## Need help with a "diabolical" puzzle!

Post the puzzle or solving technique that's causing you trouble and someone will help
bennys wrote:here is what I found
Code: Select all
`+----------------------+----------------------+----------------------+| 247    5      28     | 479    4789   1      | 6      379    3789   | | 3      1478   6      | 479    45789  2      | 578    1579   5789   | |*17    *178    9      | 3      5678   678    | 2     *157    4      | +----------------------+----------------------+----------------------+| 79     679    4      | 5      3      679    | 1      8      2      | | 1279   123679 23     | 8      679    4      | 57     35679  3579   | | 8      3679   5      | 1      2      679    | 4      3679   379    | +----------------------+----------------------+----------------------+| 6      2489   1      | 479    4789   5      | 3      27     78     | | 245    2348   238    | 6      478    378    | 9      257    1      | | 59     389    7      | 2      1      389    | 58     4      6      | +----------------------+----------------------+----------------------+R3C2=8 => R8C2=8 => R9C6=8 (the only 8 left in C6)=>R9C7=5R3C2<>8 =>R3C8=5 => R9C7=5which mean that R9C7=5 and that solve the puzzle.`

1) There's a typo in the first line -- it should be R8C3=8 not r8c2=8.

2) r8c3=8 does not by itself imply r9c6=8. Shouldn't it be: r3c2=8 => (r8c3=8 AND r3c6<>8) => R9C6=8 => R9C7=5?

3) How did you find this deduction?
tso

Posts: 798
Joined: 22 June 2005

1.thanks i fixed it
2. probably like that "R3C2=8 => (R3C2=8 and R8C3=8) => R9C6=8 (the only 8 left in C6)=>R9C7=5"
3.luck I guess i tried to follow the 8's and 5's
bennys

Posts: 156
Joined: 28 September 2005

tso wrote:You haven't spelled out what your chains are or how you arrived at them, or how we could find them ourselves. Without other information, I'd have to guess that you entered each possible number into a cell, thus trifurcating the single puzzle into three descrete puzzles, solved them all from that point using simpler logic and looked for cells in all three that ended up with the same number. It's a forcing *net* or trial and error or backtracking or brute force or ... i dunno for sure ... but it isn't forcing chains

Having looked into what has been used by the majority on the net & checking definitions, my technique is not forcing chains in that sense.

It is a trifurcation & using simple techniques (single elimination) & observing the state of the grid afterwards.

There is no contradiction elimination here & there is no backtracking, so it doesn't fit T&E Definitions used by the majority.

Solving the Sudoku is a series of FORCED conclusions.

Now, I haven't changed the state of the original cell at the end, & it was an observetion that a certain cell will constantly contain certain candidtaes due to an observation. So you make the deduction & therefore elimination. So I think we do agree that this is FORCING.

Now if I am using simple elimination techniques to observe an end result, A does lead to C & that is a CHAIN isn't it?

tarek

Posts: 2755
Joined: 05 January 2006

tarek wrote:Solving the Sudoku is a series of FORCED conclusions.

Exactly. But if you called "naked triples" "forcing chains", you would confuse people.

tarek wrote:Now, I haven't changed the state of the original cell at the end, & it was an observetion that a certain cell will constantly contain certain candidtaes due to an observation. So you make the deduction & therefore elimination. So I think we do agree that this is FORCING.

Again, this would apply to many tactics that are not forcing chains.

tarek wrote:Now if I am using simple elimination techniques to observe an end result, A does lead to C & that is a CHAIN isn't it?

No. You are arbitrarily moving the line to allow simple elimination techinques. Why not include intermediate elimination techniques? Or advanced? The line is defined already.

If one connects links together one after the other, each link connecting to exactly two others, a chain is formed. If, on the other hand, each link connects to 3 or 4 others, CHAIN MAIL or a CHAIN LINK FENCE might be formed. Neither of these could be described as a "chain".

There are several different types of forcing chains but they all have one thing in common -- each step *in a vaccuum* leads to the next step without considering any other steps. The chains can be literally mapped out on the grid *without requiring any candidates to be removed*.

When you say "any value of r1c1 leads to r9c9=1" but leave out all intervening steps, we are forced to take your word for it. I was unable to follow your logic in several cases. I think the point of giving a complete or partial solution is that reader will be able to reproduce the logic themselves and possibly learn the technique. By labeling your steps as "forcing chains", most of your audience will assume something is there than very well may not be.

I tried to follow some of the chains. Some took many, many steps requiring removing candidates from several poly-value cells -- nothing I could accomplish in my head, nothing I could do without using an eraser or making multiple copies of the grid. Yes, only "simple elimination" aka "singles" were required -- but some of these simple eliminations are only made available after a series of candidate exclusions. This doesn't seem to be a human implemental tactic.
tso

Posts: 798
Joined: 22 June 2005

bennys wrote:2. probably like that "R3C2=8 => (R3C2=8 and R8C3=8) => R9C6=8 (the only 8 left in C6)=>R9C7=5"

???

Should be either:

--- r3c2=8 => (r8c3=8 AND r3c6<>8) => r9c6=8 => r9c7=5

or:

--- r3c2=8 => r789c2<>8 => r8c3=8 => r8c6<>8;
--- r3c2=8 => r3c6<>8;
--- (r8c6<>8 AND r3c6<>8) => r9c7=5

Also, how do the asterisks figure in?
tso

Posts: 798
Joined: 22 June 2005

Thanx tso,

It is not forcing chains then. what would I call it then (The last thing I want would be confusing my audience )???

I disagree that a human would not be able to do it using a pencil & eraser. It is an advanced technique for humans to do, I've placed it after xy wing, so it will be used only when simpler techniques fail. at that level -even with a pencil & erace & spare time- it won't be easy with any advanced techniques(I do agree that this technique wil take you up & down the grid though)

regards,
tarek

tarek

Posts: 2755
Joined: 05 January 2006

If R3C2=8 and R8C3=8 then the only cell in C6 that can be 8 is R9C6
what is the problem?
bennys

Posts: 156
Joined: 28 September 2005

tarek wrote:Thanx tso,

It is not forcing chains then. what would I call it then (The last thing I want would be confusing my audience )???

I don't know. It's some sort of deep-look-ahead restricted to singles elimination. How about -- Look-Ahead Forcing Using Single Eliminations -- "LA FUSE"

tarek wrote:I disagree that a human would not be able to do it using a pencil & eraser.

Actually, we agree on this point.
tso

Posts: 798
Joined: 22 June 2005

Thanks tso,

I started a new thread in the advanced techniques forum to discuss this issue. I think this diabolical puzzle has had enough.

tarek

Posts: 2755
Joined: 05 January 2006

It was interesting to read a thread which was started by yourself tso concerning the same issue. I couldn't find the link to it but the Title was: Elementary form of logic consistantly ignored !!!