I've been trying this for hours, and I cannot seem to go any further!! All my moves are correct so far. Any help would be much appreciated:

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I've been trying this for hours, and I cannot seem to go any further!! All my moves are correct so far. Any help would be much appreciated:

- Spazactaz
**Posts:**6**Joined:**29 September 2005

There's a quite involved tactic you can use that will fix r9c7 (9th row down; 7th column across). It's all about the 4 cells at r3c7, r3c8, r9c7, r9c8. If they were all 4s and 5s, then, once you've finished the puzzle, you'd be able to swap round the 4s and 5s in those four cells and you'd get another valid solution (Think about it). So one of those cells has to be something else. The only one that can be is r9c7, which can be an 8. So it has to be that.

I'm sure there's probably something more abvious, though.

Edit: Look how early it is! And I'm all up and posting!

I'm sure there's probably something more abvious, though.

Edit: Look how early it is! And I'm all up and posting!

- PaulIQ164
**Posts:**533**Joined:**16 July 2005

That's very clever - I'd have struggled long and hard with it! Is there a name for this technique (I'm still grasping hidden and naked singles and pairs)?

Is this the only option for a next step, or another that might be easier to pick up but still assist towards a solution?

Spazactaz, did the puzzle have a difficulty rating?

Is this the only option for a next step, or another that might be easier to pick up but still assist towards a solution?

Spazactaz, did the puzzle have a difficulty rating?

- Shazbot
**Posts:**220**Joined:**24 September 2005

There's also an elimination to be made from colouring 7s

S

- Code: Select all
`Colouring 7: double exclusion found, eliminating 7 from r6c5, (r1c5 => r1c2 => r4c2 => r6c1)`

S

SadMan Software

http://www.sadmansoftware.com/sudoku/

http://www.sadmansoftware.com/sudoku/

- simes
**Posts:**324**Joined:**11 March 2005**Location:**UK

I'm not happy about using that technique! Suppose the puzzle composer was careless and posted a puzzle that doesn't have a unique solution.

You're supposed to be able to solve sudoku using logic, but this technique makes an extra assumption, that there is a unique solution. Logic alone does not lead to that conclusion.

You're supposed to be able to solve sudoku using logic, but this technique makes an extra assumption, that there is a unique solution. Logic alone does not lead to that conclusion.

- ab
**Posts:**451**Joined:**06 September 2005

This has been discussed before but not by me, so sadly I can't point you to the relevant threads, Paul probably can. If I remember correctly, the argument for the technique is the stonger, on the reasoning that sudoku have only one solution by definition, and can be solved logically. As a result of this fact, any puzzle which has more than one solution must involve a placement at some point which Sadman's software excitedly describes as "A Guess!" So: were you to stumble upon an arrangment such as

you would have arrived at a point where a guess was the only way forward, so the puzzle does not have one solution. In the reverse, therefore:

the fourth cell must be a '3', as if it were not you would have arrived back at the earlier position, and logic could take you no further. I know it seems a bit like saying 2+2=4 because 4=2+2, but it isn't, as the Uniqueness Rule is essential and inherent to the puzzle you are solving.

I think.

Paul?

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`{1,2}{1,2}`

{1,2}{1,2}

you would have arrived at a point where a guess was the only way forward, so the puzzle does not have one solution. In the reverse, therefore:

- Code: Select all
`{1,2}{1,2}`

{1,2}{1,2,3}

the fourth cell must be a '3', as if it were not you would have arrived back at the earlier position, and logic could take you no further. I know it seems a bit like saying 2+2=4 because 4=2+2, but it isn't, as the Uniqueness Rule is essential and inherent to the puzzle you are solving.

I think.

Paul?

- Karyobin
**Posts:**396**Joined:**18 June 2005

Hello! There's a thread about this tactic here (as well as the topic that you've evidently already found, having posted in it). I think Karyobin got the arguments for it pretty much right. There's no getting around the fact that the tactic does require you to 'assume' the puzzle has a unique solution, but that's surely something you should assume anyway. If there are multiple solutions it would be a guess, but you'd have to guess anyway!

A question that, to my knowledge, remains open is whether you can construct a multiple-solution puzzle that, if you do use this tactic, fails to work. If you can't, that's surely the last objection done away with, as then if you used the tactic on a multiple solution puzzle you could just consider it the guess that you'd have to make anyway, safe in the knowledge that you'll be alright in the end.

What distinguishes this puzzle from others I've seen is that, putting it into the Susser, I see that without this tactic you in fact can't actually solve it without dead clever advanced tactics (forcing chains in this case).[/url]

A question that, to my knowledge, remains open is whether you can construct a multiple-solution puzzle that, if you do use this tactic, fails to work. If you can't, that's surely the last objection done away with, as then if you used the tactic on a multiple solution puzzle you could just consider it the guess that you'd have to make anyway, safe in the knowledge that you'll be alright in the end.

What distinguishes this puzzle from others I've seen is that, putting it into the Susser, I see that without this tactic you in fact can't actually solve it without dead clever advanced tactics (forcing chains in this case).[/url]

- PaulIQ164
**Posts:**533**Joined:**16 July 2005

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