## ALC-sos

Advanced methods and approaches for solving Sudoku puzzles

### ALC-sos

Almost Locked Candidates - sector overlapping sets

this primer is for advancement of sets using a new approach that dawned on me this fine Christmas evening

Code: Select all
`764..592.291.67..3538..267.387.261..942....676157.423.4762..395129..3786853679412`

this first version take two Almost Hidden Sets in 2 sectors
Row 1 & col 4

ahs a) 18 @ r1c459 or LS a) 138 @ r1c456
AHS b) 138 @ r1235c4

the two sectors are both missing 138 twice for 6 digits, the total number of cells from the two sets is also 6

6 cells with 6 digits
every digit is placed twice with in the two sectors, so that all cells with the 3 digits may only contain those three digits.
r5c4 <> 5

any sector that intersects r1 & c3 ie box 2 cells not in r1,c3 cells also cannot contain the ALC found with in the sets as they are locked to the two sectors
r3c5 <> 1

{full eliminations presented in this xsudo grid}
Code: Select all
`+---------+---------------------------+---------------------+| 7  6  4 | -245679(138)  (138)  5    | 9   2   -245679(18) || 2  9  1 | 4(8)          6-18   7-18 | 58  45  3           || 5  3  8 | 49(1)         49-18  2-18 | 6   7   14          |+---------+---------------------------+---------------------+| 3  8  7 | 59            2      6    | 1   45  49          || 9  4  2 | -245679(138)  1358   18   | 58  6   7           || 6  1  5 | 7             89     4    | 2   3   89          |+---------+---------------------------+---------------------+| 4  7  6 | 2             18     18   | 3   9   5           || 1  2  9 | 45            45     3    | 7   8   6           || 8  5  3 | 6             7      9    | 4   1   2           |+---------+---------------------------+---------------------+`

the next version is also accomplished in the same fashion:

sector box 2, col 2: missing sets 49 , 459 (5 digits)
AHS 49 @ r2c3,r3c45
ALS 459 @ r48c9

5 cells 5 digits
Code: Select all
`+---------+-------------------+------------+| 7  6  4 | 138    138     5  | 9   2   18 || 2  9  1 | 8(4)   6       7  | 58  45  3  || 5  3  8 | 1(49)  -1(49)  2  | 6   7   14 |+---------+-------------------+------------+| 3  8  7 | (59)   2       6  | 1   45  49 || 9  4  2 | 138-5  1358    18 | 58  6   7  || 6  1  5 | 7      89      4  | 2   3   89 |+---------+-------------------+------------+| 4  7  6 | 2      18      18 | 3   9   5  || 1  2  9 | (45)   45      3  | 7   8   6  || 8  5  3 | 6      7       9  | 4   1   2  |+---------+-------------------+------------+`

type 3
Code: Select all
`+---------+---------------------+------------+| 7  6  4 | (138)    138     5  | 9   2   18 || 2  9  1 | (48)     6       7  | 58  45  3  || 5  3  8 | (149)    -1(49)  2  | 6   7   14 |+---------+---------------------+------------+| 3  8  7 | 59       2       6  | 1   45  49 || 9  4  2 | -5(138)  1358    18 | 58  6   7  || 6  1  5 | 7        89      4  | 2   3   89 |+---------+---------------------+------------+| 4  7  6 | 2        18      18 | 3   9   5  || 1  2  9 | 45       45      3  | 7   8   6  || 8  5  3 | 6        7       9  | 4   1   2  |+---------+---------------------+------------+`

{AHS - XZ }
ahs 49 @ r2c4,r3c45
ahs 138 @ r1235c4
RC R3C4, R4C4 => r3c5 <> 1, r5c4 <> 5

the idea is thus:
M sectors with M : combinations of { LS,AHS, ALS }:
so that

Total Cells found in M sectors have N candidates for a 1/1 ratio.

then
M sectors are Locked to X cells all intersections sector of the N sectors may be excluded for the N set
all cells within the combined sets are also exclusive to the N set

i'll probably need some help revising this math as written constructs aren't my best subject
Some do, some teach, the rest look it up.
stormdoku

StrmCkr

Posts: 1336
Joined: 05 September 2006