## A Pure Swordfish Collection

Everything about Sudoku that doesn't fit in one of the other sections
tarek wrote:Does this make sense to anybody

yes
if you go step by step then there will be multiple solution paths with different methods and method application counts
if you go that route then it will involve a heavy hitting optimization algorithm to determine the
best solution path, and just might involve even more time coming up with a definition for best

if you go with batching then, given a constraint method order, there is no ambiguity, because
there is only one solution path, and that path is straightforward to compute

the key to batching is the elimination of ordering bias at each ply
this may not be how a human attacks the solution
but it is algorithmically tractable:
at any ply determine all of the instances of the constraint method in scope that can apply,
determine all of the possible placements/eliminations
but don't apply them until all instances have been identified
gsf
2014 Supporter

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

thanx gsf...

what I would propose to do (to avoid manual checking) is to check total batched SF steps & total RECORDED SFs in that batching. this would be checked in 2 modes:
1. Singles+SF
2. Category techniques (Lenient or Rigorrous)+SF

if results are equal then it is safe to assume that the same Swordfishes would be used either way.

The 1st casualties of this decision would my puzzles (7th & 8th submitted).......
They are pure swordfishes when manually checked as follows (7th given as an example):
Code: Select all
`1. Lenient Category techniques+SF...*-----------------------------------------------------------------*| 5      1278   12    | 4      189    3     | 6      1279   17    || 128    6      9     | 5      7      18    | 4      12     3     || 17     4      3     | 2      6      19    | 5      179    8     ||---------------------+---------------------+---------------------|| 179    179    8     | 6      4      5     | 79     3      2     || 1279   3      4     | 179    1289   12789 | 789    5      6     || 6      279    5     | 3      289    2789  | 1      78     4     ||---------------------+---------------------+---------------------|| 3      1289   12    | 179    129    6     | 78     4      5     || 12489  1289   6     | 179    5      12479 | 3      178    17    || 14     5      7     | 8      3      14    | 2      6      9     |*-----------------------------------------------------------------*Eliminating 1 From r5c1 (Row 4 & Box 4 Box-line interaction)*-----------------------------------------------------------------*| 5      1278   12    | 4      189    3     | 6      1279   17    || 128    6      9     | 5      7      18    | 4      12     3     || 17     4      3     | 2      6      19    | 5      179    8     ||---------------------+---------------------+---------------------|| 179    179    8     | 6      4      5     | 79     3      2     || 279    3      4     | 179    1289   12789 | 789    5      6     || 6      279    5     | 3      289    2789  | 1      78     4     ||---------------------+---------------------+---------------------|| 3      1289   12    | 179    129    6     | 78     4      5     || 12489  1289   6     | 179    5      12479 | 3      178    17    || 14     5      7     | 8      3      14    | 2      6      9     |*-----------------------------------------------------------------*Eliminating 1 From r8c1 (Box 9 & Row 8 Box-Line interaction)Eliminating 1 From r8c2 (Box 9 & Row 8 Box-Line interaction)Eliminating 1 From r8c4 (Box 9 & Row 8 Box-Line interaction)Eliminating 1 From r8c6 (Box 9 & Row 8 Box-Line interaction)*-----------------------------------------------------------------*| 5      1278   12    | 4      189    3     | 6      1279   17    || 128    6      9     | 5      7      18    | 4      12     3     || 17     4      3     | 2      6      19    | 5      179    8     ||---------------------+---------------------+---------------------|| 179    179    8     | 6      4      5     | 79     3      2     || 279    3      4     | 179    1289   12789 | 789    5      6     || 6      279    5     | 3      289    2789  | 1      78     4     ||---------------------+---------------------+---------------------|| 3      1289   12    | 179    129    6     | 78     4      5     || 2489   289    6     | 79     5      2479  | 3      178    17    || 14     5      7     | 8      3      14    | 2      6      9     |*-----------------------------------------------------------------*Eliminating 1 From r1c2 (2x2x3 Swordfish in Columns 345)Eliminating 1 From r1c8 (2x2x3 Swordfish in Columns 345)Eliminating 1 From r1c9 (2x2x3 Swordfish in Columns 345)Eliminating 1 From r5c6 (2x2x3 Swordfish in Columns 345)Eliminating 1 From r7c2 (2x2x3 Swordfish in Columns 345)Eliminating 1 From r4c1 (3x3x2 Swordfish in Rows 239)Eliminating 1 From r5c6 (3x3x2 Swordfish in Rows 239)Eliminating 1 From r1c8 (3x3x2 Swordfish in Rows 239)Eliminating 1 From r8c8 (3x3x2 Swordfish in Rows 239)...2. Singles+SF...*-----------------------------------------------------------------*| 5      1278   12    | 4      189    3     | 6     -1279   17    ||*128    6      9     | 5      7     *18    | 4     *12     3     ||*17     4      3     | 2      6     *19    | 5     *179    8     ||---------------------+---------------------+---------------------||-179    179    8     | 6      4      5     | 79     3      2     ||-1279   3      4     | 179    1289  -12789 | 789    5      6     || 6      279    5     | 3      289    2789  | 1      789    4     ||---------------------+---------------------+---------------------|| 3      1289   12    | 179    129    6     | 78     4      5     ||-12489  1289   6     | 179    5     -12479 | 3     -178    17    ||*14     5      7     | 8      3     *14    | 2      6      9     |*-----------------------------------------------------------------*Eliminating 1 From r4c1 (3x3x2 Swordfish in Rows 239)Eliminating 1 From r5c1 (3x3x2 Swordfish in Rows 239)Eliminating 1 From r8c1 (3x3x2 Swordfish in Rows 239)Eliminating 1 From r5c6 (3x3x2 Swordfish in Rows 239)Eliminating 1 From r8c6 (3x3x2 Swordfish in Rows 239)Eliminating 1 From r1c8 (3x3x2 Swordfish in Rows 239)Eliminating 1 From r8c8 (3x3x2 Swordfish in Rows 239)...`

The use of Box-Line reductions has created a possible new swordfish when 1 in r8c4 was deleted, this wasn't possible when using single

That means that we have 1 batch of SFs in each mode but a total of 2 Possible SFs in one mode and a total of 1 SF in the other. So it passes point 7.1 but fails point 7.2

Done electronically it sounds fair, but in reality it is harsh because:
1. if you use any of the swordfishes, you wouldn't need to use the other (checked manually)
2. The actual new possible SF occurs when using box-line reductions (in the more difficult mode)

So puzzles that fail Point 7 especially the ones that fail sub-point 7.2 only, will need manual checking to confirm their pureness (I've checked 2).

tarek

tarek

Posts: 2917
Joined: 05 January 2006

[Edit have since changed, so ignore this post]

Electronic check for submitted puzzles (chronological order):

#Puzzle#id,Pass(category)/Fail(Point),SF_needed(>=)
2...9.....6...31....12...7...7....2.3.......8.8....4...4...86....27...1.....5...4#tarek001,Pass(Lenient),2
7...4.....5...13....62...7...7....2.9.......8.3....5...6...31....27...6.....5...4#tarek002,Pass(Lenient),2
9...6.....4...18....72...9...9....2.5.......3.6....4...7...81....29...7.....4...6#tarek003,Pass(Lenient),2
1...7.....4...31....89...6...6....9.2.......3.1....4...8...42....96...8.....5...6#tarek004,Pass(Lenient),2
8...6.....5...39....98...1...1....8.3.......7.7....4...4...73....81...9.....2...5#tarek005,Pass(Lenient),2
5...4.....4...13....97...5...5....7.2.......6.1....8...9...84....75...9.....1...8#tarek006,Pass(Lenient),2
....1.....2...34....56...7...71...6.8.......9.1...72...5...43....67...5.....2....#TTHsieh001,fail(Point 5)
....1.....2...34....56...7...73...6.8.......3.4...82...9...28....67...3.....9....#TTHsieh002,Pass(Lenient),1
5....36....9.7.....4.2....8..8.....2.3.....5.6.....1..3....6.4.....5.3....78....9#tarek007,fail(Point 7.2)
3....71....8.5.....2.8....6..6.....4.7.....3.1.....9..7....1.2.....3.7....56....8#tarek008,fail(Point 7.2)
3....94....6.5.....1.8....2..1.....8.8.....1.4.....7..5....4.3.....3.9....81....6#tarek009,Pass(Lenient),1
1....96....5.8.....8.2....7..4.....2.9.....6.6.....1..3....6.1.....5.9....27....5#tarek010,Pass(Lenient),1
9....85....4.3.....6.1....3..6.....1.1.....6.5.....2..7....5.9.....9.8....16....4#tarek011,Pass(Lenient),1
3....94....6.5.....2.8....1..1.....8.9.....3.4.....7..9....4.2.....3.9....81....6#tarek012,Pass(Lenient),1
6....18....3.5.....1.4....5..9.....4.2.....6.1.....7..7....8.2.....3.1....45....3#tarek013,Pass(Lenient),1
9....82....6.2.....5.3....1..4.....3.7.....5.2.....1..8....3.7.....9.8....35....6#tarek014,Pass(Lenient),1
4....61....8.9.....6.5....9..2.....5.7.....6.6.....3..3....1.7.....8.6....59....8#tarek015,Pass(Lenient),1
4....68....7.3.....1.5....9..4.....5.6.....4.8.....2..6....8.1.....4.6....39....7#tarek016,Pass(Lenient),1
4....69....5.3.....6.7....2..2.....7.5.....4.8.....1..1....7.6.....4.8....72....9#tarek017,Pass(Lenient),1
2....31....4.1.....6.8....4..7.....8.9.....2.1.....3..6....1.3.....2.5....84....9#tarek018,Pass(Lenient),1
7....64....5.2.....8.9....2..2.....8.9.....7.4.....6..3....4.1.....6.3....82....9#tarek019,Pass(Lenient),1
9....42....7.6.....3.1....6..5.....1.8.....9.3.....4..4....2.8.....7.3....16....7#tarek020,Pass(Lenient),1
5....61....9.8.....3.9....7..4.....8.9.....5.1.....3..6....1.3.....2.6....84....9#tarek021,Pass(Lenient),1

tarek

[Edit have since changed, so ignore this post]
Last edited by tarek on Thu Dec 27, 2007 2:58 pm, edited 1 time in total.

tarek

Posts: 2917
Joined: 05 January 2006

new puzzles
Code: Select all
` . . . | 3 2 4 | . . .   . . 6 | . . . | 3 . .   . 9 . | . . . | . 5 .  -------+-------+------  2 . . | . 9 . | . . 6   6 . . | 4 . 3 | . . 1   4 . . | . 5 . | . . 8  -------+-------+------  . 2 . | . . . | . 8 .   . . 7 | . . . | 4 . .   . . . | 7 1 2 | . . .   . . . | 5 2 8 | . . .   . . 7 | . . . | 9 . .   . 4 . | . . . | . 3 .  -------+-------+------  9 . . | . 1 . | . . 8   5 . . | 3 . 6 | . . 7   2 . . | . 4 . | . . 1  -------+-------+------  . 9 . | . . . | . 8 .   . . 2 | . . . | 5 . .   . . . | 8 6 9 | . . .   . . . | 1 9 7 | . . .   . . 9 | . . . | 2 . .   . 7 . | . . . | . 8 .  -------+-------+------  9 . . | . 1 . | . . 5   7 . . | 5 . 2 | . . 8   6 . . | . 3 . | . . 4  -------+-------+------  . 5 . | . . . | . 3 .   . . 2 | . . . | 6 . .   . . . | 8 7 5 | . . .   . . . | 3 4 5 | . . .   . . 5 | . . . | 2 . .   . 6 . | . . . | . 7 .  -------+-------+------  2 . . | . 6 . | . . 7   5 . . | 4 . 1 | . . 9   9 . . | . 2 . | . . 1  -------+-------+------  . 2 . | . . . | . 4 .   . . 1 | . . . | 6 . .   . . . | 8 9 6 | . . .   . . . | 5 6 2 | . . .   . . 5 | . . . | 8 . .   . 7 . | . . . | . 1 .  -------+-------+------  8 . . | . 7 . | . . 1   2 . . | 6 . 9 | . . 4   4 . . | . 8 . | . . 9  -------+-------+------  . 8 . | . . . | . 6 .   . . 9 | . . . | 7 . .   . . . | 3 4 7 | . . .   . . . | 6 2 9 | . . .   . . 6 | . . . | 3 . .   . 9 . | . . . | . 1 .  -------+-------+------  9 . . | . 5 . | . . 2   4 . . | 9 . 8 | . . 7   7 . . | . 4 . | . . 3  -------+-------+------  . 1 . | . . . | . 6 .   . . 5 | . . . | 8 . .   . . . | 2 6 1 | . . .   . . . | 7 4 2 | . . .   . . 4 | . . . | 9 . .   . 1 . | . . . | . 3 .  -------+-------+------  3 . . | . 8 . | . . 5   2 . . | 6 . 9 | . . 3   9 . . | . 3 . | . . 1  -------+-------+------  . 3 . | . . . | . 4 .   . . 2 | . . . | 8 . .   . . . | 8 1 6 | . . .  `
tarek

tarek

Posts: 2917
Joined: 05 January 2006

Code: Select all
` . . 1 | 2 3 . | . . . . . 4 | . . . | . . . . . 5 | . . . | 6 3 2 - - - + - - - + - - - . . . | 7 . 2 | . . 8 7 . . | . 4 . | . . 1 1 . . | 3 . 9 | . . . - - - + - - - + - - - 5 2 3 | . . . | 9 . . . . . | . . . | 5 . . . . . | . 6 1 | 8 . .`
• 001230000004000000005000632000702008700040001100309000523000900000000500000061800
TTHsieh
TTHsieh

Posts: 1390
Joined: 13 July 2007

Code: Select all
`1.....6.4.2..7..5.3...........14.....7..58.9....7.9...........3.5..9..2.4.6.....152 x Hidden Single 4 x Direct Hidden Pair 3 x Naked Single 6 x Pointing 2 x Naked Pair 6 x Hidden Pair 4 x Swordfish`

This one pass?
Eioru

Posts: 182
Joined: 16 August 2006

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

This one pass?

sorry, cannot be solved by Swordfish + "singles"
~ Pat

Pat

Posts: 3732
Joined: 18 July 2005

### from tso (2006.Jul.6)

tso (2006.Jul.6) wrote:
[ 27 clues ]
Code: Select all
` 9 . . | 4 . . | 7 . .  . 6 . | . 3 . | . 5 .  . . 1 | . . 8 | . . 4 -------+-------+------ 2 . . | 8 . . | 1 . .  . 3 . | . 4 . | . 7 .  . . 7 | . . 9 | . . 5 -------+-------+------ 5 . . | 6 . . | 2 . .  . 2 . | . 8 . | . 9 .  . . 6 | . . 1 | . . 3 `

Pat

Posts: 3732
Joined: 18 July 2005

### 33

i follow the most lenient rules --
-qNFW3-G -Q!NFBHTW2-G
most of the puzzles need just 1 Swordfish;
the only exceptions are --
puzzle 1 needs 2 at least, at most 3 ( try solving it to decide )
puzzles 2-6 need exactly 2
puzzle 8 needs <=2 ( try solving it to decide )
• puzzle number within this Topic ( 1-33, but 7 and 32 shouldn't be here )
• the puzzle
• number of clues
• number of Swordfish needed
• puzzle source
01,2...9.....6...31....12...7...7....2.3.......8.8....4...4...86....27...1.....5...4,22,2-3,tarek (2007.Dec.18)
02,7...4.....5...13....62...7...7....2.9.......8.3....5...6...31....27...6.....5...4,22,2,tarek (2007.Dec.18)
03,9...6.....4...18....72...9...9....2.5.......3.6....4...7...81....29...7.....4...6,22,2,tarek (2007.Dec.18)
04,1...7.....4...31....89...6...6....9.2.......3.1....4...8...42....96...8.....5...6,22,2,tarek (2007.Dec.18)
05,8...6.....5...39....98...1...1....8.3.......7.7....4...4...73....81...9.....2...5,22,2,tarek (2007.Dec.18)
06,5...4.....4...13....97...5...5....7.2.......6.1....8...9...84....75...9.....1...8,22,2,tarek (2007.Dec.18)

07,....1.....2...34....56...7...71...6.8.......9.1...72...5...43....67...5.....2....,22,0,TTHsieh (2007.Dec.18)
08,....1.....2...34....56...7...73...6.8.......3.4...82...9...28....67...3.....9....,22,1-2,TTHsieh (2007.Dec.18)

09,5....36....9.7.....4.2....8..8.....2.3.....5.6.....1..3....6.4.....5.3....78....9,22,1,tarek (2007.Dec.18)
10,3....71....8.5.....2.8....6..6.....4.7.....3.1.....9..7....1.2.....3.7....56....8,22,1,tarek (2007.Dec.18)
11,3....94....6.5.....1.8....2..1.....8.8.....1.4.....7..5....4.3.....3.9....81....6,22,1,tarek (2007.Dec.18)
12,1....96....5.8.....8.2....7..4.....2.9.....6.6.....1..3....6.1.....5.9....27....5,22,1,tarek (2007.Dec.18)
13,9....85....4.3.....6.1....3..6.....1.1.....6.5.....2..7....5.9.....9.8....16....4,22,1,tarek (2007.Dec.18)
14,3....94....6.5.....2.8....1..1.....8.9.....3.4.....7..9....4.2.....3.9....81....6,22,1,tarek (2007.Dec.18)
15,6....18....3.5.....1.4....5..9.....4.2.....6.1.....7..7....8.2.....3.1....45....3,22,1,tarek (2007.Dec.18)
16,9....82....6.2.....5.3....1..4.....3.7.....5.2.....1..8....3.7.....9.8....35....6,22,1,tarek (2007.Dec.18)
17,4....61....8.9.....6.5....9..2.....5.7.....6.6.....3..3....1.7.....8.6....59....8,22,1,tarek (2007.Dec.18)
18,4....68....7.3.....1.5....9..4.....5.6.....4.8.....2..6....8.1.....4.6....39....7,22,1,tarek (2007.Dec.18)
19,4....69....5.3.....6.7....2..2.....7.5.....4.8.....1..1....7.6.....4.8....72....9,22,1,tarek (2007.Dec.18)
20,2....31....4.1.....6.8....4..7.....8.9.....2.1.....3..6....1.3.....2.5....84....9,22,1,tarek (2007.Dec.18)
21,7....64....5.2.....8.9....2..2.....8.9.....7.4.....6..3....4.1.....6.3....82....9,22,1,tarek (2007.Dec.18)
22,9....42....7.6.....3.1....6..5.....1.8.....9.3.....4..4....2.8.....7.3....16....7,22,1,tarek (2007.Dec.18)
23,5....61....9.8.....3.9....7..4.....8.9.....5.1.....3..6....1.3.....2.6....84....9,22,1,tarek (2007.Dec.18)

24,...324.....6...3...9.....5.2...9...66..4.3..14...5...8.2.....8...7...4.....712...,24,1,tarek (2007.Dec.19)
25,...528.....7...9...4.....3.9...1...85..3.6..72...4...1.9.....8...2...5.....869...,24,1,tarek (2007.Dec.19)
26,...197.....9...2...7.....8.9...1...57..5.2..86...3...4.5.....3...2...6.....875...,24,1,tarek (2007.Dec.19)
27,...345.....5...2...6.....7.2...6...75..4.1..99...2...1.2.....4...1...6.....896...,24,1,tarek (2007.Dec.19)
28,...562.....5...8...7.....1.8...7...12..6.9..44...8...9.8.....6...9...7.....347...,24,1,tarek (2007.Dec.19)
29,...629.....6...3...9.....1.9...5...24..9.8..77...4...3.1.....6...5...8.....261...,24,1,tarek (2007.Dec.19)
30,...742.....4...9...1.....3.3...8...52..6.9..39...3...1.3.....4...2...8.....816...,24,1,tarek (2007.Dec.19)

31,..123......4........5...632...7.2..87...4...11..3.9...523...9........5......618..,25,1,TTHsieh (2007.Dec.22)

32,1.....6.4.2..7..5.3...........14.....7..58.9....7.9...........3.5..9..2.4.6.....1,22,0,Eioru (2007.Dec.23)

33,9..4..7...6..3..5...1..8..42..8..1...3..4..7...7..9..55..6..2...2..8..9...6..1..3,27,1,tso (2006.Jul.6)

Pat

Posts: 3732
Joined: 18 July 2005

thanx Pat for collating the puzzles here & elsewhere. I will try to put all in a databse & collate them also. (hopefully I won't miss anything).

Pat wrote:[list]
i follow the most lenient rules --
-qNFW3-G -Q!NFBHTW2-G

I have no problems with extra leniency, however, I have to disagree here. The Ideal Pure Swordfish would be:
Code: Select all
`A puzzle that ABSOLUTELY NEEDS x swordfishes to solve when combined with singles.The same puzzle ABSOLUTELY NEEDS AT LEAST x swordfishes to solve when combined with a set of techniques`

I came across several puzzles that require singles + 4 swordfishes but then require only 1 when "Leneient" criteria are applied. These would pass gsf's formula but do you realy think that they would be pure swordfishes

I will try to code a solver that will exhaustively find the least amount of swordfishes under the lenient criteria which otherwise must be done MANUALLY to make sure how many swordfishes are ultimately needed.

In the mean time I will be extremely lenient when I allow the following change in point 7.
Code: Select all
`7. Swordfish needed (Point 4) = Swordfish needed following Category techniques    7.1. batches of SF needed following singles <= batches of SF needed following category techniques    7.2. (Only when 7.1 result is '=') Total Possible SF following singles <= Total Possible SF following category techniques`

This will hopefully cover more puzzles that are being missed as being pure at the expense fo few (I think very few) that can possibly make the list & not being pure.

tarek

tarek

Posts: 2917
Joined: 05 January 2006

tarek wrote:
I have to disagree with your EXTREME leniency Pat. The Ideal Pure Swordfish would be:
A puzzle that ABSOLUTELY NEEDS x swordfishes to solve when combined with singles.
The same puzzle ABSOLUTELY NEEDS AT LEAST x swordfishes to solve when combined with a set of techniques
I came across several puzzles that require singles + 4 swordfishes but then require only 1 when "Leneient" criteria are applied. These would pass gsf's formula but do you realy think that they would be pure swordfishes ?

it seems i don't really understand
perhaps you could post one of those examples ?

Pat

Posts: 3732
Joined: 18 July 2005

Pat wrote:....could post one of those examples ?

I must have deleted them but will run the search again & hopefully 1 would show up quickly

tarek

tarek

Posts: 2917
Joined: 05 January 2006

I found 2 puzzles that fail the moified point 7.1.
Code: Select all
` 6 . . | . . 3 | 9 . .   . . 4 | . 5 . | . . .   . 8 . | 2 . . | . . 7  -------+-------+------  . . 5 | . . . | . . 2   . 9 . | . . . | . 6 .   3 . . | . . . | 1 . .  -------+-------+------  1 . . | . . 9 | . 4 .   . . . | . 1 . | 3 . .   . . 2 | 5 . . | . . 8   7 . . | . . 2 | 9 . .   . . 8 | . 1 . | . . .   . 5 . | 4 . . | . . 6  -------+-------+------  . . 1 | . . . | . . 4   . 4 . | . . . | . 3 .   2 . . | . . . | 5 . .  -------+-------+------  5 . . | . . 3 | . 9 .   . . . | . 7 . | 2 . .   . . 4 | 6 . . | . . 1  `
They should pass gsf's formula but are they pure?

How many SFs with singles do you need?
How many SFs with the rest of the techniques do you need?

to be pure IMO the 1st answer should be <= to the second answer

tarek

tarek

Posts: 2917
Joined: 05 January 2006

tarek wrote:I found 2 puzzles that fail the moified point 7.1 --

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

They should pass gsf's formula but are they pure?

How many SFs with singles do you need?
How many SFs with the rest of the techniques do you need?

to be pure IMO the 1st answer should be <= to the second answer

thanks, tarek

it will never be less
and i'm lenient enough to allow it to be greater

34,6....39....4.5.....8.2....7..5.....2.9.....6.3.....1..1....9.4.....1.3....25....8,22,3,tarek (2007.Dec.23)
35,7....29....8.1.....5.4....6..1.....4.4.....3.2.....5..5....3.9.....7.2....46....1,22,2-4,tarek (2007.Dec.23)

Pat

Posts: 3732
Joined: 18 July 2005

Pat wrote:i'm lenient enough to allow it to be greater

Thanx, I see that my 2 puzzles will make it after all:D .... In my rating post, all posted puzzles will be followed by (Pass/category) or (Failed which point)
As I will go in sequence of points from 1-7... then any puzzle that fails Point 7. should be acceptable to you
Pat wrote:it will never be less

I posted a puzzle which failed point 7.2. before I modified it, I think that puzzle needs less (More red herrings )

tarek

tarek

Posts: 2917
Joined: 05 January 2006

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