The New Sudoku Players' Forum

[Pat]

Ulterior Puzzles must be minimal (or symmetrical minimal when submitted for a symmetry class).

Puzzles must be solvable with "hidden singles" and "pointing pairs" only; this excludes "naked singles" and "locked candidates type 2".

hi Ruud,

i quite understand the desire for limiting the difficulty of the puzzles,
and for that reason i fail to understand the added requirement for the puzzles to be minimal (or symmetrical minimal).

removing all redundant clues tends to increase the puzzle's difficulty;
requiring puzzles to be minimal (or symmetrical minimal)
would seem to greatly reduce the supply of qualifying puzzles!

[tarek]

I hope u were not offended Pat by my descriptions, It is just a way to remind people of what methods we have at hand although speaking in the very absolute, I myself use (Pat's method) to solve


anyway, I am trying to count how many fruitful steps there are (where box-line resulted in extra placements compared to hidden singles only).... may be this can be utilised in some way.......

tarek

[Pat]

hey tarek, i'm not a computer — i don't always find all "hidden singles" before the box-line interactions.

i was proposing an additional method of rating the puzzles — by the needed box-line interactions.

I hope u were not offended Pat by my descriptions, it is just a way to remind people of what methods we have at hand.

I myself use "Pat's method" to solve.

I am trying to count how many "fruitful" steps there are (where box-line resulted in extra placements compared to "hidden singles" only) — maybe this can be utilised in some way.

thanks , tarek, i was certainly not offended in any way — and am most grateful for your effort to count "fruitful" box-line interactions which helps turn my attention to those puzzles which may be more interesting to solve.

~ Pat

[Pat]

Ruud (2006.May.29) added a new requirement,
not present in the original definition of the "ulterior" puzzles:

all puzzles now must qualify as FN : (invalid),
which is even stronger than F : (invalid).

Since I initially welcomed this new requirement, let me state that I've reconsidered, and it now seems to me that this requirement is too strong. The present Topic is based on Ruud's suggestion that "naked singles" are tougher than box-to-line exclusions; an idea which I'm now inclined to accept; accordingly, we shouldn't care if "naked singles" solve the puzzle, just as we don't care if a duo or trio will do it.


How about a compromise of F : (invalid)?

[tarek]

it now seems to me that this requirement is too strong.
.
.
.
How about a compromise of F : (invalid)?

It is certainly tougher to find & create High steppers & low steppers which are FN invalid, but I myself enjoy a challenge, the puzzles themselves shouldn't be that tough, this my easiest low-stepper which is FN invalid & was posted previously here http://forum.enjoysudoku.com/viewtopic.php?t=4193&postdays=0&postorder=asc&start=78

Code: Select all

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

tarek

[gsf]

here 2 ulterior ({B2:N}-valid) {FN}-invalid low steppers from a 10 min search
and a range of high steppers
the low steppers are less frequent, at least for the random puzzles searched

Code: Select all

# VI 6 steps 30 clues horizontal symmetric minimal

. 7 4  2 . .  . . 6
. . .  . 7 8  . . 2
. . .  . . 9  7 8 .

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

. . .  . . 4  1 9 .
. . .  . 9 5  . . 8
. 6 9  3 . .  . . 5

# VII 7 steps 26 clues antidiagonal symmetric minimal

. . .  . 8 .  5 6 .
. 6 .  . . .  . 7 .
. . .  4 1 .  . . 3

. . 3  . . 1  . . 2
2 . 5  . . .  . 1 .
. . .  7 . .  . . 6

9 . .  . . .  . . .
1 5 .  . 3 .  . . 8
. . 8  5 . 2  . 3 1


(edit) pat pointed out offlist that my solver sometimes counts naked singles as hidden singles
(this has been fixed but not posted)
the following puzzles suffer from that -- so they are not ulterior

Code: Select all

# VI 20 steps 25 clues vertical symmetric minimal

. . .  6 . 4  . . .
1 . .  . . .  . . 2
5 6 .  . . .  . 3 1

. . 7  8 . 3  9 . .
6 . .  . . .  . . 8
. 3 .  . . .  . 2 .

. . 5  2 . 9  1 . .
. 4 .  . 6 .  . 8 .
. . .  5 . 7  . . .

# VI 21 steps 28 clues vertical symmetric minimal

. 8 .  4 . 5  . 1 .
2 . .  . . .  . . 8
7 . .  . 6 .  . . 3

. . .  9 . 6  . . .
. . 4  1 . 3  9 . .
1 9 .  . 4 .  . 3 7

. . .  . . .  . . .
. 5 .  6 . 7  . 8 .
9 . 3  . . .  1 . 6

# VI 22 steps 27 clues vertical symmetric minimal

. . .  4 . 5  . . .
2 . 9  . . .  5 . 8
7 . .  . 6 .  . . 3

. . .  9 . 6  . . .
. . 4  1 . 3  9 . .
1 . .  . . .  . . 7

8 . .  . . .  . . 4
. 5 .  6 . 7  . 8 .
. . 3  8 . 4  1 . .

# VI 23 steps 26 clues vertical symmetric minimal

. 5 .  7 . 3  . 8 .
. . .  6 . 8  . . .
. . 9  2 . 4  7 . .

. . .  . . .  . . .
. . 5  . . .  8 . .
4 . 3  . . .  2 . 5

6 . 2  . . .  4 . 7
. . .  . . .  . . .
. 4 8  5 . 1  6 9 .

# VI 24 steps 27 clues vertical symmetric minimal

4 . .  . 9 .  . . 6
. 1 .  . . .  . 9 .
. 5 9  . . .  8 4 .

. . 7  9 . 2  5 . .
. . .  3 . 7  . . .
. 2 .  . . .  . 8 .

. 6 .  . . .  . 3 .
. . 8  2 . 3  6 . .
. . 2  5 . 6  9 . .

# VII 25 steps 26 clues diagonal symmetric minimal

. . 4  3 . 7  . . .
. 2 .  . . .  . . .
3 . 1  . 4 6  . . .

4 . .  . . 3  7 . 6
. 7 .  2 . .  9 . .
. . .  . 8 .  . . 5

5 . 2  . . .  6 . 9
. . .  . 1 .  . 5 .
. . 9  . . 2  4 . .

# VI 26 steps 25 clues horizontal symmetric minimal

. . .  9 . .  5 . .
. . .  . . 2  9 . .
7 5 .  . . .  . . 3

3 . .  . 2 .  . 4 1
1 . .  8 . .  . 6 .
8 . .  . 1 .  . 5 7

4 8 .  . . .  . . 2
. . .  . . 1  7 . .
. . .  6 . .  4 . .

# VI 27 steps 27 clues vertical symmetric minimal

4 . .  . 9 .  . . 6
. 1 .  . . .  . 9 .
. 5 9  . . .  8 4 .

. . 7  9 . 2  5 . .
. . 1  3 . 7  4 . .
. 2 .  . . .  . 8 .

. 6 .  . . .  . 3 .
. . .  2 . 3  . . .
. 3 .  5 . 6  . 7 .

# VI 28 steps 25 clues vertical symmetric minimal

. . 9  . . .  3 . .
. . .  4 . 5  . . .
. . 6  8 . 3  2 . .

. 1 .  . . .  . 3 .
4 5 .  1 . 2  . 7 6
7 . .  . . .  . . 8

2 . .  . . .  . . 3
. 9 .  . . .  . 5 .
. . .  5 6 1  . . .

# VI 29 steps 26 clues horizontal symmetric minimal

. 8 3  . . .  5 6 .
. . .  . . .  3 7 .
2 . .  . . .  . . 9

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

9 . .  . . .  . . 1
. . .  . . .  7 8 .
. 1 7  . . .  4 9 .

# VI 30 steps 25 clues vertical symmetric minimal

. . .  8 . 6  . . .
4 . .  . . .  . . 9
. 9 .  5 . 4  . 7 .

. . 9  . 8 .  4 . .
. 8 .  1 . 3  . 2 .
6 . .  . . .  . . 3

8 . .  . . .  . . 6
3 . 5  . . .  7 . 4
. . .  7 . 1  . . .

# VI 32 steps 27 clues vertical symmetric minimal

. . 1  . . .  9 . .
8 6 .  . . .  . 7 2
9 . .  . 2 .  . . 6

. . .  3 . 5  . . .
1 . .  8 . 7  . . 5
. . 7  . . .  3 . .

3 . 2  . . .  6 . 7
5 . .  4 . 3  . . 1
. 9 .  . . .  . 5 .


[minnseoelite]

wow those look really challenging thanks for posting

[gsf]

wow those look really challenging thanks for posting

due to a bug those high steppers are not ulterior (naked singles crept in)
so as tarek noted the high steppers seem hard to find
I've edited the post

[gsf]

here's an ulterior high stepper

Code: Select all

# ulterior VII 28 steps 29 clues diagonal symmetric minimal

3 4 .  8 . .  . 6 .
. 5 .  . 1 4  . . 2
. . 2  3 . .  . . .

5 . .  . 8 .  . 9 .
. . .  5 . 7  . 4 .
7 . .  4 6 .  5 . 8

. 7 .  . . .  9 . .
. . 3  . . .  . 8 4
. . .  7 . 8  . . 3


[Pat]

qualification-puzzle - - - [ 26 clues ]

Code: Select all

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

[tarek]

qualification-puzzle - - - [ 26 clues ]

Code: Select all

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

12 Step ulterior....

tarek

[tarek]

here is a 23 clue 7 step ulterior (non symmetrical ):

Code: Select all

 . . . | . . . | 7 . . 
 . 2 . | . . . | . 1 . 
 7 . . | . 8 4 | . . 9 
-------+-------+------
 . . 9 | . 1 . | 5 . . 
 . . . | 2 . 8 | . . . 
 . . 4 | . 7 . | 9 . . 
-------+-------+------
 . . . | 9 5 3 | . . 8 
 . 3 . | . . . | . 7 . 
 . . 1 | . . . | 2 . .

tarek

[Pat]

qualification-puzzle - - - [ 26 clues ]

12 Step ulterior....

tarek, thanks for checking the number of "steps" which i had neglected to do

my own interest is in the greatest amount of box-line interactions (rather than the number of "steps") -
therefore i noted this puzzle which did seem to require more than just one box-line interaction

[tarek]

my own interest is in the greatest amount of box-line interactions (rather than the number of "steps") -
therefore i noted this puzzle which did seem to require more than just one box-line interaction

12 ulterior steps..........
9 possible type 1 box line eliminations
6 in theory should be friutful (6/9)

tarek

[Pat]

- - - - - - -[ 22 clues ]

Code: Select all

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