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*--------------------------------------------------------------------------------*
| 289 3 28 | 5 1 4 | 279 27 6 |
| 2569 7 256 | 2369 23 2-6 | 14 14 8 |
|b269 4 1 |a269 7 8 | 259 3 259 |
|--------------------------+--------------------------+--------------------------|
| 12578 1258 2578 | 4 6 19 | 12579 1257 3 |
| 4 15 9 | 23 23 7 | 8 6 15 |
| 3 6 27 | 8 5 19 | 12479 1247 1249 |
|--------------------------+--------------------------+--------------------------|
| 2568 9 3 | 1 48 256 | 2456 245 7 |
|c1256 125 4 | 7 9 d256 | 3 8 125 |
| 125678 1258 25678 | 2-6 48 3 | 12456 9 1245 |
*--------------------------------------------------------------------------------*
Your next move would be a Skyscraper in 6's.
Note that there are 2 6's in Rows 3 and 8 in the cells marked a,b,c & d.
If you assume that the 6 in cell a is False => 6 in b is True => 6 in c is False => 6 in d is True.
If you assume that the 6 in cell d is False => 6 in c is True => 6 in b is False => 6 in a is True.
The net result of this is that at least 1 of the 6's in cells a and d must be True.
Since r2c6 and r9c4 can see both of these cells then you can remove the 6's from those cells.
Several basic eliminations should get you to here:
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*--------------------------------------------------------------------------------*
| 289 3 28 | 5 1 4 | 279 27 6 |
| 569 7 56 | 69 3 2 | 14 14 8 |
| 269 4 1 | 69 7 8 | 259 3 259 |
|--------------------------+--------------------------+--------------------------|
| 12578 1258 2578 | 4 6 19 | 12579 1257 3 |
| 4 *15 9 | 3 2 7 | 8 6 *15 |
| 3 6 27 | 8 5 19 | 12479 1247 1249 |
|--------------------------+--------------------------+--------------------------|
| 2568 9 3 | 1 48 56 | 2456 245 7 |
|f1256 *125 4 | 7 9 56 | 3 8 *125 |
| 15678 58-1 5678 | 2 48 3 | 1456 9 145 |
*--------------------------------------------------------------------------------*
There is a finned XWing in 1's in r58/c29 with a fin at r8c1, which removes the 1 from r9c2. Hopefully you understand how finned XWings work.
The next move is not the simplest, but it solves a cell and makes the solution shorter.
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*--------------------------------------------------------------------------------*
| 289 3 28 | 5 1 4 | 279 27 6 |
| 569 7 56 | 69 3 2 | 14 14 8 |
| 269 4 1 | 69 7 8 | 259 3 g29-5 |
|--------------------------+--------------------------+--------------------------|
| 12578 1258 2578 | 4 6 19 | 12579 1257 3 |
| 4 b15 9 | 3 2 7 | 8 6 a15 |
| 3 6 27 | 8 5 19 | 12479 1247 f1249 |
|--------------------------+--------------------------+--------------------------|
| 2568 9 3 | 1 48 56 | 2456 245 7 |
| 1256 125 4 | 7 9 56 | 3 8 125 |
| 15678 c58 5678 | 2 d48 3 | 1456 9 e145 |
*--------------------------------------------------------------------------------*
The chain notation for this move is (5=1) r5c9 - (1=5) r5c2 - (5=8) r9c2 - (8=4) r9c5 - (4) r9c9 = (4-9) r6c9 = (9) r3c9
Basically what it says that if you assume 5 is False in r5c9 and follow the True/False implications in cells abcdefg then you must conclude that 9 is True in r3c9, in particular 5 is False in r3c9.
Obviously if 5 is True in r5c9 then 5 is False in r3c9. So, since 5 can only be True or False in r5c9 it can be removed from r3c9.
This solves r3c7 = 5 and leads you to here:
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*--------------------------------------------------------------------------------*
| 289 3 28 | 5 1 4 | 279 27 6 |
| 569 7 56 | 69 3 2 | 14 14 8 |
|b269 4 1 | 69 7 8 | 5 3 a29 |
|--------------------------+--------------------------+--------------------------|
| 12578 1258 2578 | 4 6 19 | 1279 1257 3 |
| 4 15 9 | 3 2 7 | 8 6 15 |
| 3 6 27 | 8 5 19 | 12479 1247 1249 |
|--------------------------+--------------------------+--------------------------|
|c2568 9 3 | 1 48 56 |d246 e245 7 |
| 1256 125 4 | 7 9 56 | 3 8 15-2 |
| 15678 58 5678 | 2 48 3 | 146 9 145 |
*--------------------------------------------------------------------------------*
This move is a grouped Skyscraper in 2's. The logic is similar to the previous Skyscraper except that there are 3 2's in Row 7.
Basically this shows that at least one of cells a, d or e must be 2. Since r8c9 can see all of these cells the 2 there can be removed.
Only basic moves are then required to solve the puzzle.
Take a look at the following site which gives explanations of the solving methods I've used :
http://hodoku.sourceforge.net/en/techniques.phpOn that site the second last move is an AIC type 2. The grouped skyscraper can also be thought of as a Sashimi finned XWing.
Leren