The New Sudoku Players' Forum

[Bob Hanson]

In a previous post on the original thread I alluded to the idea that bennys's "almost-locked sets" could be transferred to the plane of the board and carried out in terms of X-cycles and simple coloring. Here I show how that works using bennys's example:

Code: Select all

+-------------------+-------------------+-------------------+
| 136   1346  24    | 12467 9     8     | 23    245   3457  |
| 3689  34689 7     | 5     246   24    | 1     248   3489  |
| 18    5     2489  | 1247  3     124   | 289   6     478   |
+-------------------+-------------------+-------------------+
| 4    *18   *58    | 9    *168   35    | 368   7     2     |
| 1258  7     3     |*26    1268 *25    | 4     9     168   |
| 1289  189   6     | 234   1248  7     | 5     18    138   |
+-------------------+-------------------+-------------------+
| 7     2     489   | 14    5     149   | 689   3     1468  |
| 3589  3489  1     | 234   24    6     | 7     2458  4589  |
| 356   346   459   | 8     7     12349 | 29    1245  145   |
+-------------------+-------------------+-------------------+

A={R4C2,R4C3,R4C5}
B=(R5C4,R5C6}
x=6
z=5
and we get r4c6<>5

Here A is {18 58 168} and B is {26 25}.
A and B are mutually weakly linked on 6.
Any 5 that weakly links to both A and B can be eliminated.

If we read these not as two sets of cells, but rather two sets of rows, we might have an analogous situation. (Sorry, no ACTUAL example)

Code: Select all

   |---c1--|---c2--|---c3--||---c4--|---c5--|---c6--||---c7--|---c8--|---c9--
-----------------------------------------------------------------------------
r1 |   3   |       |   3   ||       |       |       ||       |       |       
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r2 |       |       |       ||       |   3   |       ||   3   |   3   |       
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r3 |       |       |       ||       |       |       ||   3   |       |   3   
===========================||=======================||=======================
r4 |       |       |       ||       |       |       ||       |       |       
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r5 |       |   3x  |       ||       |       |       ||       |   3x  |   3* 
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r6 |       |       |   3   ||       |   3   |       ||       |       |       
===========================||=======================||=======================
r7 |       |       |       ||       |       |       ||       |       |       
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r8 |   3   |   3   |   3   ||       |       |       ||       |       |       
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r9 |       |       |       ||       |       |       ||       |       |       
-----------------------------------------------------------------------------
      A        A       A                B                        B
-----------------------------------------------------------------------------


Here A is {18 58 168} and B is {26 25}. We're just looking at the rows for possibilities of placing candidate 3 instead of cells for placing specific candidates.

A and B are mutually weakly linked in row 6. (Placing the 6 in a position for one forces no 6 at all for the other.)
Note that the 3 with the * in row 5 can be eliminated. Why? Because if it is NOT eliminated, then the 3s with the x are gone, and we have a 3x3 swordfish-like set for A' and a 2x2 grid X-wing-like pattern for B' AND THEY ARE MUTUALLY EXCLUSIVE, because they would BOTH require a 6 in row 5.

Neat, huh?