I have just invented universal technique AIroot, which solves all puzzles (at least have solved so far). It is based on the fact that, there can arrive three types on conflicts, when solving.
1. basic conflicts - there are only N-1 different candidates in N cell in the area
2. fish conflicts - when eliminating number from N rows/columns, it will disappear also from N+1 columns/rows.
3. unique conflicts - this pattern means multiple solutions
When all candidates, which cause conflict immediately, have been eliminated (AIroot link 1), it is time to start linking. Linking take into account all candidates, which cause any type of conflict immediately in the new situation. If any of the conflicts appear in second link, the number can be eliminated by some AIroot link 2 technique. So, the AIroot method is some kind of enlargement of the Trebor's Tabling, because it takes into account all conflict types.
All other techniques can be also be converted to the AIroot. For example: single = AIroot link 1 technique. In normal single all candidates, which can be seen by single cell, can be eliminated. In the AIroot the way of thinking is opposite, illegal candidate cause basic conflict (empty cell), so it can be eliminated. Respectively all fish like and UR techniques are AIroot link 1 techniques.
XY-wings and Bowman Bingo are AIroot link 2 techniques and so on.
It is also quite easy to invent new solving techniques by using simple principles of AIroot. For example:
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Double UR, AIroot link 2:
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| 128 348 x | x x x | x 348 128 |
| 127 347 y | y y y | y 347 127 |
number 8 can be eliminated from cells x and number 7 from cells y
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Unique-fin-fish, AIroot link 2:
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| 1 1 x | x 1 x | x x 1 |
| . . . | . . . | . . . |
| 187 187 . | . . . | . . . |
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| y . . | . . . | . . . |
| y 1 1 | x 1 x | x x 1 |
| y . . | . . . | . . . |
-----------------------------------------------
| 187 187 . | . . . | . . . |
| . . . | . . . | . . . |
| 1 1 x | x 1 x | x x 1 |
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1 = candidate 1 exist in these cells
187 = only these candidates exist
x = candidate 1 doesn't exist
y = candidate 1 can be eliminated
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subset-fish AIroot link 2:
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| x 1y x | x 1 x | x x 1 |
| . y . | . . . | . . . |
| . y . | . . . | . . . |
-----------------------------------------------
| y 132 y | . . . | . . . |
| 1y 1y 1y | x 1 x | x x 1 |
| y 132 y | . . . | . . . |
-----------------------------------------------
| . y . | . . . | . . . |
| . y . | . . . | . . . |
| x 1y x | x 1 x | x x 1 |
-------------------------------------------------
1 = candidate 1 exist in these cells
132 = only these candidates exist
x = candidate 1 doesn't exist
y = candidate 2 can be eliminated
Maybe some of these examples have been already invented.
Regards,
Arto I