skfr 7.7
..5..237.1...5...42..3....13..9....64......5..1...89..........5...8.........4621.
.-------------------------.--------------------.-------------------.
|x689 4689 5 | 146 1689 2 | 3 7 #89 |
| 1 36789 36789 | 67 5 79 | 68 2 4 |
| 2 46789 46789 | 3 6789 479 | 5 689 1 |
:-------------------------+--------------------+-------------------:
| 3 2578 278 | 9 127 45 | 1478 48 6 |
| 4 26789 26789 | 1267 12367 137 | 178 5 2378 |
| 567 1 267 | 45 2367 8 | 9 34 237 |
:-------------------------+--------------------+-------------------:
| 6789 2346789 12346789 | 127 12379 1379 | 4678 34689 5 |
| 5679 2345679 1234679 | 8 12379 13579 | 467 3469 379 |
|x89-57 35789 3789 | 57 4 6 | 2 1 x3789 |
'-------------------------'--------------------'-------------------'
kirara0048 wrote:This ALS XZ pattern should also be the WXYZ-Wing, but not detected as latter.
[/code][/hidden]
.-----------------------.---------------------.--------------.
| 3 1568 568 | 16 18 9 | 7 4 2 |
| 2479 1279 247 | 5 1347 1247 | 6 8 39 |
| 246789 26789 24678 | 23467 3478 24678 | 39 1 5 |
:-----------------------+---------------------+--------------:
| 2478 23578 234578 | 2479 4579 247 | 2389 6 1 |
| 1 2357 9 | 8 6 247 | 23 57 34 |
| 24678 25678 245678 | 12479 14579 3 | 289 57 49 |
:-----------------------+---------------------+--------------:
| 789 789 1 | 479 2 478 | 5 3 6 |
| 268 4 2368 | 36 38 5 | 1 9 7 |
| 5 3679 367 | 13679 1379 167 | 4 2 8 |
'-----------------------'---------------------'--------------'
Sue de Coq(Cannibalized): r23c6 - {124678} (r1c45 - {168}, r457c6 -{2478}) => r2c5<>1 r3c4<>6 r9c6<>7 r1c2<>8 r1c3<>8 r3c5<>8 r3c6<>8 r7c1<>8 r7c2<>8 r8c5<>8
+-----------------------+--------------------------+--------------+
| 3 156-8 56-8 | (16) (+8-1) 9 | 7 4 2 |
| 2479 1279 247 | 5 347-1 (1247) | 6 8 39 |
| 246789 26789 24678 | 2347-6 347-8 (2467-8) | 39 1 5 |
+-----------------------+--------------------------+--------------+
| 2478 23578 234578 | 2479 4579 (247) | 2389 6 1 |
| 1 2357 9 | 8 6 (247) | 23 57 34 |
| 24678 25678 245678 | 12479 14579 3 | 289 57 49 |
+-----------------------+--------------------------+--------------+
| 79-8 79-8 1 | 479 2 (+8-47) | 5 3 6 |
| 268 4 2368 | 36 3-8 5 | 1 9 7 |
| 5 3679 367 | 13679 1379 16-7 | 4 2 8 |
+-----------------------+--------------------------+--------------+
2 ALS 2 restricted common rule
------------------------------
If A have degrees of freedom of 2
and B and C are ALS
with
x restricted common to A and B
y restricted common to A and C
and z common to A B C
then you cant have z in a cell that can see all the z candidates in A B C
doubly linked rule : {see 2nd example}
with
w,x restricted common to A & B
y,z restricted common to A & C
all Restricted commons cannot be in A as it can only occupy 2 of the 4 thus B,C must contain at least 1 of each of the RC's
digits w x of A & B are restricted to A & B
digits y z of A & C are restricted to A & C
Digis not equal to wxyz of ABC are restricted to ABC
+-----------------+---------+--------------+
| . . . | . . . | . . . |
| . (123) . | . . . | (14) -2 -2 |
| (34) -2 -2 | . . . | (24) . . |
+-----------------+---------+--------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------------+---------+--------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------------+---------+--------------+
AaLS - 2RC
Set a) [123] @ R2C2
Set b) [234] @ R3C17
Set C) [124] @ R23C7
X:3,Y:1
Z:2 => R2C89, R3C23 <> 2
+----------------------+------------------------+----------------------+
| 12789 3 1489-7 | 5 (278) (78) | 6 147 1248 |
| 1278 128 6 | (2378) 4 9 | 1237 5 1238 |
| 5 28 478 | (2367-8) 1 36-78 | 2347 347 9 |
+----------------------+------------------------+----------------------+
| 169 7 159 | 29-36 2356 356 | 123459 8 12345 |
| 1689 1589 2 | 4 35678 35678 | 13579 1379 135 |
| 3 4 589 | 2789 2578 1 | 2579 79 6 |
+----------------------+------------------------+----------------------+
| 4 (159) (1579) | (367) 356-7 2 | 8 136-9 135 |
| 278-9 28-59 3 | 1 5678 45678 | 459 469 45 |
| (18) 6 (158) | (38) 9 345-8 | 1345 2 7 |
+----------------------+------------------------+----------------------+
Aals -2rc
a) 3 6 7 8 @ 57 75
b) 2 3 6 7 8 @ 4 5 12 21
c) 1 5 7 8 9 @ 55 56 72 74
rc: 3 6 7 8
z: 1 2 3 5 6 7 8 9
potential eliminations:
54 63 64 65 73 <> 1,5
3 13 14 22 23 <> 2
3 30 39 48 66 <> 3,6
54 58 59 60 61 62 <> 7
73 76 77 78 79 80 <> 8
54 58 59 60 61 62 63 64 65 73 <> 9
n ALS n restricted common rule
-----------------------------
If A have degrees of freedom of n
and we have a collection S of n disjoint ALS (that are also disjoint with A)
each of the ALS has different restricted common with A
and z common to A and all the members of S
then we cant have z in a cell that can see all the z candidates in A and all the members of S.
+--------------------+--------------------+---------------------+
| 39-1 (1379) 2579 | (17) 1247 8 | 1459 123459 6 |
| (16) 4 257 | 3 1267 9 | 8 125 12 |
| 8 (1369) 29 | 5 1246 46 | 7 12349 1234 |
+--------------------+--------------------+---------------------+
| 39 58 1 | 679 34679 34567 | 2 4679 478 |
| 7 (39) 4 | 2 8 36 | 169 169 5 |
| 2 58 6 | 179 1479 457 | 3 479 478 |
+--------------------+--------------------+---------------------+
| 4 267 3 | 8 567 1 | 56 2567 9 |
| 169 1679 79 | 4 35679 2 | 156 8 137 |
| 5 12679 8 | 679 3679 367 | 146 123467 12347 |
+--------------------+--------------------+---------------------+
A={R1C2,R3C2,R5C2}
B={R2C1}
C={R1C4}
X=6
Y=7
Z=1
Elimination: R1C1 <> 1
StrmCkr wrote:http://forum.enjoysudoku.com/almost-locked-rules-for-now-t2510-15.html some stuff to add if you have time