SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Sat Feb 29, 2020 12:30 am

All times are UTC




Post new topic Reply to topic  [ 2 posts ] 
Author Message
 Post subject: Renban ORC 1
PostPosted: Sun Sep 01, 2019 7:12 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 608
Renban ORC 1

As we are playing around with renban groups I thought to try one on an ORC background.

All cages are good renban groups i.e. they have a set of consecutive non-repeating numbers in any order. I'm thinking about doing one with bad renban groups which may/must have repeats.

To remind you renban is Japanese and means sequence in this context, so the numbers in the cage are consecutive but in any order.

Note that
given the layout the renban groups are NC so very restricted e.g. 1234 is [2413] or [3142] and 12345 has 14 solutions.

Odd Row and Column - ORC - so it is:
ORC: odd rows and columns are 1-9 no repeat; even ones are not (i.e. they can repeat).
NN: no nonets

For all cells:
AK: Anti-King - diagonally adjacent are not equal (of course horizontally and vertically adjacent cells can repeat if in an even row or column)
FNC: Ferz Non-consecutive - diagonally adjacent are not consecutive
NC: horizontally and vertically adjacent cells are not consecutive

I solve these in JSudoku control-right click allows you to remove the row and column constraints. Note recursively solve works but deduce a move is flawed, so if you are using it stop when you get to X-wing as this fails.


Image


Top
 Profile  
Reply with quote  
 Post subject: Re: Renban ORC 1
PostPosted: Wed Oct 02, 2019 11:21 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1703
Location: Lethbridge, Alberta, Canada
Thanks HATMAN. A fun puzzle! After an easy start, first time through I then found it fairly hard going but then, while checking my walkthrough, I kept finding simplifications so a couple of harder steps have been deleted. So many AK,FNC,NC eliminations to make, I've probably still missed a few; that's what comes from solving with Excel worksheets, no doubt the same for paper & pencil solvers.

Here is my walkthrough for Renban ORC 1:
Cages are Renban groups, containing consecutive non-repeating numbers in any order.
AK so diagonally adjacent cells cannot be equal, also FNC and NC so horizontally/ vertically/diagonally adjacent cells.
Odd numbered rows and columns are normal; repeats are allowed on even numbered rows and columns.

Prelims
The 6-cell cages containing 1 must be {123456} and the 7-cell cages containing 1 must be {1234567}
Cage at R3C2 = {123456}
Cage at R3C4 = {1234567}
Cage at R4C7 = {1234567}
Cage at R5C5 = {123456}
Clean-ups, AK, FNC and NC, separately or together, only when stated.

1a. R3C2 = 1, placed for R3 and cage at R3C2
1b. R4C7 = 1, placed for C7 and cage at R4C7
1c. R5C3 = 1, placed for R5, C3 and cage at R3C4
1d. R7C4 = 1, placed for R7 and cage at R5C5
1e. R6C4 = 9
Clean-ups:
R2C8 = 1 -> no 1,2 in R1C9, no 2 in R1C78 + R2C79 + R3C789
R3C2 = 1 -> no 1,2 in R24C1, no 2 in R2C23 + R3C13 + R4C23
R4C7 = 1 -> no 2 in R3C6 + R4C68 + R5C678
R5C3 = 1 -> no 1,2 in R6C2, no 2 in R4C4 + R5C24 + R6C3
R7C4 = 1 -> no 1,2 in R8C5, no 2 in R6C5 + R7C35 + R8C34
R8C2 = 1 -> no 1,2 in R9C1, no 2 in R7C12 + R8C1 + R9C23

2a. R1C1 = 1 (hidden single in C1), placed for R1
2b. R1C3 = 2 (hidden single in C3), placed for R1
2c. R3C4 = 2 (hidden single in cage at R3C4), placed for R3
2d. R6C1 = 2 (hidden single in cage at R3C2), placed for C1
Clean-ups:
R1C1 = 1 -> no 1 in R2C2
R1C3 = 2 -> no 1,2,3 in R2C4, no 3 in R1C24 + R2C23
R3C4 = 2 -> no 1,2,3 in R24C5, no 3 in R3C35 + R4C34
R6C1 = 2 -> no 3 in R5C12 + R6C2 + R7C12
R5C2 = {456} -> no 5 in R4C13 + R5C1 + R6C3
R7C1 = {456} -> no 5 in R67C2 + R8C1

3a. R9C5 = 1 (hidden single in C5), placed for R9
3b. R5C5 = 2 (hidden single in C5), placed for R5 and cage at R5C5
Clean-ups:
R5C5 = 2 -> no 1,3 in R4C6, no 1,2,3 in R6C6, no 3 in R5C46 + R6C5
R9C5 = 1 -> no 2 in R89C6
R6C5 = {456} -> no 5 in R5C46 + R7C56

4. 3 in cage at R3C4 only in R678C3, locked for C3
Clean-up:
3 in R678C3 -> no 4 in R7C23

5. Cage at R1C9 doesn’t contain 2 -> no 1 in R2C9 + R4C8

6. 3 in cage at R3C2 only in R4C2 + R8C1 -> no 3 in R3C1 (AK)

7. Hidden killer pair 8,9 in R7C2 and R7C89 for R7, R7C89 cannot be {89} (NC) -> R7C2 = {89}, R7C89 contain one of 8,9
Clean-up:
R7C89 contain one of 8,9 -> no 8,9 in R68C9

[4-cell cages cannot have their lowest or highest numbers at the ends.]
8a. Cage at R1C4 = {4567/5678/6789}
8b. {4567} can only have 4 in the middle cells -> no 4 in R1C4 + R4C3
8c. {6789} can only have 9 in the middle cells -> no 9 in R1C4 + R4C3
Clean-up:
R4C3 = {678} -> no 7 in R3C3 + R5C4
R5C4 = {46} -> no 5 in R4C45 + R6C5

9a. Naked pair {46} in R5C4 + R6C5 (because of AK), CPE no 4,6 in R5C6
9b. 5 in cage at R5C5 only in R89C4 -> no 4 in R89C4, no 4,6 in R8C35, no 4,5,6 in R9C3
9c. 4 in cage at R5C5 only in R67C5 -> no 3 in R7C5
9d. Naked pair {46} in R67C5, locked for C5, 6 locked for cage at R5C5
9e. R7C5 = {46} -> no 5 in R8C4
9f. R89C4 = [35], 5 locked for R9, no 4 in R7C5, no 5 in R8C3
9g. R7C3 = 5 (hidden single in cage at R3C4), placed for R7 and C3, no 4,6 in R6C3
9h. R7C5 = 6, placed for R7, R6C5 = 4, R7C1 = 4, placed for R7, C1 and cage at R3C2, no 4 in R5C4, no 3,7 in R7C6, no 3 in R8C1
9i. R8C1 = 6, placed for C1 and cage at R3C2 -> R5C2 = 5, placed for R5, R4C2 = 3, R5C4 = 6, placed for R5 and cage at R3C4, no 7 in R4C4 + R6C3
9j. R4C4 = 4, R68C3 = [37], 7 placed for C3, no 8 in R7C2 + R9C3
9k. R7C2 = 9, placed for R7
9l. R9C3 = 9, placed for R9 and C3
9m. R7C6 = 2, placed for R7 and cage at R4C7, no 3 in R7C7
9n. R7C7 = 7, placed for R7, C7 and cage at R4C7, no 8 in R7C8
9o. R7C89 = [38], 8 placed for C9 and cage at R6C9
Clean-ups:
R4C4 = 4 -> no 4 in R3C3, no 5 in R3C5
R5C4 = 6 -> no 6 in R4C3, no 7 in R4C5
R7C2 = 9 -> no 8 in R6C2
R7C3 = 5 -> no 4,6 in R6C2
R7C5 = 6 -> no 5,6,7 in R6C6, no 5,7 in R8C5, no 5,6 in R8C6
R7C6 = 2 -> no 3 in R6C7 + R8C56, no 2,3 in R8C7
R7C7 = 7 -> no 8 in R6C6, no 6 in R6C7, no 6,7,8 in R6C8, no 6,8 in R8C7, no 6,7 in R8C8
R7C8 = 3 -> no 4 in R68C7, no 2,4 in R68C8, no 2,3,4 in R68C9
R7C9 = 8 -> no 9 in R68C8, no 7 in R68C9
R8C1 = 6 -> no 7 in R9C1
R8C3 = 7 -> no 6,7,8 in R9C2
R4C5 = {89} -> no 8,9 in R3C56 + R5C6
R6C2 = {79} -> no 8 in R5C1
[A few clean-ups have been deliberately, or accidentally, omitted in this and later steps.]

10a. R6C7 = 5, placed for C7, R8C6 = 4, R5C7 = 3, placed for R5 and C7, R9C6 = 6, placed for R9
10b. R5C6 = 7, placed for R5 and cage at R1C7, no 8 in R4C5
10c. R5C1 = 9, placed for R5, C1 and cage at R1C2
10d. R5C89 = [84], placed for cage at R1C9, 4 placed for C9
10e. R4C5 = 9, placed for C5
Clean-ups:
R5C1 = 9 -> no 8 in R4C1, no 9 in R6C2
R5C6 = 7 -> no 6,8 in R4C6
R5C8 = 8 -> no 7,9 in R4C89
R5C9 = 4 -> no 3,5 in R4C89 + R6C8, no 5 in R6C9
R6C7 = 5 -> no 4 in R6C6
R9C2 = {34} -> no 3 in R9C1

11a. R234C3 = [468], 6 placed for R3, 6,8 placed for cage at R1C4, no 5,7 in R2C4
11b. Cage at R1C4 can only be {6789} -> R12C4 = [79], 7 placed for R1
11c. R1238C5 = [3578], 3 placed for R1, 7 placed for R3, no 4,5 in R3C6
11d. R3C6 = 3, placed for R3, no 4 in R2C7
11e. R35C6 = [37] -> cage at R1C7 = {34567} -> R4C6 = 5, R12C7 = [46], 4 placed for R1 and C7
11f. R9C1 = 8, placed for R9 and C1
11g. R3C1 = 5, placed for R3, C1 and cage at R1C2
11h. R3C9 = 9, placed for R3 and C9
11i. R3C78 = [84]
11j. R9C7 = 2, placed for R9
Clean-ups:
R1C5 = 3 -> no 2,3,4 in R2C6
R2C7 = 6 -> no 5,6 in R1C68, no 5,7 in R2C6
R3C3 = 6 -> no 6,7 in R2C2
R3C5 = 7 -> no 6,8 in R2C6
R3C7 = 8 -> no 9 in R2C6
R3C8 = 4 -> no 3,5 in R2C9
R9C7 = 2 -> no 1,3 in R8C8, no 3 in R9C8

12a. R4C8 = 6, R12C9 = [57], placed for C9, no 8 in R1C8
12b. R1C268 = [689], no 7 in R2C1
12c. R24C1 = [37], no 4 in R2C2
12d. R9C289 = [473], no 6 in R8C9
12e. R468C9 = [261]

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