## Question

Everything about Sudoku that doesn't fit in one of the other sections
There are puzzles that meet that criteria yes, such as Papocom V.Hard
Pi

Posts: 389
Joined: 27 May 2005

No Way. Papocom V.Hard obviously can be solved by the Papocom V.Hard
techniques.
bennys

Posts: 156
Joined: 28 September 2005

Ah, but the Pappocom V.Hards use more tactics than the Pappcom Hards - well, one more tactic - the X-Wing. I would have thought they could be solved using judicious guesswork and Hard tactics though.
PaulIQ164

Posts: 533
Joined: 16 July 2005

If X wing is the only "advance" tactic that is needed it will not create any problem (put the value and get the contradiction to remove the candidate)
bennys

Posts: 156
Joined: 28 September 2005

Animator to me it looks that all your answer is dubious but it just me.
bennys

Posts: 156
Joined: 28 September 2005

the X wing may not create a problem for you but it would for a less experienced player.

A chain or swordfish may be a problem for you though
Pi

Posts: 389
Joined: 27 May 2005

Pi probably it’s my (bad) English but I feel that you don’t understand my Question.
I am looking for a sudoku in a specific stage including candidates in which
I will not be able to make any progress (progress is – finding placement or removing candidate) using elementary techniques.
And for any pick of candidate in any cell if I move foreword using
Elementary techniques I will get stucked again.
bennys

Posts: 156
Joined: 28 September 2005

so you are looking for a puzzle where you will get to a atage where no move can be made
Pi

Posts: 389
Joined: 27 May 2005

Yes, using the Method described.
bennys

Posts: 156
Joined: 28 September 2005

what do you define as "No move can be made"
Pi

Posts: 389
Joined: 27 May 2005

bennys wrote:Pi probably it’s my (bad) English but I feel that you don’t understand my Question.
I am looking for a sudoku in a specific stage including candidates in which
I will not be able to make any progress (progress is – finding placement or removing candidate) using elementary techniques.
And for any pick of candidate in any cell if I move foreword using
Elementary techniques I will get stucked again.

I'm not sure if I understand. I think you are looking for a 2-constrained puzzle, as defined here:
http://www.setbb.com/phpbb/viewtopic.php?t=248&mforum=sudoku

A magic cell is a cell where, if you make the right guess for this cell, everything else can be solved with your "elementary techniques".

I think you are looking for a puzzle with 2 magic cells, called a 2-constrained puzzle. There are examples at the above link. Here is one.

1....6.8.45..9.1.2........5.....1.....76...2.9.....8..3........5..14.3....2..5..7

No 3-constrained puzzle is known.
Moschopulus

Posts: 256
Joined: 16 July 2005

I think its close but it’s not the same thing.

Correct me if I am wrong but a magic cell exists for a sudoku if and only if the following algorithm will work.

Pick a cell, pick a value and start applying elementary techniques if you get to solve the puzzle you stop (and you did find a magic cell) if not (you get stuck or get a contradiction) you move to the next candidate or the next cell if you finished checking the candidates for that cell without changing the candidates list.

What I am talking about is similar but if I get a contradiction I remove that candidate from the candidates list and start all over again.

Regarding the example its not what I looking for because

Code: Select all
`Using elementary technics we get+----------------------+----------------------+----------------------+| 1      29     39     | 23457  2357   6      | 479    8      349    | | 4      5      368    | 378    9      378    | 1      367    2      | | 7      289    3689   | 2348   1      348    | 469    3469   5      | +----------------------+----------------------+----------------------+| 2      346    45     | 345789 3578   1      | 45679  34679  3469   | | 8      134    7      | 6      35     349    | 459    2      1349   | | 9      1346   145    | 23457  2357   347    | 8      13467  1346   | +----------------------+----------------------+----------------------+| 3      1489   14     | 789    6      789    | 2      5      1489   | | 5      7      89     | 1      4      2      | 3      69     689    | | 6      1489   2      | 389    38     5      | 49     149    7      | +----------------------+----------------------+----------------------+now placing  7 in r2c8 will create a contradiction so we remove 7 from  r2c8now placing  r4c8=6 solve the puzzle`
bennys

Posts: 156
Joined: 28 September 2005

bennys wrote:I think its close but it’s not the same thing.

Correct me if I am wrong but a magic cell exists for a sudoku if and only if the following algorithm will work.

Pick a cell, pick a value and start applying elementary techniques if you get to solve the puzzle you stop (and you did find a magic cell) if not (you get stuck or get a contradiction) you move to the next candidate or the next cell if you finished checking the candidates for that cell without changing the candidates list.

sudoku magic cells are equivalent to CSP backdoors
bennys, you might be thinking of "magic cell" as a single entity,
but magic cells, like backdoors, may come in tuples
for a given set of constraints ("elementary techniques" say)
an N-constrained puzzle has minimal backdoor set size N
meaning that there exists N cells, that when assigned the correct
value, trivially solve the puzzle using the constraints *and*
there exists no N-1 tuple of cells that trivially solves the puzzle

you seem to have requested a backdoor size of 2
(a 2-constrained puzzle)
this puzzle has 11 size 2 FN constraint (elementary technique) backdoors (and no size 1)
Code: Select all
`. . 3 | . . . | 7 8 9. . . | 7 8 . | 1 3 .. . . | . . . | . . .---------------------2 . . | . . 4 | . . 86 1 . | . . . | . . .. . . | 3 . . | . . 1---------------------. 6 7 | . . 5 | 9 2 .. . . | . . . | . . .. 4 . | . . 2 | . . .`

the backdoors are
Code: Select all
`[1,1]=1[4,5]=9[1,5]=5[5,7]=4[3,3]=9[5,7]=4[3,3]=9[9,1]=8[3,6]=1[4,5]=9[3,7]=5[8,5]=4[3,9]=6[5,7]=4[3,9]=6[5,9]=3[3,9]=6[9,7]=3[5,7]=4[6,1]=9[6,1]=9[8,1]=5`

and this one has 550
Code: Select all
`. 2 3 | 4 . . | . . 9. . . | 1 . . | . . .7 8 . | 6 . . | . . 5---------------------. . 4 | . . . | 5 . .. 6 . | . 2 . | . . .. . . | . 6 . | . 3 .---------------------5 . . | . . . | . 9 3. 1 . | . . 8 | . . .. . . | . . . | . 6 2`
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

Its not what I am looking for .look at the example in my previous post where I show that using the method that I am talking about it can be solved
And that is because I allow removing candidates.
bennys

Posts: 156
Joined: 28 September 2005

bennys wrote:Its not what I am looking for .look at the example in my previous post where I show that using the method that I am talking about it can be solved
And that is because I allow removing candidates.

your magic cell algorithm is not correct because it only considers singletons

for some 9x9 sudoku, like the one below, the elementary technique magic cells come in pairs

`. . 3 | . . . | 7 8 9. . . | 7 8 . | 1 3 .. . . | . . . | . . .---------------------2 3 . | . . 4 | . . 86 1 . | . . . | . . .. . . | 3 . . | . . 1---------------------. 6 7 | . . 5 | 9 2 .. . . | . . . | . . .. 4 . | . . 2 | . . .`