SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Thu Mar 28, 2024 5:05 pm

All times are UTC




Post new topic Reply to topic  [ 2 posts ] 
Author Message
 Post subject: Ed's Extra Groups 4
PostPosted: Wed Dec 17, 2014 4:12 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
Ed's Extra Groups X OL 4


I liked the extra group Ed used recently so I've used 4 of them - hence they overlap at r28c5 and r5c28, also Old Lace in the middle.

All cages are triplets and the X is in two cages.
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.

Again the difficulty should be about paper solvable - interested in your views.


Image

Solution:

756142389
423698715
891537624
317925846
942386157
685714932
174263598
538479261
269851473


Top
 Profile  
Reply with quote  
 Post subject: Re: Ed's Extra Groups 4
PostPosted: Wed Dec 24, 2014 7:51 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks for this interesting puzzle. Almost Paper Solvable but by no means trivial.

Almost Paper Solvable:
Well probably Paper Solvable for those with excellent visualisation of what goes where and the ability to see chains in their head. I've written my walkthrough as Almost Paper Solvable. I started by putting in the candidates for first, second and final cells of cages, then solved from there. No further numbers were inserted in the grid until they were placements, so after step 3 everything is written as Paper Solvable including the chains in steps 10 and 11.

Here is my walkthrough for Ed's Extra Groups 4:
Cages are ordered, increasing from left to right and top to bottom.
Cages are digital, last digit of the sum is in one of the cells.
The first two cells are consecutive, the last is non-consecutive.

Possible permutations; from the digital condition two of the cells must total 10.
1,9: [129]
2,8: [128], [238]
3,7: [237], [347]
4,6: [346] (cannot be [456] because the three digits would be consecutive)

There are four coloured groups which overlap at R28C5 and R5C28, these groups are green, blue, pink and yellow in the posted puzzle diagram (others may see some of the colours differently), also an Old Lace.

Old Lace property. R37C5 must exactly equal R5C46 and R46C5 must exactly equal R5C37.

Prelims

a). First cell of each cage must contain 1, 2 or 3 -> R1C4, R2C8, R4C1, R4C5, R5C3, R6C5 and R7C4 all {123}
b). Second cell of each cage must contain 2, 3 or 4 -> R1C6, R3C8, R5C2, R5C4 (shared by two cages), R7C4 and R7C6 all {234}
c). Final cell of each cage must contain 6, 7, 8 or 9 -> R2C5, R4C7, R5C5, R6C1, R6C4, R8C3 and R8C5 all {6789}

2. R7C4 is both first cell of cage at R7C4 and second cell of the cage at R6C5 -> R7C4 = {23}, R6C5 = {12}, R7C6 = {34}, R8C3 = {789}, R8C5 = {678}

3. Old Lace Property R46C5 must exactly equal R5C37, R4C5 = R5C3 because they are both the first cells of cages with shared second cell R5C4 -> R6C5 = R5C7 = {12}
3a. Cage at R5C2 cannot be [128/129] (because R5C23 = [12] clashes with R5C7), -> no 1 in R5C2, no 2 in R5C3
3b. Naked triple {234} in R5C234, locked for R5 -> R5C7 = 1 -> R6C5 = 1 (Old Lace), R7C4 = 2, placed for pink group, R7C6 = 3, placed for yellow group, R8C3 = {89}, R8C5 = {78}

4. Naked pair {34} in R5C24, locked for R5 -> R5C3 = 2, R5C4 = 3, R4C5 = 2, R5C2 = 4, placed for green and pink groups, R4C1 = 3, placed for green group, R1C4 = 1, placed for green group, R1C6 = 2, placed for blue group, R2C5 = {89}, R6C1 = {67}
4a. R2C8 = {13} -> R3C8 = {24}

5. R4C5 = 2, R5C3 = 2, R5C4 = 3 -> R5C5 = {78}, R6C4 = {78}
5a. Naked pair {78} in R58C5, locked for C5 -> R2C5 = 9, placed for green and blue groups

6. R3C5 = 3 (hidden single in Old Lace)

7. R4C2 = 1 (hidden single in N4)

8. R6C8 = 3 (hidden single in R6) -> R2C8 = 1, placed for D/ and blue group, R3C8 = 2, R4C7 = 8 (because 9 placed in R2C5 for blue group), placed for blue group

9. Hidden singles, some may be dependent on third cell of a cage occupying a cell
R3C3 = 1 (hidden single in N1), placed for D\
R7C1 = 1 (hidden single in pink group)
R9C6 = 1 (hidden single in yellow group)
R8C9 = 1 (hidden single in N9)
R1C7 = 3 (hidden single in blue group)
R2C2 = 2 (hidden single in green group), placed for D\
R2C3 = 3 (hidden single in N1)
R8C8 = 3 (hidden single in pink group), placed for D/
2 in yellow group must be in R6 -> R8C7 = 2 (hidden single in N9) -> R6C9 = 2 (hidden single in yellow group)
R9C9 = 3 (hidden single in N9), placed for D\
R1C9 = 2 (hidden single in R9), placed for D/
R7C3 = 4 (hidden single in C3), placed for D/
4 in Old Lace must be on D\ -> R2C1 = 4 (hidden single in N1)
4 in Old Lace must be on D\ -> 4 in N9 must be in R9 -> R1C5 = 4 (hidden single in C5)
R3C9 = 4 (hidden single in R3), placed for blue group

10. Naked pair {78} in R58C5, CPE no 8 in R8C8 using D\, 8 on D\ only in R1C1 + R5C1, CPE no 8 in R5C1 -> R5C5 = 8 (hidden single in R5), placed for both diagonals, R6C4 = 7, placed for D/ -> R6C1 = 6, placed for pink group, R8C5 = 7, placed for pink and yellow groups
10a. R7C9 = 8 (hidden single in yellow group)
10b. R1C8 = 8 (hidden single in N3)

11. R79C5 = {56} (hidden pair in C5), Old Lace Property R5C6 = R7C5 -> R5C6 = {56}, 9 in N3 only on D/ -> R4C4 + R6C6 = {49} (hidden pair in N5) -> R45C6 = {56}, R14C3 = [67] (hidden pair in C3), placed for green group -> R3C14 = {58} (hidden pair in green group) -> R3C267 = {679} (hidden triple in R3) -> R3C6 = 7, placed for blue group, R3C2 = 9, R3C7 = 6, placed for D/, R4C5 = 5, R5C6 = 6 -> R7C5 = 6 (Old Lace Property), R9C5 = 5

12. More hidden singles
R1C9 = 9 (hidden single on D/)
R3C1 = 8 (hidden single in N1) -> R3C4 = 5 (hidden single in R3)
R2C46 = [68] (hidden pair in N2)
R5C8 = 5 (hidden single in blue group), placed for yellow group
R4C9 = 6 (hidden single in blue group)
R8C8 = 6 (hidden single on D\)
R6C3 = 5 (hidden single in pink group)
R5C9 = 7 (hidden single in R5)
R2C9 = 5 (hidden single in C9)
R2C7 = 7 (hidden single in N3)
R7C7 = 5 (hidden single in C7), placed for D\
R1C12 = [75] (hidden pair in N1)

13. R9C34 = {89} (hidden pair in pink group), locked for R9 -> R6C7 = 9 (hidden single in yellow group), R9C7 = 4 (hidden single in yellow group)
13a. R4C4 = 9 (hidden single on D\), R9C34 = [98]

and the rest is hidden singles, without using the diagonals, coloured groups and Old Lace.


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 7 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