The New Sudoku Players' Forum

[Gee]

I got to this point in this Sudoku when I could go no further. The program that keeps track of the candidates told me "No hints Available".

I was stumped but after hours of frustration I came up with this bizarre ALS. It solved the puzzle but was I lucky or was I correct in my logic?

AlS A... r7c7,r7c9,r8c7,r8c9,r9c7,r9c8 1,2,4,5,7,8,9

ALS B... r1c7,r2c7,r2c9 2,4,5,9

5 Restricted to A & B

2 is common to A & B

I then eliminated (2) from r5c7 and r5c9

This solved the puzzle so my questions are:

(1) Was I lucky or was I using the proper logic?
(2) Rather than doing what I did, how would you have solved this puzzle?
(3) I have an extremely hard time locating ALS'S. Is there a trick to locating them or is it just an time consuming challenge?

ThanK you for you patience and help.

*-----------*
|2..|...|..1|
|.3.|...|.8.|
|...|6..|7..|
|---+---+---|
|.2.|814|.9.|
|...|.7.|...|
|.8.|235|.4.|
|---+---+---|
|..1|..3|...|
|.5.|...|.3.|
|8..|.5.|..6|
*-----------*


*-----------*
|2..|3..|.61|
|.36|5..|.8.|
|...|6..|7.3|
|---+---+---|
|.27|814|.95|
|...|976|...|
|.89|235|.47|
|---+---+---|
|.61|..3|...|
|.52|.6.|.3.|
|8.3|.5.|..6|
*-----------*


*--------------------------------------------------------------------*
| 2 479 458 | 3 489 789 | 459 6 1 |
| 17 3 6 | 5 249 17 | 249 8 249 |
| 1459 149 48 | 6 2489 1289 | 7 25 3 |
|----------------------+----------------------+----------------------|
| 36 2 7 | 8 1 4 | 36 9 5 |
| 1345 14 45 | 9 7 6 | 1238 12 28 |
| 16 8 9 | 2 3 5 | 16 4 7 |
|----------------------+----------------------+----------------------|
| 479 6 1 | 47 289 3 | 24589 257 2489 |
| 479 5 2 | 147 6 89 | 1489 3 489 |
| 8 479 3 | 147 5 29 | 1249 127 6 |
*--------------------------------------------------------------------*

[re'born]

You can only eliminate the 2 from a cell which sees every 2 in both A and B. Since r5c7 and r5c9 do not see every instance of 2 in both A and B, you cannot safely eliminate 2 from these cells.

[Edit: Sorry, the first step in my solution was nonsense.]

Okay, here is a reasonably understandable solution. First, there is an xy-cycle (see here for details)
[r5c8]-2-[r3c8]-5-[r1c7]=5=[r1c3]-5-[r5c3]-4-[r5c2]-1-[r5c8].

Code: Select all

 *--------------------------------------------------------------------*
 | 2      479    458*   | 3      489    789    | 459*   6      1      |
 | 17     3      6      | 5      249    17     | 249    8      249    |
 | 1459   149    48     | 6      2489   1289   | 7      25*    3      |
 |----------------------+----------------------+----------------------|
 | 36     2      7      | 8      1      4      | 36     9      5      |
 | 1345-  14*    45*    | 9      7      6      | 1238-  12*    28     |
 | 16     8      9      | 2      3      5      | 16     4      7      |
 |----------------------+----------------------+----------------------|
 | 479    6      1      | 47     289    3      | 24589  257-   2489   |
 | 479    5      2      | 147    6      89     | 1489   3      489    |
 | 8      479    3      | 147    5      29     | 1249   127-   6      |
 *--------------------------------------------------------------------*


Thus, we get the eliminations r5c1<>4, r5c17<>1 and r79c8<>2. From here, we may apply the ALS xz-rule to
A={1,4,7,8,9} on r8c1679
B={1,7} on r9c8
x=1
z=7
giving r9c2<>7, which solves the puzzle.