The New Sudoku Players' Forum

[eleven]

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

Finding interesting puzzles is just too time consumimg Back to home office tomorrow ...

[Leren]

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*--------------------------------------------*
| 1679-3 16789 168 | 56 89  2  | 358 69  4   |
|a2369c  2689  5   | 4  1   89 | 8-3 269 7   |
|a269c   4     268 | 56 7   3  | 58  269 1   |
|------------------+-----------+-------------|
| 579c   579   3   |b78 2   6  | 1   4   89  |
| 8      1267  126 | 17 349 49 | 26  5   39  |
|a1269c  1269  4   |b18 39  5  | 26  7   389 |
|------------------+-----------+-------------|
| 15c    158   18  | 9  6   7  | 4   3   2   |
|a26c    26    7   | 3  48  48 | 9   1   5   |
| 4      3     9   | 2  5   1  | 7   8   6   |
*--------------------------------------------*

(3=1) r2368c1 - (1=7) r46c4 - (7=3) r234678c1 => - 3 r1c1, r2c7; stte

Leren

[eleven]

Same solution. In this presentation it looks like it would be very hard to spot it manually.

But if you see
7r4c4 -> 7r1c1 and
1r6c4 -> 269r368c1 -> 3r2c1
you already have it.

[Cenoman]

(3=1) r2368c1 - (1=7) r46c4 - (7=3) r234678c1 => - 3 r1c1, r2c7; stte

In this presentation it looks like it would be very hard to spot it manually.

Why not use AHSs rather than cumbersome ALSs ?
(571)r147c1 = r6c1 - (1=87)r46c4 - r4c1 = (7)r1c1 => -3r1c1; ste
Such logic is definitely equivalent to yours (altough it seems not) AHSs are easier to spot, as they are made of bilocation values only.

My solution:

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 +------------------------+------------------+--------------------+
 | e13679   16789   168   |  56  b89#   2    | d358   69    4     |
 |  2369    2689    5     |  4    1    c89   | c38    269   7     |
 |  269     4       268   |  56   7     3    |  58    269   1     |
 +------------------------+------------------+--------------------+
 | e579     579     3     | a8-7  2     6    |  1     4    a89#   |
 |  8       1267    126   |  17   349*  49   |  26    5     39*   |
 |  1269    1269    4     |  18   39*   5    |  26    7     389*  |
 +------------------------+------------------+--------------------+
 |  15      158     18    |  9    6     7    |  4     3     2     |
 |  26      26      7     |  3    48    48   |  9     1     5     |
 |  4       3       9     |  2    5     1    |  7     8     6     |
 +------------------------+------------------+--------------------+

UR(39)r56c59 using externals
(89)r4c49 == (9)r1c5 - (9=83)r2c67 - r1c7 = (37)r14c1 => -7 r4c4; lclste

...or a bit longer, but with ste finish, using mixed external internal:

Hidden Text: Show

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 +------------------------+------------------+--------------------+
 | F13679   16789   168   | A56  B89#   2    | G38-5 A69    4     |
 |  2369    2689    5     |  4    1     89   | c38    269   7     |
 |  269     4       268   |  56   7     3    |  58    269   1     |
 +------------------------+------------------+--------------------+
 | F579     579     3     |  78   2     6    |  1     4    a89    |
 |  8       1267    126   |  17   349*  49   |  26    5     39*   |
 | E1269    1269    4     | D18   39*   5    |  26    7    C389*  |
 +------------------------+------------------+--------------------+
 | F15      158     18    |  9    6     7    |  4     3     2     |
 |  26      26      7     |  3    48    48   |  9     1     5     |
 |  4       3       9     |  2    5     1    |  7     8     6     |
 +------------------------+------------------+--------------------+

(5=69)r1c48 - (9)r1c5 == (8)r6c9 - (8=1)r6c4 - r6c1 = (157-3)r147c1 = (3)r1c7 => -5r1c7; ste

[Leren]

Cenoman wrote : Why not use AHSs rather than cumbersome ALSs

I thought of replacing that last large ALS myself but I was a bit tired at the time.

Now I've had more time, I think the best way is (3=1) r2368c1 - (1=7) r46c4 - [ (7) r4c1 = (7-3) r1c1 = (3) r1c2 ], which uses less cells.

The part in [ ] is a Purple Cow snippet, which I find can often be used instead of a large ALS. Leren

[eleven]

Why not use AHSs rather than cumbersome ALSs ?
(571)r147c1 = r6c1 - (1=87)r46c4 - r4c1 = (7)r1c1 => -3r1c1; ste

You are right. At least RW would have solved it quickly without pencilmarks.