## Ulterior Puzzles

Everything about Sudoku that doesn't fit in one of the other sections
ab wrote:I disagree with this order. On the second step and subsequent steps some hidden singles will be uncovered by pointing pairs on the first step, so in a sense the first step is a different kind of step from all the others. I think you should look for pointing pairs first, after all they exist in the initial state of the puzzle. That way all steps will be the same.

so you want to do box-line before singles?
gsf
2014 Supporter

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

This seems like an interesting thread. Even though the rules clearly excluded me, I will still have an opinion!

I do agree with Ruud that locked candidates (type 1) are on the same line with hidden singles when solving without pencilmarks, when I solve, I actually spot them sooner than I spot hidden singles in rows/columns. Example:

Code: Select all
` *-----------* |5..|.37|.1|| |4--|198|-|5| |1.8|.54|-||| |---+---+---| |9..|.41|.5|| |.15|.63|24|| |.4.|.25|.|1| |---+---+---| |...|51.|3|*| |3.1|489|5|7| |.5.|37.|1|*| *-----------*`

I'd think: The '4' in box 6 tells me that the '4' in box 9 must be in column 9, therefore the '4' in box 3 must be in column 7 and there's only one possibility for number for in box 3 column 7: r1c7.

I actually often solve hidden singles in rows/columns as a slightly twisted version of locked candidates type 2:

Code: Select all
` *-----------* |...|...|...| |..1|...|2..| |23.|1.4||5.| |---+---+---| ||.2|.4.|6..| ||.||7.5||..| ||.8|.2.|1..| |---+---+---| ||5||9|3||7.| |--6|---|9--| |---|---|---| *-----------*`

My trail of thought: In box 7 the '2' has to be in either row 8 or 9, in box 8 this is also the case (draw mental lines), the 2 in box 9 must be in row 7, only one possible cell: r7c9. Instead of drawing 4 vertical lines to row 7 and find one empty cell, I draw 2 horizontal lines (locked candidates) and one vertical line to box 9 and find the empty cell. Finding the singles within boxes is so much easier, but that's just me.

Anyway, I do not understand why singles - pointing pairs - singles should count as one step (as Ruuds example told). I do agree that whenever you enter solved numbers a new step should start. ab seems to have found the best way to do it, pointing pairs before the singles. If I would try to simulate my 'real human'-solving style in a computer program, that would be the closest I could get (unless there are any interesting uniqueness patterns that catch my attention first... ).

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

Thanks for all the replies, especially the one that came from the 'exclusion zone'.

It is interesting to read that others employ similar methods of solving. It's just the step counting that is interpreted differently.

The majority of support goes to ab's method. Since this is a democratic thread, we'll let the majority decide before the majority changes its mind.

Here's the technique:

1. Find all locked pairs (type 1), but pretend they do not exist.
2. Make eliminations based on the locked pairs found in step 1.
3. Find all hidden singles, but pretend they do not exist.
4. Place the hidden singles found in step 3 and perform eliminations.
5. Increment step counter and repeat from step 1.

Conditions:

a. The puzzle must be completely solved using the above steps (duuh)
b. The FN test must produce an (invalid) result.

I need to rewrite some parts of the LowRater.

Ruud.

PS. These are the ratings (old method) for Pat's puzzles:

Code: Select all
`24 clues, Symmetry Class II - Full rotational*-----------------*|1 . .|3 . 5|2 . 8||. 2 .|. 4 .|. 6 .||3 . .|. . .|. . .||-----+-----+-----||8 . .|. . .|. . 3||. 4 .|. . .|. 1 .||7 . .|. . .|. . 9||-----+-----+-----||. . .|. . .|. . 5||. 6 .|. 8 .|. 2 .||4 . 3|9 . 7|. . 6|*-----------------*Ulterior (FB) Rating: 12 steps (9 3 4 3 2 4 5 5 8 8 4 2)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 10 steps24 clues, Symmetry Class III - Horizontal and vertical reflection*-----------------*|. . 1|. 4 .|2 . .||. . .|7 . 3|. . .||3 . 5|. . .|8 . 1||-----+-----+-----||. 2 .|. . .|. 8 .||. . .|6 . 9|. . .||. 9 .|. . .|. 5 .||-----+-----+-----||5 . 6|. . .|1 . 3||. . .|5 . 1|. . .||. . 8|. 6 .|4 . .|*-----------------*Ulterior (FB) Rating: 10 steps (10 5 2 6 4 3 5 6 9 7)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 6 steps24 clues, Symmetry Class V - 180-degree rotational*-----------------*|. 4 .|1 . 8|2 . .||. 5 7|. . .|. . .||. . .|. . 2|6 . .||-----+-----+-----||. . 4|6 . .|. . .||6 . 8|. . .|4 . 9||. . .|. . 7|5 . .||-----+-----+-----||. . 1|3 . .|. . .||. . .|. . .|7 3 .||. . 9|5 . 1|. 6 .|*-----------------*Ulterior (FB) Rating: 13 steps (8 3 3 2 4 3 2 2 3 3 10 7 7)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 7 steps`
Ruud

Posts: 664
Joined: 28 October 2005

Here are four new contributions. This time the search was done only among 'FN-invalid' puzzles. Still not sure if I got the counting right.

Code: Select all
`# II. M. 24 clues. *-----------* |...|1.2|...| |...|3..|4..| |.31|.5.|6..| |---+---+---| |3..|...|.45| |..5|...|7..| |68.|...|..3| |---+---+---| |..8|.6.|52.| |..2|..9|...| |...|2.1|...| *-----------*# III. M 24 clues. *-----------* |..1|.2.|3..| |2..|...|..4| |.5.|...|.6.| |---+---+---| |.7.|2.5|.8.| |5..|...|..1| |.6.|3.8|.4.| |---+---+---| |.2.|...|.7.| |4..|...|..3| |..8|.9.|5..| *-----------*# IV. SM. 24 clues. *-----------* |..1|.2.|34.| |...|..3|..5| |3..|...|..1| |---+---+---| |...|.6.|.7.| |8..|4.1|..6| |.4.|.8.|...| |---+---+---| |5..|...|..8| |2..|6..|...| |.83|.7.|2..| *-----------*# V. M. 20 clues. *-----------* |...|...|.1.| |...|...|23.| |...|.45|...| |---+---+---| |.1.|6.2|..5| |3..|...|..7| |2..|1.4|.8.| |---+---+---| |...|38.|...| |.96|...|...| |.5.|...|...| *-----------*`
Ocean

Posts: 442
Joined: 29 August 2005

This promises to be an interesting thread, especially now FN should be invalid.

Ocean, your last entry looks to be FB1 invalid, the one before last however looks to have scored 27 steps, all are FN invalid.

Here is my entry (a shy 19 stepper).....
Code: Select all
` . . 9 | . . 6 | . 4 .   . . . | . . 1 | . . 8   2 . . | . 8 . | . . .  -------+-------+------  . . . | . . . | . 7 3   . 7 4 | . 9 . | 8 5 .   6 9 . | . . . | . . .  -------+-------+------  . . . | . 5 . | . . 2   8 . . | 7 . . | . . .   . 4 . | 1 . . | 7 . . `

tarek

Posts: 2847
Joined: 05 January 2006

a 22 stepper SM 180 symmetry
Code: Select all
` . . 6 | . 2 7 | . 1 .   . . . | . . . | . . 7   1 . . | 9 . 6 | . . .  -------+-------+------  6 . 2 | . . . | . . 3   7 . . | . 9 . | . . 4   8 . . | . . . | 5 . 1  -------+-------+------  . . . | 3 . 2 | . . 8   5 . . | . . . | . . .   . 9 . | 7 6 . | 4 . . `

tarek

tarek

Posts: 2847
Joined: 05 January 2006

My LowRater has been changed. It now uses ab-counting TM. To stay in shape, I need to use it for at least 20 minutes every day.

Recounting my own collection takes a little time, but here are the results for the latest entries:

These are Pat's puzzles, with ab-counting:

Code: Select all
`24 clues, Symmetry Class II - Full rotational*-----------------*|1 . .|3 . 5|2 . 8||. 2 .|. 4 .|. 6 .||3 . .|. . .|. . .||-----+-----+-----||8 . .|. . .|. . 3||. 4 .|. . .|. 1 .||7 . .|. . .|. . 9||-----+-----+-----||. . .|. . .|. . 5||. 6 .|. 8 .|. 2 .||4 . 3|9 . 7|. . 6|*-----------------*Ulterior (FB) Rating: 14 steps (6 5 4 3 3 2 4 5 3 5 4 6 5 2)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 13 steps24 clues, Symmetry Class III - Horizontal and vertical reflection*-----------------*|. . 1|. 4 .|2 . .||. . .|7 . 3|. . .||3 . 5|. . .|8 . 1||-----+-----+-----||. 2 .|. . .|. 8 .||. . .|6 . 9|. . .||. 9 .|. . .|. 5 .||-----+-----+-----||5 . 6|. . .|1 . 3||. . .|5 . 1|. . .||. . 8|. 6 .|4 . .|*-----------------*Ulterior (FB) Rating: 12 steps (7 4 4 2 4 6 3 5 5 8 6 3)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 9 steps24 clues, Symmetry Class V - 180-degree rotational*-----------------*|. 4 .|1 . 8|2 . .||. 5 7|. . .|. . .||. . .|. . 2|6 . .||-----+-----+-----||. . 4|6 . .|. . .||6 . 8|. . .|4 . 9||. . .|. . 7|5 . .||-----+-----+-----||. . 1|3 . .|. . .||. . .|. . .|7 3 .||. . 9|5 . 1|. 6 .|*-----------------*Ulterior (FB) Rating: 16 steps (8 2 3 2 3 4 2 1 2 2 3 4 8 4 8 1)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 10 steps`

These are Ocean's entries. Notice a nice 27 stepper. The last entry is indeed invalid, Tarek. The earlier puzzle by Ocean can be solved with FN and does not qualify (it is now a 27 stepper)

Code: Select all
`24 clues, Symmetry Class II - Full rotational*-----------------*|. . .|1 . 2|. . .||. . .|3 . .|4 . .||. 3 1|. 5 .|6 . .||-----+-----+-----||3 . .|. . .|. 4 5||. . 5|. . .|7 . .||6 8 .|. . .|. . 3||-----+-----+-----||. . 8|. 6 .|5 2 .||. . 2|. . 9|. . .||. . .|2 . 1|. . .|*-----------------*Ulterior (FB) Rating: 23 steps (6 2 1 1 2 4 3 3 3 2 3 3 1 1 1 1 1 3 4 3 4 4 1)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 13 steps24 clues, Symmetry Class III - Horizontal and vertical reflection*-----------------*|. . 1|. 2 .|3 . .||2 . .|. . .|. . 4||. 5 .|. . .|. 6 .||-----+-----+-----||. 7 .|2 . 5|. 8 .||5 . .|. . .|. . 1||. 6 .|3 . 8|. 4 .||-----+-----+-----||. 2 .|. . .|. 7 .||4 . .|. . .|. . 3||. . 8|. 9 .|5 . .|*-----------------*Ulterior (FB) Rating: 21 steps (4 2 1 1 2 2 1 1 2 3 3 1 3 3 6 5 5 4 4 2 2)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 14 steps24 clues, Symmetry Class IV - Diagonal and antidiagonal reflection*-----------------*|. . 1|. 2 .|3 4 .||. . .|. . 3|. . 5||3 . .|. . .|. . 1||-----+-----+-----||. . .|. 6 .|. 7 .||8 . .|4 . 1|. . 6||. 4 .|. 8 .|. . .||-----+-----+-----||5 . .|. . .|. . 8||2 . .|6 . .|. . .||. 8 3|. 7 .|2 . .|*-----------------*Ulterior (FB) Rating: 27 steps (2 2 1 1 1 2 1 2 1 2 2 2 3 2 3 1 3 1 2 1 2 3 3 3 5 4 2)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 16 steps20 clues, Symmetry Class V - 180-degree rotational*-----------------*|. . .|. . .|. 1 .||. . .|. . .|2 3 .||. . .|. 4 5|. . .||-----+-----+-----||. 1 .|6 . 2|. . 5||3 . .|. . .|. . 7||2 . .|1 . 4|. 8 .||-----+-----+-----||. . .|3 8 .|. . .||. 9 6|. . .|. . .||. 5 .|. . .|. . .|*-----------------*Ulterior (FB) Rating: (invalid)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 14 steps`

And finally Tarek's two:

Code: Select all
`23 clues, Symmetry Class V - 180-degree rotational*-----------------*|. . 9|. . 6|. 4 .||. . .|. . 1|. . 8||2 . .|. 8 .|. . .||-----+-----+-----||. . .|. . .|. 7 3||. 7 4|. 9 .|8 5 .||6 9 .|. . .|. . .||-----+-----+-----||. . .|. 5 .|. . 2||8 . .|7 . .|. . .||. 4 .|1 . .|7 . .|*-----------------*Ulterior (FB) Rating: 19 steps (3 1 2 3 6 2 2 1 2 2 2 2 3 3 7 5 6 5 1)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 11 steps25 clues, Symmetry Class V - 180-degree rotational*-----------------*|. . 6|. 2 7|. 1 .||. . .|. . .|. . 7||1 . .|9 . 6|. . .||-----+-----+-----||6 . 2|. . .|. . 3||7 . .|. 9 .|. . 4||8 . .|. . .|5 . 1||-----+-----+-----||. . .|3 . 2|. . 8||5 . .|. . .|. . .||. 9 .|7 6 .|4 . .|*-----------------*Ulterior (FB) Rating: 22 steps (3 2 1 1 2 5 3 4 2 4 1 2 3 3 1 2 1 2 4 3 4 3)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 13 steps`

You got your ab-counting correct, Tarek!

Ruud.
Ruud

Posts: 664
Joined: 28 October 2005

I don't have a sophisticated generator with a step counter, so I'm actually just trying my luck here... These are all symmetrically minimal and can be solved with the allowed techniques. Hope it's not too much of a problem to test them.

Code: Select all
`#1. . 6|. 5 .|. 8 .3 . .|7 . .|. . 47 . .|3 . .|. . .-----+-----+-----. . 7|. 6 .|3 . .6 8 .|. 7 .|. . .. . 9|. 4 .|1 . .-----+-----+-----1 . .|5 . .|. . .8 . .|9 . .|. . 2. . 2|. 8 .|. 5 .#2. 3 .|. 6 7|4 . .. . .|. . 8|2 . .. . 4|. . .|. 8 6-----+-----+-----. 2 .|. . .|. 9 8. 5 1|. . .|. . 3. 7 .|2 . .|. . .-----+-----+-----3 . .|. 1 .|5 . .. . .|5 8 4|. . 2. . 6|. . .|. . .#39 1 .|. 3 .|. 2 84 . .|. . 7|. . 3. . .|8 . 5|. . .-----+-----+-----. 4 3|. . .|8 . .6 . .|. . .|. . 5. . 9|. . .|4 7 .-----+-----+-----. . .|2 . 9|. . .1 . .|3 . .|. . 48 3 .|. 4 .|. 6 9#49 4 .|. . .|. . .. . .|8 . .|4 5 1. . .|5 . .|. 6 .-----+-----+-----. . 9|4 . .|. 8 2. . .|. . .|. . .1 5 .|. . 7|9 . .-----+-----+-----. 3 .|. . 5|. . .2 6 8|. . 9|. . .. . .|. . .|. 7 3#5. . .|5 . 7|. . .. 6 9|. . .|2 7 .. 7 .|. 2 .|. 1 .-----+-----+-----4 . .|8 . 5|. . 7. . 3|. . .|4 . .7 . .|4 . 2|. . 1-----+-----+-----. 1 .|. 9 .|. 3 .. 3 2|. . .|9 6 .. . .|6 . 3|. . .#6. . 8|. . .|2 . .5 . .|6 . 7|. . 33 . 7|. . .|5 . 9-----+-----+-----. . .|3 . 8|. . .6 . 3|. . .|7 . 4. . .|1 . 4|. . .-----+-----+-----4 . 9|. . .|3 . 82 . .|8 . 5|. . 7. . 5|. . .|1 . .`

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

### puzzle credits

i'm very glad to see that all puzzles now must qualify as FN : (invalid),
which is even stronger than F : (invalid).

each puzzle now needs at least one box-line interaction;
i'm still curious as to how many box-line interactions the puzzle needs — not how many are available but how many were actually needed for solving!

as for the puzzles i had posted, i knew they would qualify under this new rule — that was how i had chosen them. i do thank you for providing the ratings for these puzzles. since i had neglected to specify the exact source of the puzzles, here are the credits:
• Maariv (2006.May.19), by T. Shamir ( thanks to my SuDoku correspondent in Israel )
• The Times Su Doku: Book 2, by Wayne Gould, puzzles 69 and 73

Pat

Posts: 3699
Joined: 18 July 2005

RW,

here are your ratings:

Code: Select all
`25 clues, Symmetry Class VI - Horizontal reflection (RW#1)*-----------------*|. . 6|. 5 .|. 8 .||3 . .|7 . .|. . 4||7 . .|3 . .|. . .||-----+-----+-----||. . 7|. 6 .|3 . .||6 8 .|. 7 .|. . .||. . 9|. 4 .|1 . .||-----+-----+-----||1 . .|5 . .|. . .||8 . .|9 . .|. . 2||. . 2|. 8 .|. 5 .|*-----------------*Ulterior (FB) Rating: 15 steps (3 3 2 1 3 4 7 6 7 4 4 3 3 4 2)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 11 steps25 clues, Symmetry Class VII - Diagonal reflection (RW#2)*-----------------*|. 3 .|. 6 7|4 . .||. . .|. . 8|2 . .||. . 4|. . .|. 8 6||-----+-----+-----||. 2 .|. . .|. 9 8||. 5 1|. . .|. . 3||. 7 .|2 . .|. . .||-----+-----+-----||3 . .|. 1 .|5 . .||. . .|5 8 4|. . 2||. . 6|. . .|. . .|*-----------------*Ulterior (FB) Rating: 17 steps (5 4 4 2 6 5 1 2 2 3 3 4 3 2 4 4 2)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 10 steps28 clues, Symmetry Class II - Full rotational (RW#3)*-----------------*|9 1 .|. 3 .|. 2 8||4 . .|. . 7|. . 3||. . .|8 . 5|. . .||-----+-----+-----||. 4 3|. . .|8 . .||6 . .|. . .|. . 5||. . 9|. . .|4 7 .||-----+-----+-----||. . .|2 . 9|. . .||1 . .|3 . .|. . 4||8 3 .|. 4 .|. 6 9|*-----------------*Ulterior (FB) Rating: 12 steps (6 1 1 4 3 2 3 3 4 8 12 6)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 10 steps24 clues, Symmetry Class V - 180-degree rotational (RW#4)*-----------------*|9 4 .|. . .|. . .||. . .|8 . .|4 5 1||. . .|5 . .|. 6 .||-----+-----+-----||. . 9|4 . .|. 8 2||. . .|. . .|. . .||1 5 .|. . 7|9 . .||-----+-----+-----||. 3 .|. . 5|. . .||2 6 8|. . 9|. . .||. . .|. . .|. 7 3|*-----------------*Ulterior (FB) Rating: 15 steps (9 3 2 2 5 3 3 2 1 3 6 5 4 4 5)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 13 steps28 clues, Symmetry Class I - Full dihedral (RW#5)*-----------------*|. . .|5 . 7|. . .||. 6 9|. . .|2 7 .||. 7 .|. 2 .|. 1 .||-----+-----+-----||4 . .|8 . 5|. . 7||. . 3|. . .|4 . .||7 . .|4 . 2|. . 1||-----+-----+-----||. 1 .|. 9 .|. 3 .||. 3 2|. . .|9 6 .||. . .|6 . 3|. . .|*-----------------*Ulterior (FB) Rating: 9 steps (4 2 3 6 7 11 11 7 2)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 8 steps28 clues, Symmetry Class III - Horizontal and vertical reflection (RW#6)*-----------------*|. . 8|. . .|2 . .||5 . .|6 . 7|. . 3||3 . 7|. . .|5 . 9||-----+-----+-----||. . .|3 . 8|. . .||6 . 3|. . .|7 . 4||. . .|1 . 4|. . .||-----+-----+-----||4 . 9|. . .|3 . 8||2 . .|8 . 5|. . 7||. . 5|. . .|1 . .|*-----------------*Ulterior (FB) Rating: 10 steps (4 2 5 7 10 7 6 4 6 2)Other test results: F  : (invalid) FN : (invalid) N  : (invalid) FNB: 8 steps`

They all qualify as Ulteriors, but no records were broken.

Ruud.
Ruud

Posts: 664
Joined: 28 October 2005

Thanks Ruud for rating the puzzles. I had read somewhere that Sudocue used the "narrowness" of the path as a criteria when it rated difficulty, so I had used that when estimating the steps in these. But it turned out sudocue gives a lot more points for more line-box interactions, so it wasn't very reliable for this purpose. As a comparison:

Oceans 24 clues, Symmetry class II, Ulterior rating 23 steps:
Sudocue total score: 696 (1 Line-Box interaction)

My #2, Ulterior rating 17 steps:
Sudocue total score: 1210 (7 Line-Box interaction + one naked single)
- probably requires another Line-Box interaction to pass the naked single

I don't want to be picky, but I think the amount of required pointed pairs should somehow affect the final ratings of these puzzles. Otherwise there will be lot's of puzzles that only require one or two of them, and that doesn't make them very different from the inferior puzzles. At least there should be a separate category for puzzles with most pointing pairs. I'll give it one more shot:

Code: Select all
`#7. . .|. 8 .|. . .. . 9|. . .|3 . .. 1 .|. 2 .|. 8 .-----+-----+-----7 . 5|. . .|1 . 4. . 3|. 4 .|5 . .. 6 .|. . .|. 7 .-----+-----+-----6 . 7|5 . 1|4 . 81 . .|. . .|. . 7. . .|4 . 3|. . .`

This also requires 7 line-box interaction (according to Sudocue).

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

The issue that RW is raising (as did Pat before) is that some players exhaust single eliminations prior to box line interactions......

Now what we have here is an integrated method, reflecting an experienced player who spots type2 pointing pairs as easy as hidden singles (both less than naked singles).....

Now I tend to agree that puzzle that NEED more pointing pairs should be rated more difficult than others however our experienced player doesn't really care....

The people who care are the ones who exhaust all hidden singles available before attempting pointing pairs (a dilemma)....

One way around this is to add the number of NEEDED (batches) of pointing pairs [if needed, all pointinf pairs seen would count as 1, similar to what I've done in the superior thread]....

So a score of Total Steps + Needed batches of pointing pairs (B1) would be displayed ex (27 steps + 1 pointing pair = Total score 28)

On the side, The lowest steps in my collection of <30 clues puzzles is 9

tarek

tarek

Posts: 2847
Joined: 05 January 2006

tarek wrote:The people who care are the ones who exhaust all hidden singles available before attempting pointing pairs (a dilemma)....

I always do hidden singles and pointing pairs simultaneously, but I care because I find it more fun to do more slicing and dicing. If I do a "hard" puzzle and find the solution with singles only (plus one pointing pair that I used subconciously), I am disappointed at the puzzle.

Counting the "required" pointing pairs is probably quite hard, my #7 can be solved with only 2 pointing pairs, not 7 as reported. But I'll leave the algorithmical work to you guys.

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

hmmm,,,

Probably gsf was correct in placing box line interactions 2nd behind singles elimination...... (the overall result would not count, because you can turn it blind to DEGENERATE hidden singles)....

The difference would mean that it would show needed pointing pairs (the ones that would produce a hidden single in the same step), you can;t do that easily with single eliminations second (I'll try & compare results)

tarek

tarek

Posts: 2847
Joined: 05 January 2006

As this issue isn't complicated enough yet, I'd like to point out that using only the 'needed' pointing pairs would affect the step count in many cases. In this diagram 'X' represents any number except 'A':

Code: Select all
`X X X|X . .|. . .. X .|. . .|. . .X . X|X . .|X . .-----+-----+-----. X X|. . .|X . X. . .|. . .|X . .. . .|. A .|. . .-----+-----+-----. X .|. . .|. . .X X X|X X .|. . .. . .|. . .|. A .`

All digits 'a' can be solved without pointing pairs in 5 steps:

Code: Select all
`X X X|X . .|5 . .. X .|5 . .|. . .X 4 X|X . .|X . .-----+-----+-----2 X X|. . .|X . X. . .|. . .|X . 1. . .|. A .|. . .-----+-----+-----. X 3|. . .|. . .X X X|X X 4|. . .. . .|. . .|. A .`

But if you do the pointing pairs simultaneously, you only need three steps:

Code: Select all
`X X X|X . .|3 . .. X .|2 . .|. . .X 3 X|X . .|X . .-----+-----+-----2 X X|. . .|X . X. . .|. . .|X . 1. . .|. A .|. . .-----+-----+-----. X 3|. . .|. . .X X X|X X 1|. . .. . .|. . .|. A .`

I guess you want to count the minimum number of required steps, then the counter should use all available pointing pairs. To find the 'required' pointing pairs you might need a separate process as the path might be quite different.

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

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