- Code: Select all
1489 1489 1489
,--------------------,----------------------,-----------------------,
| 1489 2 3 | 1468 5 1469 | 7 y489–6 x1489 |
| 1489 5 6 |x1478–2 y489–1 x1479–2| 12489 2489 3 |
| 7 B189 B1489 | 12468 14689 3 | 124589 245689 12489 |
:--------------------+----------------------+-----------------------:
| 2 1789 15789 | 1458 3 145 |G1489 4789 6 |
| 3 1689 189 | 12468 7 1246 |G1489–2 2489 5 |
| 168 4 1578 | 9 168 1256 | 1238 2378 128 | \18
:--------------------+----------------------+-----------------------:
| 5 1389 1489 | 134 2 149 | 6 3489 7 |
| 4689 36789 2 | 34567 469 45679 | 34589 1 489 | \489
| 1469 13679 1479 | 134567 1469 8 | 23459 23459 249 | \149
'--------------------'----------------------'-----------------------'
JE (1489) base r3c23, cross-lines c159, cover-houses r689, targets r1c9, r2c5
mirror nodes: the digit in r1c9 must appear with 7 in r2c46 => –2r2c46,
the digit in r2c5 must appear in r1c8 => –6r1c8, –1r2c5; 11.8 skfr -> 10.5
GE (1489) base r3c23, targets r45c7 => –2r5c7; 10.5 -> 10.3
GE explanation: the JE base digits in c7 have only r45c7 left, since:
r17c7 are given as non-base,
r2c7 sees both JE targets,
r689c7 clash with the JE cover-houses.
- Code: Select all
,--------------------,--------------------,-------------------,
| 1489 2 3 | 1468 5 1469 | 7 ay489 x1489 |
| 1489 5 6 | 1478 y489 1479 | 12489 2489 3 |
| 7 B189 B1489 | 2 1489 3 | 5 6 1489 |
:--------------------+--------------------+-------------------:
| 2 1789 15789 | 1458 3 145 |G1489 4789 6 |
| 3 1689 189 | 1468 7 1246 |G1489 2489 5 |
| 168 4 d578–1 | 9 168 256–1 | 1238 c2378 128 |
:--------------------+--------------------+-------------------:
| 5 1389 1489 | 134 2 149 | 6 ab3489 7 |
| 4689 36789 2 | 34567 469 45679 | 3489 a1 489 |
| 1469 3679–1e1479 | 3467–1 1469 8 | 2349 5 249 |
'--------------------'--------------------'-------------------'
The GE restricts the false base digits of the JE. Each of them can have at most one cover-house clash, and one clash is already forced in r689c7.
Also, the base digits are in c8 left with r178c8.
We can take advantage of these properties with an AIC:
1 base = r17c8 base – 3r7c8 = (3–7)r6c8 = 7r6c3 – (7=1|4|9)r9c3 second cover-house clash
If 1 is base, it can be eliminated in the cover-houses, otherwise the cover-house clashes are in r9c3 and r689c7, so all other clashing candidates can be eliminated.
Either way, –1r6c36, –1r9c24; 10.3 -> 10.2.
- Code: Select all
,--------------------,--------------------,-------------------,
| 1489 2 3 | 1468 5 1469 | 7 489 x1489 |
| 1489 5 6 | 1478 y489 1479 | 12489 2489 3 |
| 7 lB189 lB1489 | 2 1489 3 | 5 6 1489 |
:--------------------+--------------------+-------------------:
| 2 1789 15789 | 1458 3 145 |G1489 4789 6 |
| 3 1689 189 | 1468 7 1246 |G1489 2489 5 |
|e6+18 4 f5+78 | 9 168 g2+56 | 1238 b7+238 128 |
:--------------------+--------------------+-------------------:
| 5 1389 1489 | 134 2 149 | 6 c3+489 7 |
|ik489+6 d36+789 2 | 34567 469 45679 |i489+3 1 i489 |
| 1469 d36+79 a7+149 | 3467 1469 8 |j49+23 5 h2+49 |
'--------------------'--------------------'-------------------'
We can locate the second clashing candidate. Assume there is no clash in c23, i.e. –1489r689c23.
r9c3=7, 7r6∈c8, 3c8∈r7, r89c2=36, 6c1∈r6, r6c3=5, r6c6=2, 2c9∈r9, r8c179=489
The 4|9 in r9c7 is forced into r8c1 and b1p89, making it a true base digit, but it cannot appear in the GE targets, contradiction.
Therefore, one of these candidates must be true, causing a second cover-house clash.
The remaining candidates that would cause clashes can be eliminated (1489r689c468).
Also, now we can only have one clash in c7, so one of the false base digits must hide in r2c7. –2r2c7; 10.2 -> 9.5
At this point, it's difficult to find meaningful progress. I ended up eliminating 3r7c8.
Assume 3r7c8. Per the reasoning on c8 just before the AIC, 1 is base. After basics:
- Code: Select all
,-------------------,-----------------,----------------,
|*489 2 3 |a46–8 5 b469 | 7 489 1 |
|*489 5 6 | 17 489 17 | 489 2 3 |
| 7 *189 *1489 | 2 *489 3 | 5 6 489 |
:-------------------+-----------------+----------------:
| 2 1789 15789 |f1458 3 145 | 1489 489 6 |
| 3 1689 189 |f1468 7 2 | 1489 489 5 |
| 168 4 d58 | 9 e18 c56 | 3 7 2 |
:-------------------+-----------------+----------------:
| 5 189 1489 | 14 2 149 | 6 3 7 |
|*49–6 37 2 | 357 *469 57 | 489 1 489 |
| 1469 3679 479 | 37 1469 8 | 2 5 #49 |
'-------------------'-----------------'----------------'
The 4|9 in r9c9 is restricted in r8, r3 and c1, so it must take r8c1.
6r1c4 = 6r1c6 – (6=5)r6c6 – (5=8)r6c3 – 8r6c5 = 8r45c4 => –8r1c4
contradiction with basics
So –3r7c8; 9.5 -> 9.4. After singles:
- Code: Select all
,-------------------,------------------,-----------------,
|z149–8 2 3 | 1468 5 1469 | 7 y489 x1489 |
| 1489 5 6 | 1478 y489 1479 |z149–8 2 3 |
| 7 B189 B1489 | 2 z149–8 3 | 5 6 1489 |
:-------------------+------------------+-----------------:
| 2 189 5 | 148 3 14 |G1489 7 6 |
| 3 1689 189 | 1468 7 2 |G1489 489 5 |
| 168 4 7 | 9 168 5 | 128 3 128 |
:-------------------+------------------+-----------------:
| 5 1389 1489 | 134 2 149 | 6 489 7 |
| 4689 367–89 2 | 5 469 67 | 3489 1 489 |
| 1469 367–9 z149 | 367 1469 8 | 2349 5 249 |
'-------------------'------------------'-----------------'
The cover-house clash in c23 is located in r9c3. => –89r89c2
It's a false base digit and it cannot also clash in c7, so it hides in r2c7, r3c5, r1c1, eliminating 8s.
The digit z in r7c8 is a true base digit:
If it's 4|9, it is in b6 forced into the GE targets,
if it's 8, it is forced into b7p47 and b1p89.
Therefore, in c8, the true base digits take r17c8, so 1 is a false base digit. 9.4 -> 8.3
- Code: Select all
,------------------,------------------,-----------------,
|z149 2 3 | 1468 5 1469 | 7 489 x49–8 |
| 1489 5 6 |ax47–8y489 bx479 |z149 2 3 |
| 7 B89 B489 | 2 z149 3 | 5 6 1489 |
:------------------+------------------+-----------------:
| 2 189 5 |f148 3 14 | 489 7 6 |
| 3 1689 189 |f1468 7 2 | 489 489 5 |
| 68 4 7 | 9 e68 5 | 12 3 12 |
:------------------+------------------+-----------------:
| 5 1389 1489 | 134 2 149 | 6 489 7 |
| 4689 367 2 | 5 d469 c67 | 3489 1 489 |
| 469 367 z1–49 | 367 d1469 8 | 2349 5 249 |
'------------------'------------------'-----------------'
7r2c4 = 7r2c6 – (7=6)r8c6 – 6r89c5 = (6–8)r6c5 = 8r45c4 => –8r2c4, –8r1c9
Suppose (4|9)z. zc9∈r8, 8c9∈r3. Not enough digits for the base, contradiction. z=1; 8.3 -> 7.1
After basics:
- Code: Select all
,----------------,---------------,----------------,
| 1 2 3 |#48–6 5 a46–9| 7 #489 49 |
|*489 5 6 | 47 *489 479 | 1 2 3 |
| 7 B89 B489 | 2 1 3 | 5 6 489 |
:----------------+---------------+----------------:
| 2 189 5 |#148 3 b14 |G9–8 7 6 |
| 3 16 89 |c16 7 2 |G489 #489 5 |
|*68 4 7 | 9 *68 5 | 2 3 1 |
:----------------+---------------+----------------:
| 5 *389 *489 | 134 2 149 | 6 49–8 7 |
| 469–8 367 2 | 5 469 67 | 3489 1 489 |
| 469 367 1 | 367 469 8 | 349 5 2 |
'----------------'---------------'----------------'
8r26\c15 => –8r8c1
8b7\r8 => –8r7c8
8c48\r14b6 => –8r4c7, 9r4c7, 9 base => –9r1c6
(6=4)r1c6 – (4=1)r4c6 – (1=6)r5c4 => –6r1c4
- Code: Select all
,-------------,---------------,---------------,
| 1 2 3 | 48 5 6 | 7 489 x9–4 |
|*48 5 6 | 7 y489 x9–4 | 1 2 3 |
| 7 B9 *B48 | 2 1 3 | 5 6 *48 |
:-------------+---------------+---------------:
| 2 18 5 | 148 3 d14 |G9 7 6 |
| 3 16 9 |c16 7 2 |G48 48 5 |
| 68 4 7 | 9 68 5 | 2 3 1 |
:-------------+---------------+---------------:
| 5 38 48 | 134 2 149 | 6 9–4 7 |
| 6–49#36 2 | 5 @49–6 7 | 348 1 *489 |
|@49–6 7 1 |b#36 469 8 |a34 5 2 |
'-------------'---------------'---------------'
(4G –) (4=3)r9c7 – (3=6)r9c4 – (6=1)r5c4 – (1=4)r4c6 => –4r2c6, 9r1c9, 9c8∈r7
4c9b1\r38c1 => –4r8c1
w-wing 36r8c2, r9c4 connected by 3b9 => –6r8c5, –6r9c1
w-wing 49r8c5, r9c1 connected by 4b9 => –9r8c1, stte
