## how to continue when all well-known solving techniques fail

Advanced methods and approaches for solving Sudoku puzzles

### how to continue when all well-known solving techniques fail

Hello everybody,

I wanted to know if it was possible to continue when all well-known solving techniques are exhausted?

For example, a lot of "very hard" sudokus from http://www.printsudoku.com stick me, and even stick logical computer solvers like http://www.sudokusolver.co.uk/...

Let's look at Very hard Sudoku #67 from http://www.printsudoku.com...

Code: Select all
`Solution so far :27- --- -68--4 2-- 9--6-- 8-5 ---9-- -5- 63---- -2- ----18 -3- --4--- 5-2 --9--3 --7 1--89- --- -76Pencilmarks so far :2.. 7.. 159 134 149 134 45. 6.. 8..15. 8.. 4.. 2.. 7.. 6.. 9.. 15. 3..6.. 3.. 19. 8.. 149 5.. 247 12. 27.9.. 24. 27. 147 5.. 8.. 6.. 3.. 17.3.. 45. 6.. 147 2.. 14. 8.. 9.. 15757. 1.. 8.. 6.. 3.. 9.. 257 25. 4..17. 6.. 17. 5.. 8.. 2.. 3.. 4.. 9..4.. 25. 3.. 9.. 6.. 7.. 1.. 8.. 25.8.. 9.. 25. 134 14. 134 25. 7.. 6..`

The logical solver only uses just another technique like me and it removes number 5 from r6c7 with what you call X-Wing technique.

And then it makes a guess!!!

Would have it been possible to continue without making a guess?

Thank you for your help!

P.S. : Sorry if my English isn't really correct, I am French...
Nico

Posts: 7
Joined: 01 October 2005

Yup, you kneed a Forcing Chain from r2c1 to fix r3c9 as '7'.

[Having said that, that chain I found when you fix r2c1 as '1' is Humungous, I wonder if anyone can demonstrate a shorter way?]
Last edited by Karyobin on Sat Oct 01, 2005 11:11 am, edited 1 time in total.
Karyobin

Posts: 396
Joined: 18 June 2005

### Re: how to continue when all well-known solving techniques f

Nico wrote:Would have it been possible to continue without making a guess?

Bonjour Nico. You can solve it with a fairly simple forcing chain:

Regardless of the candidate assigned in cell r6c7, the cell r5c2 must be 4.
angusj

Posts: 306
Joined: 12 June 2005

That'll do nicely.
Karyobin

Posts: 396
Joined: 18 June 2005

Thanks Karyobin and angusj, i didn't know the "Forcing Chain" technique, and i've just learnt about it at http://www.simes.clara.co.uk/programs/sudokutechnique7.htm.

By the way, angusj, did you use a specific software that draw your grid and helped you solve it?

Moreover, i'm a bit confused that the Sudoku Solver at http://www.sudokusolver.co.uk did not find this chain, because i thought this method was implemented in it, but i must mix up with what it's called Method D (http://www.sudokusolver.co.uk/solvemethods.html#methodD).

Moreoever, the "Forcing Chain" technique seems like to me a little like a "Guess and Check" technique (in part), is it?

Nicolas.
Nico

Posts: 7
Joined: 01 October 2005

my bad ,I think we can't have r6c8=5 and r9c3=2 because the 7's in box 4
but r6c8=5-> r9c3=2
Last edited by bennys on Sat Oct 01, 2005 12:25 pm, edited 1 time in total.
bennys

Posts: 156
Joined: 28 September 2005

Nico wrote:...the "Forcing Chain" technique seems like to me a little like a "Guess and Check" technique (in part), is it?

More of a "If...then...so..." really. You could describe any method as a "Guess and check", it's just that the more simple techniques would show up a contradiction so quickly that you wouldn't even think of doing anything other than the right thing.
Karyobin

Posts: 396
Joined: 18 June 2005

Karyobin wrote:
Nico wrote:...the "Forcing Chain" technique seems like to me a little like a "Guess and Check" technique (in part), is it?

More of a "If...then...so..." really. You could describe any method as a "Guess and check", it's just that the more simple techniques would show up a contradiction so quickly that you wouldn't even think of doing anything other than the right thing.

Oh yes, i see what you mean. You're right.
Nico

Posts: 7
Joined: 01 October 2005

Nico,
The online solver at http://act365.com/sudoku/ solves this puzzle using two short forcing chains (of lengths 4 and 5).
r.e.s.

Posts: 337
Joined: 31 August 2005

r.e.s. wrote:Nico,
The online solver at http://act365.com/sudoku/ solves this puzzle using two short forcing chains (of lengths 4 and 5).

Hello r.e.s.,

Thanks for this interesting solver, i didn't know about it.

Nico'.
Nico

Posts: 7
Joined: 01 October 2005

Nico wrote:
r.e.s. wrote:Nico,
The online solver at http://act365.com/sudoku/ solves this puzzle using two short forcing chains (of lengths 4 and 5).

Hello r.e.s.,

Thanks for this interesting solver, i didn't know about it.

Nico'.

This solver is the work of "rubylips", and I've found it is often able to solve puzzles for which the other well-known solvers resort to "recursion" or blatant guessing (or in the case of the Susser, to "tabling"). Definitely it has the best implementation of forcing chains of any that I know. (Not to mention the ability to construct sudokus of different sizes, and to let you modify them yourself.)
r.e.s.

Posts: 337
Joined: 31 August 2005

Nico wrote:By the way, angusj, did you use a specific software that draw your grid and helped you solve it?

Simple Sudoku - http://angusj.com/sudoku/
(It allows you to can create *.png images of the puzzle.)
angusj

Posts: 306
Joined: 12 June 2005

angusj wrote:Simple Sudoku - http://angusj.com/sudoku/
(It allows you to can create *.png images of the puzzle.)

Ok, thanks.
Nico

Posts: 7
Joined: 01 October 2005

No guessing needed on this puzzle. Just look for the binary chains where each cell contains only two values and each value in one cell forces one value in a connecting cell. There is such a chain in columns 7 and 8 ( R1c7,r2c8,r3c8,r6c8,r6c7,r1c7). Every cell in column 7 is part of the chain except r3c7. So it must be part of the chain too and we can reduce it to two candidates. Now check the two possibilities from the binary chain and find it cannot be a 7 and the rest of the puzzle is easy.

I do all this with pencil and paper by circling the cells in the chain. If necessary I rewrite the values so the first value matches the first value in the connecting cells. The joy of binary chains is that they are easy to spot, go both ways and dont have a starting point or starting value. In other words you don't have to guess. And you don't need a computer.
dgmp

Posts: 4
Joined: 01 October 2005

dgmp wrote:No guessing needed on this puzzle. Just look for the binary chains where each cell contains only two values and each value in one cell forces one value in a connecting cell.

In fact, all 3 chains proposed by Karyobin, Angus and yourself are xy-chains (or binary chains as described). They are so easy to spot indeed with no filtering required.

r.e.s. wrote:The online solver at http://act365.com/sudoku/ solves this puzzle using two short forcing chains (of lengths 4 and 5).

Could you list the 2 chains for us? Thank you.
Jeff

Posts: 708
Joined: 01 August 2005

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