The New Sudoku Players' Forum

[ChrisT]

I got stuck on the following grid:

(348)(346)(469)(7)(2)(1)(5)(389)(39)
(238)(235)(59)(6)(4)(39)(7)(12389)(1239)
(23)(1)(7)(39*)(5)(8)(26)(2369)(4)
(9)(8)(2456)(24)(167)(257)(3)(1246)(1256)
(7)(23456)(2456)(8)(136)(235)(1246)(12469)(12569)
(234)(23456)(1)(2349)(36)(2359)(246)(7)(8)
(6)(247)(24)(1)(8)(237)(9)(5)(237)
(5)(9)(8)(23)(37)(6)(124)(1234)(1237)
(1)(27)(3)(5)(9)(4)(8)(26)(267)

Code: Select all

---7215--
---64-7--
-17-58--4
98----3--
7--8-----
--1----78
6--18-95-
598--6---
1-35948--


I solved it in the end by trial and error, placing a 3 in the box marked with an asterisk - a nine there eventually produced a contradiction. Can anyone see a way of solving this puzzle that avoids resorting to trial and error? It’s possible that I missed something obvious, but when I put it into a friend’s computer program, it got stuck at the same point as I did.

Would appreciate advice on this.

PS As you can see, I’m new to this forum. What is the preferred way of writing out grids for others to see? I’ve seen various different methods as I browsed around.

NB Edited to include the nicer way of drawing it, as suggested!

[Karyobin]

4 - - - 8 - - 6 9
- 6 3 - - - - - -
5 - 1 - 7 - - - -
7 - - 9 6 - - - 8
- - - - - 7 1 - 3
2 - - - 5 - 6 - -
1 - - - - - - - -
- 4 - - - 5 9 - -
- - - - - 8 4 3 -

Isn't that much nicer? You could also select the entire thing and click on the 'Code' fundtion which will produce this:

Code: Select all

4 - - - 8 - - 6 9
- 6 3 - - - - - -
5 - 1 - 7 - - - -
7 - - 9 6 - - - 8
- - - - - 7 1 - 3
2 - - - 5 - 6 - -
1 - - - - - - - -
- 4 - - - 5 9 - -
- - - - - 8 4 3 -

You don't need to post the candidates, most solver programs will supply them for you.

From your puzzle, you need find some locked candidates in Box 1, allowing you to exclude in Box 3. And again in boxes 6 and 5. Then angusj's grinds to a halt, so I'd suggest you've got a pretty hard puzzle there. The Susser solved it, but took a lot of steps to do so.

[Cec]

As you can see, I’m new to this forum. What is the preferred way of writing out grids for others to see? I’ve seen various different methods as I browsed around.

NB Edited to include the nicer way of drawing it, as suggested!

ChrisT's query as to the preferred way of submitting grids for others to see could presumably attract varied opinions.

I personally find it easier to read and transfer a puzzle to a grid when a space is left between each of the nine boxes something like this:

--- 721 5--
--- 64- 7--
-17 -58 --4

98- --- 3--
7-- 8-- ---
--1 --- -78

6-- 18- 95-
598 --6 ---
1-3 594 8--

Alternatively, I have seen puzzles submitted where the nine boxes are distinguished (separated) by lines which likewise makes it easier to read. I'm still learning the Code button function which hopefully will enable me to do this.

Bonsai Cec

[jhenzy]

Chris, I think this puzzle must have more than one solution. Where did you get it?

[ChrisT]

I don't think that it's a Pappocom puzzle, it's from the Cherwell, one of the Oxford student newspapers. I have no idea where they get their puzzles from, it could be that they do not verify that they have a unique solution.

I thought that in this particular case there was a unique solution, which I found by trial and error, but I could have made a mistake. In any case, trial and error is not a very satisfying method to use!

Chris

[Sue De Coq]

Chris,

The puzzle has a unique solution, though it's necessary to invoke multiple forced chains in order just to make the first move. (However, once the first move has been made - a 3 in r2c2 - the rest of the puzzle follows straightforwardly).

Here's my solver log for the first move. (It might well be possible to find a simpler solution):

The value 6 in Box [1,3] must lie in Row 3.
- The moves (1,8):=6 and (1,9):=6 have been eliminated.
The value 9 in Box [2,2] must lie in Row 6.
- The move (5,6):=9 has been eliminated.
Consider the chains (4,3)~4~(4,4)~2~(8,4) and (4,3)~4~(7,3)~2~(7,6).
Whichever of the 2 candidates in Box [3,2] contains the value 2, the cell (4,3) does not contain the value 4.
- The move (4,3):=4 has been eliminated.
Consider the chains (1,3)~9~(1,9)~3~(2,9) and (2,3)~9~(2,6)~3~(2,9).
Whichever of the 2 candidates in Column 3 contains the value 9, the cell (2,9) does not contain the value 3.
- The move (2,9):=3 has been eliminated.
Consider the chains (2,9)~9~(1,9)~3~(7,9) and (2,9)~9~(2,6)~3~(7,6).
Whichever of the 2 candidates in Row 7 contains the value 3, the cell (2,9) does not contain the value 9.
- The move (2,9):=9 has been eliminated.
Consider the chains (2,8)~9~(1,9)~3~(7,9) and (2,8)~9~(2,6)~3~(7,6).
Whichever of the 2 candidates in Row 7 contains the value 3, the cell (2,8) does not contain the value 9.
- The move (2,8):=9 has been eliminated.
Consider the chains (2,3)-9-(2,6)-3-(3,4) and (2,3)~2~(3,1)~3~(3,4).
When the cell (2,3) contains the value 2, one chain states that the cell (3,4) contains the value 3 while the other says it doesn't - a contradiction.
Therefore, the cell (2,3) cannot contain the value 2.
- The move (2,3):=2 has been eliminated.
Consider the chains (1,3)~9~(1,9)~3~(2,8) and (2,3)-9-(2,6)~3~(2,8).
Whichever of the 2 candidates in Column 3 contains the value 9, the cell (2,8) does not contain the value 3.
- The move (2,8):=3 has been eliminated.
Consider the chains (2,2)~2~(3,1)~3~(3,4)-3-(2,6) and (2,2)-5-(2,3)-9-(2,6).
When the cell (2,2) contains the value 2, one chain states that the cell (2,6) contains the value 3 while the other says it doesn't - a contradiction.
Therefore, the cell (2,2) cannot contain the value 2.
- The move (2,2):=2 has been eliminated.
The value 2 in Column 1 must lie in Box [1,1].
- The move (6,1):=2 has been eliminated.
The values 1, 2 and 8 occupy the cells (2,1), (2,8) and (2,9) in some order.
- The move (2,1):=3 has been eliminated.
Consider the chains (2,2)~5~(6,2)-5-(6,6) and (2,2)-3-(2,6)-9-(6,6).
When the cell (2,2) contains the value 5, one chain states that the cell (6,6) contains the value 5 while the other says it doesn't - a contradiction.
Therefore, the cell (2,2) cannot contain the value 5.
- The move (2,2):=5 has been eliminated.
The value 3 is the only candidate for the cell (2,2).

PS I haven't bothered to changed the cell labels from the format e.g. (1,2) [standard mathematical matrix notation] to the forum standard of r1c2.

[ChrisT]

Well, I gave myself a headache but had a lot of fun following that logic through! I feel a lot better having gone through that - makes me feel a little less ashamed for resorting to trial and error. Something tells me that I could have stared at the puzzle for years and not seen all (or any!) of those chains...

I assume that if there was a simpler way to progress (eg colouring, swordfish...) then your program would have used that preferrentially?

...it's necessary to invoke multiple forced chains in order just to make the first move.

It wasn't in fact the first move - the grid that I gave in the posting was the position I'd reached after filling a few numbers in. They were kind enough to give a couple of easy ones to start it off!

PS I haven't bothered to changed the cell labels from the format e.g. (1,2) [standard mathematical matrix notation] to the forum standard of r1c2.

Personally, I think the way you've labelled it is much easier to read!

Anyway, Sue, thanks for the help on that, it's good to have it cleared up.

Chris

[Sue De Coq]

I assume that if there was a simpler way to progress (eg colouring, swordfish...) then your program would have used that preferrentially?

My solver regards Swordfish, X-Wings and Turbot Fish as special cases of a more general technique called Single-Valued Chains, which the solver invokes before it looks for Many-Valued Chains. Therefore, it's safe to infer from the absence of Single-Valued Chains in the solver log that no Swordfish etc. exists.

The solver doesn't implement colouring per se because I prefer to produce a log that explicitly explains each deduction and I think I'm right when I say that colouring can't provide such an explanation. Furthermore, I believe that Colouring is algorithmically equivalent to Forced Chains, so it's not really simpler and it doesn't provide any further information.

When I say that a simpler solution might exist, I mean that the solver lists chains as it finds them, not as they are found to be strictly necessary in order to make progress. Therefore, the set of chains listed isn't necessarily minimal and you might be able to remove a few.