Wow - you've given so much to chew over. Taken a few days to catch up to you - so thanks for slowing down for me
Richard those HUGE ALS are so hard to find. Congratulations. Any tips for a wanna be?
Step 14 is quite pretty actually Para - especially compared to the desperation moves later.Para wrote:I am resulting to raw moves nothing beautiful.
15. is great - love those diagonals when they 'line' up like that - at least, they lined up after you pointed it out. Good one.
16. is very clever. This uses 2 7's in one ALS as restricted common. Never thought of that before - only ever look for ALS with a single isolated digit.
17-19. Chains. Finally get rid of some of those ubiquitous 6's. Couldn't work them out at first - but are very clever, and are pretty easy to see once you get the hang.
With these chains, why just stop at 9 links? When is an xy chain too long?
For example, using the same technique with both the 2's in n8 starting from the end of step 16, the xy chains for both just keep going and going. It seems to me that in this case, why not just keep them going? There is so much info they can tell you.
1. An xy chain may eventually reach a contradiction. Of course, that tells you that candidate cannot be in that first cell ( which does happen with one of these chains with the 2's)
But even if there is no contradiction, there is still so much they can tell you.
2.For example, with these 2's in n8, many of the same cells are filled for both chains -> only those two candidates can be in that cell, any others eliminated.
3. Some of the cells have identical placements for both chains - so obviously they are definites.
Any-way, just for the exercise I followed this through. Not right to the end, but with an equal number of links for both chains.
XY Chains with 2 in r8c4 end up with marks here
Code: Select all
.---------------.---------------.---------------.
| 3 1 689 | 7 5 689 | 4 2 69 |
| 2 689 5 | 4 3 689 | 1 689 7 |
| 469 4689 7 | 689 2 1 | 3 689 5 |
:---------------+---------------+---------------:
| 69 5 3 | 689 1 2 | 69 7 4 |
| 1 7 69 | 69 4 3 | 2 5 8 |
| 8 2 4 | 5 7 69 | 69 3 1 |
:---------------+---------------+---------------:
| 469 4689 1 | 3 68 7 | 5 689 2 |
| 5 68 68 | 2 9 4 | 7 1 3 |
| 7 3 2 | 1 68 5 | 689 4 69 |
'---------------'---------------'---------------'
Code: Select all
.---------------.---------------.---------------.
| 3 1 69 | 8 5 79 | 67 4 2 |
| 2 8 56 | 4 137 137 | 167 9 1567|
| 49 459 7 | 6 2 19 | 3 8 15 |
:---------------+---------------+---------------:
| 169 59 3569| 2 137 8 | 167 567 4 |
| 16 7 356 | 9 4 13 | 2 56 8 |
| 8 2 4 | 5 17 6 | 9 3 17 |
:---------------+---------------+---------------:
| 49 49 1 | 3 8 2 | 5 67 67 |
| 5 6 2 | 7 9 4 | 8 1 3 |
| 7 3 8 | 1 6 5 | 4 2 9 |
'---------------'---------------'---------------'
Which gets the puzzle to here. There are more chains in one of the marks pics, so more info could be had this way. And this is just with one of the potential chains.
Code: Select all
.---------------------.---------------------.---------------------.
| 3 1 689 | 78 5 6789 | 46789 24 269 |
| 2 689 5689 | 4 13678 136789| 16789 689 15679 |
| 469 45689 7 | 689 2 1689 | 3 689 1569 |
:---------------------+---------------------+---------------------:
| 169 569 3569 | 2689 1367 28 | 1679 5679 4 |
| 169 7 3569 | 69 4 1369 | 2 569 8 |
| 8 2 4 | 5 167 69 | 1679 3 1679 |
:---------------------+---------------------+---------------------:
| 469 4689 1 | 3 68 27 | 5 26789 2679 |
| 5 68 268 | 27 9 4 | 78 1 3 |
| 7 3 28 | 1 68 5 | 4689 24 269 |
'---------------------'---------------------'---------------------'
OK, now getting back on track.
This is where I think we are at at the end of step 24
Code: Select all
.---------------------.---------------------.---------------------.
| 3 1 2689 | 6789 5 6789 | 46789 246789 269 |
| 269 689 25689 | 4 13678 136789| 16789 689 125679|
| 469 45689 7 | 689 2 1689 | 3 689 1569 |
:---------------------+---------------------+---------------------:
| 1269 2569 23569 | 2689 1367 26789 | 1679 5679 4 |
| 169 7 3569 | 69 4 1369 | 2 569 8 |
| 8 269 4 | 5 17 269 | 1679 3 1679 |
:---------------------+---------------------+---------------------:
| 2479 2489 1 | 3 68 2678 | 5 26789 2679 |
| 5 68 268 | 27 9 4 | 78 1 3 |
| 279 3 289 | 1 678 5 | 46789 246789 269 |
'---------------------'---------------------'---------------------'