The New Sudoku Players' Forum

[rekres]

Greetings,

I live in NW Indiana. My local newspaper, The Post-Tribune, has been running Sudoku puzzles for the last month or so. They appear to be Universal Press Syndicate, but at the very bottom they include a blurb and URL for this website, even though they aren't Pappocom puzzles... ?

What prompted me to post here is because of a puzzle in Saturday's paper with a listed difficulty of 6 stars (on a scale of 1-5?). It doesn't appear to have a logical solution and I can't even get the program to verify it (too many or too few clues). To make matters worse the paper didn't print the answer in the Sunday edition, instead printing both Sunday puzzle and answer...

Here it is:

Code: Select all

6 _ 3 | _ _ 1 | _ 8 _
_ 8 4 | 3 _ _ | 2 _ _
5 2 _ | _ _ _ | _ _ _
------+-------+-------
_ 7 _ | _ _ _ | _ _ 4
_ _ _ | 6 5 7 | _ _ _
2 _ _ | _ _ _ | _ 1 _
------+-------+-------
_ _ _ | _ _ _ | _ 4 5
_ _ 8 | _ _ 3 | 1 7 _
_ 5 _ | 4 _ _ | 8 _ 3


Well, first thing I noticed was there was no 9 in the original, but that was easy to place by looking at the upper left block... only three possible numbers 1, 7, and 9. r1c2 can't be 1 or 7 so it has to be 9. After some fiddling around I've narrowed it down some and I've got the rest of the possibilities penciled in, but I don't see any way to narrow it down further without guessing.... *shrug*

Here's my current state on this puzzle...

Code: Select all

6 9 3 | 2 4 1 | 5 8 7
_ 8 4 | 3 _ 5 | 2 _ _
5 2 _ | _ _ _ | 4 3 _
------+-------+-------
_ 7 _ | _ _ _ | _ 5 4
_ _ _ | 6 5 7 | _ _ _
2 _ 5 | _ _ 4 | _ 1 _
------+-------+-------
_ _ _ | _ _ _ | _ 4 5
_ _ 8 | 5 _ 3 | 1 7 _
_ 5 _ | 4 _ _ | 8 _ 3


If anyone can give me a hint, a solution, or even tell my if my current work is correct? Thank you in advance...

-- Chris J. Whitcomb

P.S. I recall some Sudoku puzzles in an issue of Games magazine from a couple of years ago. They also included some rectangular/non-square puzzles. I was wondering if anyone knows a website/source for more of these non-square puzzles?

[Shazbot]

There's a hidden single in box 6. After that I couldn't get any further.

[r.e.s.]

Here are two routes to the solution that rubylips' solver found -- one using chains and one using Sherlocking ...

Using chains:

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START
1. The cell (6,7) is the only candidate for the value 7 in Row 6.
2. The value 1 in Box [2,1] must lie in Row 5.
- The moves (4,1):=1 and (4,3):=1 have been eliminated.
Consider the chain (7,2)~6~(6,2)-6-(4,3)-6-(4,7)-6-(7,7).
When the cell (7,2) contains the value 6, so does the cell (7,7) - a contradiction.
Therefore, the cell (7,2) cannot contain the value 6.
- The move (7,2):=6 has been eliminated.
Consider the chain (7,1)~7~(2,1)-7-(2,5)~7~(3,4)-7-(7,4).
When the cell (7,1) contains the value 7, so does the cell (7,4) - a contradiction.
Therefore, the cell (7,1) cannot contain the value 7.
- The move (7,1):=7 has been eliminated.
Consider the chain (4,5)-3-(6,5)-3-(6,2)-6-(4,3)-6-(4,7).
When the cell (4,7) contains the value 3, some other value must occupy the cell (4,5), which means that the value 6 must occupy the cell (4,7) - a contradiction.
Therefore, the cell (4,7) cannot contain the value 3.
- The move (4,7):=3 has been eliminated.
The cell (5,7) is the only candidate for the value 3 in Column 7.
3. The values 1, 2, 3 and 8 occupy the cells (4,1), (4,4), (4,5) and (4,6) in some order.
- The moves (4,1):=9, (4,4):=9, (4,5):=9 and (4,6):=9 have been eliminated.
The value 9 in Row 6 must lie in Box [2,2].
- The move (6,9):=9 has been eliminated.
Consider the chain (5,1)-8-(4,1)-3-(6,2)-6-(8,2)-4-(8,1).
When the cell (5,1) contains the value 4, so does the cell (8,1) - a contradiction.
Therefore, the cell (5,1) cannot contain the value 4.
- The move (5,1):=4 has been eliminated.
The cell (5,2) is the only candidate for the value 4 in Row 5.
[after this point, only simple moves are needed]

Using Sherlocking ("permutate sectors"):

Code: Select all

START
1. The cell (6,7) is the only candidate for the value 7 in Row 6.
2. The value 1 in Box [2,1] must lie in Row 5.
- The moves (4,1):=1 and (4,3):=1 have been eliminated.
The 14 permutations of Row 4 and 7 permutations of Row 5 combine legally in 32 different ways.
Row 4:
3-7-6-1-2-8-9-5-4
3-7-9-1-2-8-6-5-4
8-7-6-1-2-9-3-5-4
9-7-6-1-2-8-3-5-4
3-7-6-1-8-2-9-5-4
3-7-9-1-8-2-6-5-4
8-7-6-1-3-2-9-5-4
8-7-9-1-3-2-6-5-4
8-7-6-1-9-2-3-5-4
9-7-6-1-8-2-3-5-4
3-7-6-8-1-2-9-5-4
3-7-9-8-1-2-6-5-4
8-7-6-9-1-2-3-5-4
9-7-6-8-1-2-3-5-4
Row 5:
1-4-9-6-5-7-3-2-8
4-1-9-6-5-7-3-2-8
3-4-1-6-5-7-9-2-8
4-3-1-6-5-7-9-2-8
8-4-1-6-5-7-3-2-9
9-4-1-6-5-7-3-2-8
8-4-1-6-5-7-3-9-2
In each combination, the value 9 in Box [2,3] appears in Row 4 or Row 5.
- The move (6,9):=9 has been eliminated.
The value 9 in Box [2,2] must lie in Row 6.
- The moves (4,4):=9, (4,5):=9 and (4,6):=9 have been eliminated.
The 11 permutations of Row 4 and 3 permutations of Row 6 combine legally in 5 different ways.
Row 4:
3-7-6-1-2-8-9-5-4
3-7-9-1-2-8-6-5-4
9-7-6-1-2-8-3-5-4
3-7-6-1-8-2-9-5-4
3-7-9-1-8-2-6-5-4
8-7-6-1-3-2-9-5-4
8-7-9-1-3-2-6-5-4
9-7-6-1-8-2-3-5-4
3-7-6-8-1-2-9-5-4
3-7-9-8-1-2-6-5-4
9-7-6-8-1-2-3-5-4
Row 6:
2-3-5-8-9-4-7-1-6
2-3-5-9-8-4-7-1-6
2-6-5-9-3-4-7-1-8
In each combination, the value 3 in Box [2,1] appears in Row 4 or Row 6.
No combination has the value 3 as a candidate for the cell (4,7).
No combination has the value 9 as a candidate for the cell (4,1).
- The moves (5,1):=3, (5,2):=3, (4,7):=3 and (4,1):=9 have been eliminated.
The cell (5,7) is the only candidate for the value 3 in Row 5.
3. The 9 permutations of Column 1 and 3 permutations of Column 2 combine legally in 4 different ways.
Column 1:
6-1-5-3-8-2-7-4-9
6-1-5-3-8-2-9-4-7
6-1-5-8-4-2-3-9-7
6-1-5-8-9-2-3-4-7
6-7-5-8-1-2-3-4-9
6-7-5-3-8-2-1-4-9
6-7-5-3-8-2-9-4-1
6-7-5-8-4-2-3-9-1
6-7-5-8-9-2-3-4-1
Column 2:
9-8-2-7-1-3-6-4-5
9-8-2-7-1-6-3-4-5
9-8-2-7-4-3-1-6-5
No combination has the value 1 as a candidate for the cell (7,1).
No combination has the value 3 as a candidate for the cell (4,1).
Each combination has the value 3 as a candidate for the cell (6,2).
No combination has the value 3 as a candidate for the cell (7,2).
In each combination, the value 6 in Box [1,3] appears in Column 1 or Column 2.
No combination has the value 7 as a candidate for the cell (7,1).
Each combination has the value 8 as a candidate for the cell (4,1).
No combination has the value 8 as a candidate for the cell (5,1).
No combination has the value 9 as a candidate for the cell (7,1).
- The moves (7,1):=1, (4,1):=3, (6,2):=6, (7,2):=3, (7,3):=6, (9,3):=6, (7,1):=7, (5,1):=8 and (7,1):=9 have been eliminated.
The value 8 is the only candidate for the cell (4,1).
[after this point, only simple moves are needed]

[r.e.s.]

P.S. I recall some Sudoku puzzles in an issue of Games magazine from a couple of years ago. They also included some rectangular/non-square puzzles. I was wondering if anyone knows a website/source for more of these non-square puzzles?

You may want to try Simon Tatham's (free) SOLO program
or the online source at http://www.menneske.no/sudoku/eng/index.html (check out the varieties in the left panel).
And if you want irregular-shaped "jigsaw" boxes, take a look at
http://www.latinsquares.com/LSQ.html
http://www.bumblebeagle.org/dusumoh/index.html