The New Sudoku Players' Forum

[Leren]

Well, that seemed to be an on topic puzzle. Try this one.

Code: Select all

*-----------*
|...|...|...|
|...|...|...|
|...|...|...|
|---+---+---|
|...|...|...|
|...|.12|...|
|...|...|345|
|---+---+---|
|...|16.|...|
|..7|.5.|...|
|.24|...|8..|
*-----------*
........................................12.........345...16......7.5.....24...8..

Leren

[m_b_metcalf]

Well, that seemed to be an on topic puzzle. Try this one.

Thanks. That was more interesting and longer. But I slipped up near the end

[Hajime]

After the basics I ended here:

Code: Select all

+----------------+---------------+----------------+     
|  48  3579 12356|34789 23789 156| 156 36789 24789|     
|23679  48  12356|34789 23789 156| 156  2789 13789|     
|23679 3579   23 |34789 23789 156|2479 36789 13789|     
+----------------+---------------+----------------+     
| 789   789   89 |  5     4    3 | 16    26    12 |     
|  34   345   35 |  6     1    2 | 79   789   789 |     
|  26    1    26 | 789   789   79|  3    4     5  |     
+----------------+---------------+----------------+     
| 389   389   89 |  1     6    4 | 27    5     27 |     
|  1     6    7  |  2     5    8 | 49    39   349 |     
|  5     2    4  | 379   379   79|  8    1     6  |     
+-------------------------------------------------+     
                                                       
Generalized Intersections:
 (2)c7,r3,\ => (-2)r3c3
 (2)\,r3,c7 => (-2)r3c7
 (3)\,r3,c8 => (-3)r3c8
 (2)\,r7 => (-2)r7c9

but I could not find all 4 Generalized Intersections manually.

btte

[m_b_metcalf]

Here's a third:

Code: Select all

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

[Leren]

Hajime, only the first Generalised Intersection is needed. After marking off r3c3 = 3, the next single is r1c8 = 3, only 3 in Column 8. Further singles follow almost to the end.

And another puzzle for pencil, paper - and a big rubber ! .......................................1...23.456.....3........27..........85.9..

Leren

[Hajime]

and a big rubber ! .......................................1...23.456.....3........27..........85.9.. Leren

I learned, after basics next sitiation:

Code: Select all

+-------------------+----------------------+--------------------+     
|56789 123689 123467|234579 1234679 1236789| 4678  456789   12  |     
|56789 123689 123467|234579 1234679 1236789| 4678    13   456789|     
|56789 123689 123467|234579 1234679 1236789|  123  456789 456789|     
+-------------------+----------------------+--------------------+     
| 189    23     23  |  79     789      5   | 1468   14689  14689|     
| 6789   689    67  |   1      89      4   |   5      2      3  |     
| 189     4      5  |   6      23      23  |  178   1789   1789 |     
+-------------------+----------------------+--------------------+     
|  3      5     89  | 2479   124679  12679 |124678  14678 124678|     
|  2      7     89  |  349   13469    1369 | 13468 134568  14568|     
|  4     16     16  |   8      5      237  |   9     37     27  |     
+---------------------------------------------------------------+     


Than gen. intersections: (2)r9,c6,\ => (-2)r6c6 , stte

Edit: added interim situation

[Hajime]

Here's a third:

Code: Select all

...........1......2..3451.........6..46...57..5.........2173..8......4...........

After basics

Code: Select all

+------------+------------+-----------+     
| 389 38   4 | 67  1   67 |289  289  5|     
|  5   7   1 | 89  29  289| 3    4   6|     
|  2   6  89 | 3   4    5 | 1   89   7|     
+------------+------------+-----------+     
|  1   2 3789| 5   38  79 | 89   6   4|     
| 389  4   6 | 2   38   1 | 5    7  39|     
|3789  5 3789| 79  6    4 |289 2389  1|     
+------------+------------+-----------+     
|  4   9   2 | 1   7    3 | 6    5   8|     
| 378 38 3578|689 259 2689| 4    1  39|     
|  6   1  358| 4   59  89 | 7   39   2|     
+-------------------------------------+     


An XY-wing [length 3 cells] (3)(3=8)r4c5-(8=9)r4c7-(9=3)r5c9 => (-3)r5c5
Then some naked singles

Code: Select all

+---------+---------+---------+     
| 3  8  4 |67  1  67| 29 29  5|     
| 5  7  1 |89 29 289| 3   4  6|     
| 2  6  9 | 3  4  5 | 1   8  7|     
+---------+---------+---------+     
| 1  2  78| 5  3  79| 89  6  4|     
| 9  4  6 | 2  8  1 | 5   7  3|     
|78  5  3 |79  6  4 |289 29  1|     
+---------+---------+---------+     
| 4  9  2 | 1  7  3 | 6   5  8|     
|78  3 578|68 25 268| 4   1  9|     
| 6  1  58| 4 59  89| 7   3  2|     
+-----------------------------+     


Another XY-wing [length 3 cells] (8)(8=7)r4c3-(7=9)r4c6-(9=8)r9c6 => (-8)r9c3
naked singles to the end
of course not a manual solve

[Pat]

Code: Select all

*-----------*
|...|...|...|
|...|...|...|
|...|...|...|
|---+---+---|
|...|...|...|
|...|...|.12|
|.3.|.45|...|
|---+---+---|
|.5.|...|67.|
|...|2.8|...|
|...|1..|4..|
*-----------*
...........................................12.3..45....5....67....2.8......1..4..

Here is a puzzle from me. Only 12 clues. This should be tough.

Leren

i have now re-posted your puzzle,
hoping my solution-path is OK

[m_b_metcalf]

The theme of this thread is well taken though. In X solving there are often a lot of intersection moves and it's easy for a manual solver to miss one, making an otherwise easy puzzle seem hard.

Indeed. Here is a prime example involving lots of such moves (my program counts 17!).

Code: Select all

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

...1.2.......3.......4.5...2.6...7.3.8.....2.7.5...1.9...9.6.......7.......5.3...

Regards,

Mike

[Leren]

Hi Mike, I solved this puzzle with 11 "Intersections". I suspect that there is some definitional ambiguity as to what is, or is not, an Intersection move.

Leren

[m_b_metcalf]

Hi Mike, I solved this puzzle with 11 "Intersections". I suspect that there is some definitional ambiguity as to what is, or is not, an Intersection move.

Leren, I think there are two points. The first is that I notice that using an intersection doesn't necessarily yield a useful elimination. So one could distinguish between useful ones that advance the solution and redundant ones that don't. Secondly, as you point out, there is the question of definition. I use:

1) If a value occurs exactly twice on a diagonal, say at i,i and j,j, then that value cannot occur at at i,10-i and j,10-j.

2) If a value ocuurs exaclty twice on a row (column) and one of those positions is on a diagonal, say at i,i and i,j, then that value cannot occur at j,j.

In the meantime, I've found an easy 12-clue puzzle with, by my count, 19 intersections:

Code: Select all

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

................1...2..................3.4..........5..3....6.......74..7..85....

Regards,

Mike

[Hajime]

Hi Mike, I solved this puzzle with 11 "Intersections". I suspect that there is some definitional ambiguity as to what is, or is not, an Intersection move.

I use:
1) If a value occurs exactly twice on a diagonal, say at i,i and j,j, then that value cannot occur at at i,10-i and j,10-j.
2) If a value ocuurs exaclty twice on a row (column) and one of those positions is on a diagonal, say at i,i and i,j, then that value cannot occur at j,j.

This is exactly what Pat pointed out to me in http://forum.enjoysudoku.com/post333515.html#p333515
For me it are still 3 houses that intersect where the candidate k is locked in a diagonal in 2 cells and the cell that see both (via row and col) can eliminate k.
Part of Generalized locked candidates or singles in http://forum.enjoysudoku.com/generalized-methods-t38209.html#p294161

[Leren]

Hi Mike, I see that I'm cross posting with Hajime but I'll continue on anyway.

Something you don't appear to have covered is this move in the second puzzle.

Code: Select all

*---------------------------------------------------------*
| 5     1789 136789 | 129  13789  1689 | 2789  2689 4     |
| 3689  4    36789  | 29   3789   689  | 5     1    2679  |
| 689   1789 2      | 5    4      1689 | 3     689  679   |
|-------------------+------------------+------------------|
| 23689 189  13689  | 7    129-8  5    | 1289  4    12369 |
| 2689  5    16789  | 3   *89     4    | 12789 2689 12679 |
| 4     1789 13789  | 6    129-8 *189  | 12789 5    12379 |
|-------------------+------------------+------------------|
| 189   3    89     | 4    19     2    | 6     7    5     |
| 19    2    5      | 19   6      7    | 4     3    8     |
| 7     6    4      | 8    5      3    | 129   29   19    |
*---------------------------------------------------------*

This is the diagonal equivalent of a claiming intersection : if there are 2 or 3 X's on a diagonal in the one box then X can be removed from the 6 cells in the box not on the diagonal.

Other possible (not substantial, but stylistic) quirks about intersections.

A. In your 1) if there is a naked or hidden pair on a diagonal, this can show up as two intersections using the same two cells but two different values.

B. It may be possible that a program looks for all intersections before reverting to singles logic. Depending on the puzzle that may speed up execution time but result in more intersections.

As I've cross posted I'll stop here.

<Edit> Re-reading the title of this thread I've realised that A and or B (to some extent) is what a human solver might do sometimes. It all depends on their experience and pattern spotting skills.

I think A happened twice for the first puzzle, so a clever human solver might have solved the puzzle with 4 less intersection moves than I said plus 2 Naked/Hidden pair moves.

Cheers, Leren

[m_b_metcalf]

This is the diagonal equivalent of a claiming intersection : if there are 2 or 3 X's on a diagonal in the one box then X can be removed from the 6 cells in the box not on the diagonal.

Yes, I have this coded but count it under a different heading.
Thanks for your interest.

Regards,

Mike

[m_b_metcalf]

Here are two more jolly, 12-clue puzzles:

Code: Select all

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

.................1..2.....3........245............1..6..............67..8.....5..     

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

....................1.2..34...........2.........5.........3....67....5.88........     


Regards,

Mike