It is not true, that without the extra candidates you always would run into a BUG.
This is a counter example with the grid after singles. Only 0 or 2 candidates of 349 in unsolved cells except in r3c9.
But r3c9=2, not 3.
- Code: Select all
.....25....15......6.1.7.8..32..4...1.....7.......89.4....7....6.52.....94.....7.
+-------------------+-------------------+-------------------+
|*34 8 7 |*49 6 2 | 5 *149 *139 |
|*34 2 1 | 5 8 *39 |*346 *469 7 |
| 5 6 9 | 1 *34 7 |*234 8 #2+3 |
+-------------------+-------------------+-------------------+
| 8 3 2 | 7 9 4 | 16 156 156 |
| 1 9 4 | 6 2 5 | 7 3 8 |
| 7 5 6 | 3 1 8 | 9 2 4 |
+-------------------+-------------------+-------------------+
| 2 1 8 |*49 7 *369 |*346 *4569 *3569 |
| 6 7 5 | 2 *34 *139 | 8 *149 *139 |
| 9 4 3 | 8 5 16 | 126 7 126 |
+-------------------+-------------------+-------------------+
[Added for clarity:] The problem is the same as with "normal" BUGs: Not every grid with 2 candidates per cell is a BUG, additionally each candidate has to be exactly twice in each unit.