Cec wrote:Hi tarek. I can identify this xy-wing which would exclude candidate3 from r9c7. Could you please define how the notation would be written to explain this xy-wing?
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*-----------------------------------------------*
| 1 3 4 | 9 7 2 | 6 5 8 |
| 9 278 27 | 18 6 5 | 4 12 3 |
| 6 258 25 | 18 4 3 | 12 9 7 |
|---------------+---------------+---------------|
|*45 29 8 | 7 29 1 |*35 34 6 |
| 7 249 6 | 3 259 8 | 15 14 29 |
| 35 1 23 | 4 259 6 | 7 8 29 |
|---------------+---------------+---------------|
| 2 57 357 | 6 1 9 | 8 37 4 |
| 8 67 1 | 2 3 4 | 9 67 5 |
|*34 46 9 | 5 8 7 |-23 236 1 |
*-----------------------------------------------*
Eliminating 3 From r9c7 (5 & 4 in r4c1 form an XY wing with 3 in r4c7 & r9c1)
I'm not sure that I understood your question Cec, is it the proof your after? ....if it is, then the shortest forcing chains & xy chains of the discontinuous type would do the trick:
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Candidates in r4c1 will force r9c7 to contain only 2:
r4c1=5 => r4c7=3 => r9c7=2
r4c1=4 => r9c1=3 => r9c7=2
Therefore r9c7<>3 & r9c7=2
If you're after a NICE loop then I'm not your guy, but I've noticed NICE guys would start from r9c7 using links ending again in r9c7 using the cells forming the xy wing.......
[Edit: the proper term was links]
tarek