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Can anyone provide me with an example of forced guessing?? I've heard it many times but haven't seen it.So i'd be grateful if someone can show me a good example.Thanks

- Kent
**Posts:**98**Joined:**28 February 2006

I don't know what you are refering to by "forced guessing". I don't think that phrase has ever been used in this forum.Kent wrote:Can anyone provide me with an example of forced guessing?? I've heard it many times but haven't seen it.So i'd be grateful if someone can show me a good example.Thanks

If you mean "forcing chains", there are many examples that have been posted in the forum -- but guessing has nothing to do with this.

Here's one puzzle that can be solved with a simple forcing chain:

- Code: Select all
`4 . . | 8 . 1 | . 5 .`

9 . . | . . . | . 6 .

. 5 7 | 3 . . | 4 . .

-------+-------+------

. . . | . 1 . | 7 . 2

. . . | . 3 . | . . .

7 . 8 | . 4 . | . . .

-------+-------+------

. . 5 | . . 9 | 8 2 .

. 4 . | . . . | . . 6

. 9 . | 5 . 4 | . . 1

- Code: Select all
`4 . . | 8 . 1 | . 5 .`

9 8 . | 4 5 . | . 6 .

. 5 7 | 3 . 6 | 4 . .

-------+-------+------

. . . | . 1 . | 7 . 2

. . . | . 3 . | . . .

7 . 8 | . 4 . | . . .

-------+-------+------

3 7 5 | 1 6 9 | 8 2 4

. 4 . | . . 3 | 5 9 6

. 9 . | 5 . 4 | 3 7 1

- Code: Select all
`*-----------------------------------------------------------*`

| 4 {x26} 236 | 8 279 1 |[29] 5 37 |

| 9 8 123 | 4 5 27 | 12 6 37 |

|[12] 5 7 | 3 29 6 | 4 [18] [89] |

|-------------------+-------------------+-------------------|

| 56 36 49 | 69 1 58 | 7 348 2 |

| 256 126 49 | 2679 3 2578 | 169 148 589 |

| 7 1236 8 | 269 4 25 | 169 13 59 |

|-------------------+-------------------+-------------------|

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

| 128 4 12 | 27 278 3 | 5 9 6 |

| 268 9 26 | 5 28 4 | 3 7 1 |

*-----------------------------------------------------------*

Any value in any of the four cells in [brackets] forces the value of '6' in {r1c2}.

This is one of the simplest and easiest to find (for me at least) type of forcing chain -- a short, xy-type or bivalue forcing chain that uses ONLY cells with two possible values. The trouble is, puzzles in which this tactic is useful are rare. Published puzzles are nearly always much less complex. There are many puzzle generators that can create puzzles that are more complex -- but unless someone manually sifts though the output, most of the puzzles created that are at least this complex will be *more* complex and a simple xy-type forcing chain won't help.

- tso
**Posts:**798**Joined:**22 June 2005

tso wrote:a short, xy-type or bivalue forcing chain that uses ONLY cells with two possible values.

Would you make that same statement if the "elimination cell" -- (r1c2) in your example -- had MORE than two candidates?

TIA, Ron

- ronk
- 2012 Supporter
**Posts:**4764**Joined:**02 November 2005**Location:**Southeastern USA

ronk wrote:tso wrote:a short, xy-type or bivalue forcing chain that uses ONLY cells with two possible values.

Would you make that same statement if the "elimination cell" -- (r1c2) in your example -- had MORE than two candidates?

TIA, Ron

I have a much greater chance of overlooking a short forcing chain that includes one polyvalue cell. When solving on paper, I might not fill in all the cells with candidates -- only the ones with just 2 or maybe 3 -- at least not at first. This might mean I'll find a longer, but for me, easier, chain before a shorter one that includes a polyvalue cell. If there are *lots* of bivalue cells, there maybe dozens of easy to find chains that do not require the polyvalue cells. To be fair, I'll find forcing chains like this in situations where it is very likely that there are simpler tactics still available. I don't care. I like finding a long, xy-type chain even though there might be a hidden pair available.

- tso
**Posts:**798**Joined:**22 June 2005

tso wrote:I have a much greater chance of overlooking a short forcing chain that includes one polyvalue cell.

Temporarily disregard the likelihood of your finding an elimination involving exactly one polyvalued cell -- with an elimination at that polyvalued cell.

If you found one, would you refer to that chain as a bivalue chain? More to my concern, would you refer to it as a "pure" bivalue chain?

Again TIA, Ron

- ronk
- 2012 Supporter
**Posts:**4764**Joined:**02 November 2005**Location:**Southeastern USA

ronk wrote:Temporarily disregard the likelihood of your finding an elimination involving exactly one polyvalued cell -- with an elimination at that polyvalued cell.

If you found one, would you refer to that chain as a bivalue chain? More to my concern, would you refer to it as a "pure" bivalue chain?

Yes.

- tso
**Posts:**798**Joined:**22 June 2005

Kent,

Lets take one of Tso's 4 bracketed cells, namely cell (3,1). The two possible values are 1 and 2. If (3,1)2, then obviously (1,2)!2. If (3,1)1, then (3,8)8 > (3,9)9 > (1,7)2 > (1,2)!2. Since either case implies that (1,2) is not 2, cannot be 2. One of the nice things about this type of chain is that we can start anywhere in the chain and arrive at the same conclusion.

rep'nA

Lets take one of Tso's 4 bracketed cells, namely cell (3,1). The two possible values are 1 and 2. If (3,1)2, then obviously (1,2)!2. If (3,1)1, then (3,8)8 > (3,9)9 > (1,7)2 > (1,2)!2. Since either case implies that (1,2) is not 2, cannot be 2. One of the nice things about this type of chain is that we can start anywhere in the chain and arrive at the same conclusion.

rep'nA

- re'born
**Posts:**551**Joined:**31 May 2007

Lots of names, discontinuous xy-cycle, xy-loop, nice loop, bivalue chain.

Another way of looking at it.

Ignore the cell where the deduction takes place.

The other cells form a 29-98-81-12 chain (each link in the chain sees the next link). Note the endpoints are the same digit, 2. Thus, any cell which sees both endpoints cannot be a 2. Therefore r1c123 and r3c789 <> 2.

Another way of looking at it.

Ignore the cell where the deduction takes place.

The other cells form a 29-98-81-12 chain (each link in the chain sees the next link). Note the endpoints are the same digit, 2. Thus, any cell which sees both endpoints cannot be a 2. Therefore r1c123 and r3c789 <> 2.

- Myth Jellies
**Posts:**593**Joined:**19 September 2005

Kent wrote:Is there a name for this method??

As I said in my reply to your original question -- four times -- this tactic is called "forcing chains".

This particular forcing chain is an "xy-type" or "bivalue" forcing chain -- which I also stated in my first post.

In this type of forcing chain, each cell (except the cell in which the exclusion will be made) has only two candidates. Each consecutive pair of cells in the chain or loop share (at least) one candidate. The value of one cell "forces" a value into the next along the "chain". A forcing chain of this type that is only 4 cells long is called an "xy-wing".

More on forcing chains here.

More on many other advanced tactics here.

- tso
**Posts:**798**Joined:**22 June 2005

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