this primer is for advancement of sets using a new approach that dawned on me this fine Christmas evening
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764..592.
291.67..3
538..267.
387.261..
942....67
6157.423.
4762..395
129..3786
853679412
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}
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+---------+---------------------------+---------------------+
| 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
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+---------+-------------------+------------+
| 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
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+---------+---------------------+------------+
| 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
