## A big problem for a small mind ;)

Advanced methods and approaches for solving Sudoku puzzles

### A big problem for a small mind ;)

Hi I`ve started playing sudoku about 2 weeks ago so I`m not a pro.. anyway. Could anyone help me with this :

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

Posts: 3
Joined: 05 September 2005

Well, the Sudoku Susser software can't do it without using its two most complicated tactics: 'Trebor's Tables' or 'Bowman Bingo'. What this essentially means is that it's pretty much unsolveable by mere humans without using trial and error (as the program puts it: "you'd run through several pencils working them out by hand!") so it's not your fault you can't go any further. Where's it a puzzle from?
PaulIQ164

Posts: 533
Joined: 16 July 2005

Not a valid puzzle. Does it include some player input already?
RickM

Posts: 22
Joined: 18 August 2005

It`s from add to polish magazine called "Polityka" (or should I say in english "Politics") Well.. the oryginal Sudoku looks something like this :

+-----+------+-----+
| . . . | 1 . . | . 3 . |
| 2 . 3 | . 6 . | 7 . . |
| . 8 . | . . . | . 2 . |
+-----+------+-----+
| . . . | . 7 . | . . 3 |
| . 2 . | 6 . 8 | . 4 . |
| 1 . . | . 5 . | . . . |
+-----+-----+------+
| . 4 . | . . . | . 8 . |
| . . 7 | . 3 . | 1 . 2 |
| . 3 . | . . 2 | . . . |
+-----+------+-----+
carosh

Posts: 3
Joined: 05 September 2005

RickM wrote:Not a valid puzzle. Does it include some player input already?

The puzzle is perfectly valid. It has a unique solution. Remember, Pappocom software will reject a vast number of difficult but perfectly valid puzzles as "invalid" or "arguably unfair."

On the other hand, not the best puzzle for a beginner who wants to avoid using T&E.
tso

Posts: 798
Joined: 22 June 2005

carosh

Agreed, this is not the best puzzle for a beginner.

You would need a forcing chain to solve it.
Jeff

Posts: 708
Joined: 01 August 2005

Jeff wrote:carosh

Agreed, this is not the best puzzle for a beginner.

You would need a forcing chain to solve it.

Yeah.. I think you`re right.. oh.. if you can just show me what "forcing chain" really is (or at least some link or something)
carosh

Posts: 3
Joined: 05 September 2005

Quite a few chains can be identified. The first one is a simple one which will enable a 7 to be fixed in two places, but does not lead to a total solution. The second one can lead directly to the solution, but it is longer.

r1c1=4 => r1c6=7
r1c1<>4 => r4c1=4 => r6c3<>4 => r6c6=4 => r3c6=3 => r1c6=7
Therefore r1c6=7

r1c9=8 => r7c9=5
r1c9=5 => r1c7=8 => r4c7<>8 => r4c3=8 => r4c2=6 => r8c2=5 => r8c8=9 => r7c9=5
Therefore r7c9=5

I found these chains by means of a bilocation/bivalue plot and a set of combination chain rules.
Jeff

Posts: 708
Joined: 01 August 2005

### This puzzle was fun!

I liked this puzzle a lot - it was difficult enough to be of interest, but not so difficult to be boring. I liked the start, when you could just fill in all the 1s, and the finish, when you had to think a bit to find some useful chain.

@Jeff: your chain is much shorter than mine, congratulations! - I established a contradiction by combining the bilocation/bivalue graphs, but the path had about 10 nodes; still, it was quite easy to follow this path (I just assumed one number in one of the last three blocks, then followed the path in c9 up to block 1 (which collapsed), then noticed that all 5s collapsed and then established a contradiction with two 8 in the same column)
[BTW, thanks a lot for the puzzle you sent me - I will be offline for 2 weeks, but I'll comment on the puzzle afterwards]

Probably this works also without graphical methods (I am sure it does), but it is sooo much fun to draw these graphs and follow the links...
Big Blue

Posts: 28
Joined: 01 August 2005

### solver for this problem

try solving thie problem by the solver available at this link..it solves..

http://pradipjain.8m.com/Su_Doku_Solver.html
pradipjain

Posts: 4
Joined: 20 September 2005

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