9 but R5C8 = 8 -> R7C9 = 9 -> R8C6 = 9 (hidden single in darker pink house)
9d. R6C2 = R7C9 (LoL for R789), R7C9 = 9 -> R6C2 = 9
9e. R9C3 = 9 (hidden single in turquoise house)

10. Cage at R1C1 must be [128] -> R3C3 = 8, placed for D\

11. 9 on D\ only in R4C4 + R5C5, locked for Old Lace -> R4C8 = 9 (hidden single in N6)
11a. 9 on D\ only in R4C4 + R5C5 -> cage at R4C3 must be [128] -> R6C4 = 8, placed for D/
11b. R1C7 = 9 (hidden single in N3)
11c. R3C1 = 9 (hidden single in pale green house)
11d. R2C4 = 2 (hidden single in N2)
11e. R5C5 = 9 (hidden single in N5), placed for both diagonals
11f. R4C1 = 8 (hidden single in R4)

12. R2C7 = 8 (hidden single in N3) -> R2C6 = 6 (hidden single in purple house)
12a. R8C9 = 8 (hidden single in N9), R9C9 = 7 (hidden single in N9), placed for D\ -> R4C4 = 5, R8C7 = 5

13. R4C6 = 7 (hidden single in Old Lace), placed for D/

14. R3C9 = 6 (hidden single in N3)
14a. R5C7 = 6 (hidden single in N6)
14b. R4C5 = 6 (hidden single in N5) -> R5C4 = 4
14c. R6C9 = 4 (hidden single in N6) -> R5C9 = 5
14d. R4C2 = 4 (hidden single in R4)
14e. R3C5 = 4 (hidden single in Old Lace) -> R3C2 = 5
14f. R1C2 = 6 (hidden single in orange house)
14g. R1C3 = 4 (hidden single in N1)
14h. R2C8 = 4 (hidden single in R2), placed for D/, R1C8 = 5 (hidden single in C8)

15. R2C5 = 5 (hidden single in R2)
15a. R1C6 = 8 (hidden single in darker green house)
15b. R9C6 = 4 -> R7C6 = 5 (hidden singles in C6)
15c. R9C5 = 8 (hidden single in C5)

16. R9C1 = 5 (hidden single on D/) -> R7C3 = 6 (remaining single on D/)
16a. R6C3 = 5 (hidden single in R6) -> R6C1 = 6
16b. R8C1 = 4 (hidden single in C1)
16c. R7C2 = 8 (hidden single on R7) -> R7C4 = 7
16d. R1C5 = 7 (hidden single in R1) -> R1C4 = 3
16e. R9C4 = 6 (hidden single in C4) -> R8C5 = 3 -> R8C3 = 7 -> R9C2 = 3 -> R5C2 = 7 -> R5C1 = 3 -> R2C1 = 7 -> R2C3 = 3


Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 2 posts ] 

All times are UTC


Who is online

Users browsing this forum: No registered users and 8 guests


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

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