The New Sudoku Players' Forum

[tarek]

Code: Select all

Rules(v6.0):
1. Valid vanilla 9*9 sudoku
2. NEEDS a Swordfish to solve after applying the following set of techniques:
   2.1. Singles (Hidden/Naked)
   2.2. Box-Line/Line-Box interactions
   2.3. Subsets (doubles,triples,quads) (Hidden/Naked)
   2.4. X-Wing
3. Solved using the following set of techniques:
   3.1. Singles (Hidden/Naked)
   3.2. Swordfish (SF)
4. Swordfish needed (Point 2)>=Swordfish needed (Point 3), achieved electronically through solving 1000 isomorphs of the same puzzle according to:
    a. Point 2 (1000 isomorphs)
    b. Point 3 (1000 isomorphs)
    minimum number of swordfish recorded in "a" is compared to
    the minimum number of swordfish recorded in "b"
5. Symmetric (I-VII)
6. Minimal
7. NEEDS a Swordfish to solve after applying the following set of techniques:
   7.1. Singles (Hidden/Naked)
   7.2. Box-Line/Line-Box interactions
   7.3. Subsets (doubles,triples,quads) (Hidden/Naked)
   7.4. X-Wing
   7.5. Finned X-Wing (incl. Sashimi)
   7.6. Simple Colouring
   7.7. XYZ-Wing
   7.8. XY-Wing
   7.9. Uniqueness (1-4)
   7.10. Empty Rectangle
   7.11. BUG+1
   This is approximated electronically by using gsf's sudoku
   -q{FNB2B3H2T2T3H3T4H4W2X}{W3}-G I2>0 options

--Puzzles will be checked against the sequence of rules starting from 1 & ending at 7.
--Checking will stop when a puzzle fails to satisfy a ceratin rule.
--Each Puzzle will acquire a Score equal to the highest rule being checked against.
--if a puzzle passes all rules (1-7) then it will score an "8"

Score interpretaion:
Score = 1 ==> Invalid puzzle
Score = 2 ==> Requires other than a Swordfish to solve
Score >=3 ==> Requires a Swordfish to solve
Score >=4 ==> Pure Swordfish (Pat's Extra Lenient criteria)
Score >=5 ==> Pure Swordfish (Tarek's Lenient criteria but with Symmetry & Minimality not obligatory)
Score >=6 ==> Pure Swordfish (Tarek's Lenient criteria with Minimality not obligatory)
Score >=7 ==> Pure Swordfish (Tarek's Lenient criteria)
Score = 8 ==> Pure Swordfish (Tarek's Rigorous criteria)

Following ocean's "A Pure X-Wing collection", I decided to start this thread.
The rules above are not written in stone. Any suggestions will be discussed & changes can be made.

The aim is to create puzzles that provide many "Red herrings" when only Swordfish are needed.

tarek

[tarek]

1st puzzles

Code: Select all

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

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

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

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

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

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

tarek

[TTHsieh]

Are these 2 puzzles pure swordfish ?

Code: Select all

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



Code: Select all

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



TTHsieh

[Pat]

Are these 2 puzzles pure swordfish ?

Code: Select all

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



Code: Select all

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



hi TTHsieh,
i wonder how you're testing the puzzles?

the first puzzle cannot be solved by Swordfish + "singles"

[Pat]

the 2nd puzzle may qualify --
it can be solved by Swordfish + "singles"

(if X-wing is accepted as a special case of Swordfish.
i'm not sure how tarek would rule on this question!)

[tarek]

Thanx TTHsieh for your submissions..........

I'm going to relax the rules to allow more valid puzzles according to rules adjusted according to Pat (You see, I'm nice after all ).

However the rules above will filter the valid puzzles into a second Pot.
the 1st Pot would be the "Lenient" Pot the 2nd Pot will be the "Rigorous" Pot. I will update the rules to reflect that.

regarding TTHsieh puzzles ..... as the second puzzle has an x-wing disguised as a swordfish.... it will always fail rule number 7 (The swordfish after singles should be the same as the Swordfish following all category techniques).

The 1st puzzle can't be solved with singles+swordfish (fails point 4)

tarek

[tarek]

The following {Swordfish} are Swordfish between Curly Brackets quite literally

Code: Select all

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tarek

[Pat]

as TTHsieh's second puzzle has an x-wing disguised as a swordfish....
it will always fail rule 7

The swordfish after singles
should be the same as the Swordfish following all category techniques

sorry, tarek, i'm not following you,
have you looked at the solution-path for this puzzle ?

if you allow X-wing as a special case of Swordfish
then it seems to me that the puzzle does qualify

[ronk]

regarding TTHsieh puzzles ..... as the second puzzle has an x-wing disguised as a swordfish.... it will always fail rule number 7 (The swordfish after singles should be the same as the Swordfish following all category techniques).

But what if the digit order is reversed during the swordfish searches

[tarek]

following are the 2 solution paths

Code: Select all

Lenient Category techniques:
*-----------------------------------------------------------------*
| 349    7      3489  |*24589  1      459   | 6     *2589  -259   |
| 6      2      189   | 589    7      3     | 4      1589   159   |
| 149    18     5     | 6      248    49    | 3      7      129   |
|---------------------+---------------------+---------------------|
| 1259   15     7     | 3      245    1459  | 159    6      8     |
| 8      6     *129   |*1259  -25     7     | 159    4      3     |
| 1359   4      139   | 159    6      8     | 2      159    7     |
|---------------------+---------------------+---------------------|
| 7      9      14    | 145    3      2     | 8      15     6     |
| 1245   158    6     | 7      458    145   | 159    3      12459 |
|-1245   3     *1248  | 1458   9      6     | 7     *125   -1245  |
*-----------------------------------------------------------------*
Eliminating 2 From r1c9 (2x2x2 Swordfish in Columns 348)
Eliminating 2 From r5c5 (2x2x2 Swordfish in Columns 348)
Eliminating 2 From r9c1 (2x2x2 Swordfish in Columns 348)
Eliminating 2 From r9c9 (2x2x2 Swordfish in Columns 348)
.
.
.
*-----------------------------------------------------------------*
| 349    7      3489  | 24589  1      459   | 6      2589   59    |
| 6      2      189   | 589    7      3     | 4      1589   159   |
| 149    18     5     | 6      248    49    | 3      7      129   |
|---------------------+---------------------+---------------------|
|-1259  *15     7     | 3      24     149   |*159    6      8     |
| 8      6      129   | 129    5      7     | 19     4      3     |
| 1359   4      139   | 19     6      8     | 2      159    7     |
|---------------------+---------------------+---------------------|
| 7      9      14    | 145    3      2     | 8      15     6     |
|-1245  *158    6     | 7      48    -145   |*159    3     -12459 |
| 145    3      1248  | 1458   9      6     | 7      125    145   |
*-----------------------------------------------------------------*
Eliminating 5 From r4c1 ( XWing in Columns 27)
Eliminating 5 From r8c1 ( XWing in Columns 27)
Eliminating 5 From r8c6 ( XWing in Columns 27)
Eliminating 5 From r8c9 ( XWing in Columns 27)



Singles+Swordfish techniques:
*-----------------------------------------------------------------*
| 349    7      3489  |*24589  1      459   | 6     *2589  -259   |
| 6      2      189   | 589    7      3     | 4      1589   159   |
| 149    18     5     | 6      248    49    | 3      7      129   |
|---------------------+---------------------+---------------------|
| 1259   15     7     | 3      245    1459  | 159    6      8     |
| 8      6     *129   |*1259  -25     7     | 159    4      3     |
| 1359   4      139   | 159    6      8     | 2      159    7     |
|---------------------+---------------------+---------------------|
| 7      9      14    | 145    3      2     | 8      15     6     |
| 1245   158    6     | 7      458    145   | 159    3      12459 |
|-1245   3     *1248  | 1458   9      6     | 7     *125   -1245  |
*-----------------------------------------------------------------*
Eliminating 2 From r1c9 (2x2x2 Swordfish in Columns 348)
Eliminating 2 From r5c5 (2x2x2 Swordfish in Columns 348)
Eliminating 2 From r9c1 (2x2x2 Swordfish in Columns 348)
Eliminating 2 From r9c9 (2x2x2 Swordfish in Columns 348)
.
.
.
*-----------------------------------------------------------------*
| 349    7      3489  |-24589  1     *459   | 6     -2589  -59    |
| 6      2      189   | 589    7      3     | 4      1589   159   |
| 149    18     5     | 6      248    49    | 3      7      129   |
|---------------------+---------------------+---------------------|
|-1259  *15     7     | 3      24     149   |*159    6      8     |
| 8      6      129   | 129    5      7     | 19     4      3     |
| 1359   4      139   | 19     6      8     | 2      159    7     |
|---------------------+---------------------+---------------------|
| 7      9      14    | 145    3      2     | 8      15     6     |
|-1245  *158    6     | 7      48    *145   |*159    3     -12459 |
| 145    3      1248  | 1458   9      6     | 7      125    145   |
*-----------------------------------------------------------------*
Eliminating 5 From r1c4 (2x2x2 Swordfish in Columns 267)
Eliminating 5 From r1c8 (2x2x2 Swordfish in Columns 267)
Eliminating 5 From r1c9 (2x2x2 Swordfish in Columns 267)
Eliminating 5 From r4c1 (2x2x2 Swordfish in Columns 267)
Eliminating 5 From r8c1 (2x2x2 Swordfish in Columns 267)
Eliminating 5 From r8c9 (2x2x2 Swordfish in Columns 267)

The X-Wing is Labelled as X-Wing then Labelled as Swordfish. X-Wing<>Swordfish

We can allow X-wings to be Swordfishes if have Swordfishes only in our arsenal....But why call it Swordfish if we spotted it as X-Wing. That is the idea behingd POINT 7

tarek

[tarek]

regarding TTHsieh puzzles ..... as the second puzzle has an x-wing disguised as a swordfish.... it will always fail rule number 7 (The swordfish after singles should be the same as the Swordfish following all category techniques).

But what if the digit order is reversed during the swordfish searches

Here is a batch Swordfish search following singles:

Code: Select all

.
.
.
*-----------------------------------------------------------------*
| 349    7      3489  | 24589  1      459   | 6      2589   259   |
| 6      2      189   | 589    7      3     | 4      1589   159   |
| 149    18     5     | 6      248    49    | 3      7      129   |
|---------------------+---------------------+---------------------|
| 1259   15     7     | 3      245    1459  | 159    6      8     |
| 8      6      129   | 1259   25     7     | 159    4      3     |
| 1359   4      139   | 159    6      8     | 2      159    7     |
|---------------------+---------------------+---------------------|
| 7      9      14    | 145    3      2     | 8      15     6     |
| 1245   158    6     | 7      458    145   | 159    3      12459 |
| 1245   3      1248  | 1458   9      6     | 7      125    1245  |
*-----------------------------------------------------------------*
Eliminating 2 From r1c9 (2x2x2 Swordfish in Columns 348)
Eliminating 2 From r5c5 (2x2x2 Swordfish in Columns 348)
Eliminating 2 From r9c1 (2x2x2 Swordfish in Columns 348)
Eliminating 2 From r9c9 (2x2x2 Swordfish in Columns 348)
Eliminating 5 From r4c1 (2x3x3 Swordfish in Columns 257)
Eliminating 5 From r4c6 (2x3x3 Swordfish in Columns 257)
Eliminating 5 From r5c4 (2x3x3 Swordfish in Columns 257)
Eliminating 5 From r8c1 (2x3x3 Swordfish in Columns 257)
Eliminating 5 From r8c6 (2x3x3 Swordfish in Columns 257)
Eliminating 5 From r8c9 (2x3x3 Swordfish in Columns 257)
Eliminating 2 From r9c1 (2x2x2 Swordfish in Rows 348)
Eliminating 2 From r5c5 (2x2x2 Swordfish in Rows 348)
Eliminating 2 From r1c9 (2x2x2 Swordfish in Rows 348)
Eliminating 2 From r9c9 (2x2x2 Swordfish in Rows 348)
.
.
.
Complete Solution

We have 3 possible Swordfishes .... none solves the puzzle on its own. From the List we could tell that we need 2 Swordfishes following singles.

The x-wing in 5s comes after the swordfish in 2s

So -as ronk suggests-, if we pick the swordfish in 5s 1st then we only have a swordfish in 2s & we wouldn't encounter an x-wing (a dilemma)

Now, It is left to decide if 2 Swordfishes that can become 1 Swordfish + 1 X-wing can be considered a Pure Swordfish

I'll leave it to Pat to decide on these hanging matters

tarek

[daj95376]

[Withdrawn: All of the constraints and permutations make my head spin and wonder why!]

[ronk]

I suggest that you review ronk's scenario again. The two Swordfish in <2> produce identical eliminations. Applying either obliterates the other.

I agree that complementary swordfish should be counted as one, but I think tarek is saying something else. As I understand it now ...

If first applying swordfish A (and singles) reduces swordfish B to something smaller then, according to the rules of this thread(?), we don't really have two swordfish ... and this is true even if swordfish A remains viable after first applying swordfish B (and singles).

Should there be three simultaneous (non-complementary) swordfish, one might possibly need to check six different solution paths.

[gsf]

this is the old stepwise vs batch argument
to avoid solution path explosion it might be best to assume all applications of a given
technique at a given step are made simultaneously and independently
i.e., first identify all of the applications at the current step and collect the placements/eliminations,
but don't apply them until all have been identified

you can see that the swordfish in TTHsieh's 2nd puzzle are required
and that there are no Xwings when the swords are batched by noting that
the solution path for both of these option sets in my solver are the same

Code: Select all

-v2 -qFNW3-G -Q!FNBTHW2-G -e 'valid&&symmetric&&minimal'

-v2 -qFNW2W3-G -Q!FNBTHW2-G -e 'valid&&symmetric&&minimal'


[tarek]

What I was after is this:

in applying only singles+swordfish: we get 2 Swordfish
in applying the "Lenient" category techniques+Swordfish: we get Either 2 Swordfish or 1 swordfish & 1 X-wing depending on which swordfish you catch 1st

This example shows the problem with BATCHING: in the path that has the x-wing, the swordfish is spotted 1st then the x-wing. The batching would give a result for Swordfish ranging from 1-3 & a 0 for x-wing.

Any suggestions of how to know this information without needing to check the solution paths

if the exact number of swordfishes needed to solve is not important a rough measure would be to report the number of swordfishes needed to solve puzzles as >= (batches of swordfish needed to solve)

Therefore TTHsieh's 2nd puzzle needs >= 1 swordfish to solve

One more thing: We can't say that a puzzle that needs singles+ 6 batches swordfishes to solve when eventually only 1 batch is needed with the full arsenal. On a similar note if that batches are equal but each containing a different number of swordfishes, there is no way of telling what the outcome would be without examining the solution path

Therefore Point 7 would mean that: batches of swordfishes needed to solve following singles = batches of swordfishes needed to solve following category techniques. with the total number of swordfishes possible also equal on both sides. This would probably eliminate some puzzles.

In TTHsieh's 2nd puzzle they are equal (1=1) & (3=3) & would then qualify to be in the "Lenient Category" requiring >=1 swordfish to solve

Does this make sense to anybody

tarek