HP04 Solving “hardest puzzles” continued

 

More on p1 SK loop

 

If I have a look on my data base of external hardest having the SK loop, I find 838 puzzles spread over 168 patterns.

 

The 2 that seem the hardest,

 

500000009020100070008000300040600000000050000000207010003000800060004020900000005 m_b_metcalf

500000009020100070008000300040002000000050000000706010003000800060004020900000005 StrmCkr

 

Are the only ones found on a 20 clues pattern (the same one). Some patterns have been looked much more and one pattern has 89 puzzles included in that data base. Easter Monster is part of that group.

 

Compared to the EXOCET and especially to the 3 digits EXOCET, this is a relatively low frequency.

 

However, I noticed, competing in the pattern game that some pattern generated many puzzles having the SK loop. During that game, I personally generated more than 37 000 such puzzles.

 

The entire list corresponding to that generation is on my web site here.

 

In the same game, I only found 16 puzzles having an EXOCET pattern (all of them 3 digits);

 

Puzzles having the SK loop pattern cover nearly all the top list of SE ratings for that pattern.

 

 

4..8....2.....578.....9..1......1.9.....7.5...6.4....36.9......2..6......43.....8 10.6/10.6/10.5 K

2..3....6.....473.....9..1......1.4.....7.9...6.2....35.4......8..5......12.....8 10.6/10.6/9.8  K

2..8....4.....978.....5..1......1.9.....7.5...4.2....34.9......8..6......32.....8 10.6/10.6/9.5  K

3..6....2.....973.....5..1......1.9.....7.5...6.2....34.9......8..4......32.....8 10.6/10.6/9.4  K

2..8....6.....978.....5..1......1.9.....7.5...6.2....36.1......8..4......32.....8 10.6/10.6/9.3  K

2..3....6.....453.....9..1......1.9.....7.4...6.2....34.5......3..7......29.....8 10.6/10.6/9.3 

3..6....4.....973.....5..1......1.9.....7.5...6.2....36.7......8..4......23.....8 10.6/10.6/8.4  K

5..3....2.....473.....9..1......1.9.....7.4...8.2....32.1......3..6......65.....8 10.6/1.2/1.2   K

6..3....4.....573.....9..1......1.9.....7.5...8.2....33.7......8..6......42.....8 10.6/1.2/1.2   K

 

In that list of my best ratings, only one  puzzle does not have the SK loop.

Reversely, I found some puzzles having the SK loop with very low ratings.

Here some puzzles with a rating ER 7.2

 

8..6....5.....478.....9..1......1.9.....7.1...6.2....37.9......2..5......13.....8 7.2/7.2/7.2

8..3....2.....978.....5..1......1.9.....7.1...3.2....47.9......2..6......14.....8 7.2/7.2/7.2

8..6....2.....478.....9..1......1.9.....7.1...6.2....37.9......4..5......13.....8 7.2/7.2/7.2

8..4....2.....578.....9..1......1.7.....7.5...6.2....31.5......4..3......72.....8 7.2/7.2/7.2

3..8....6.....473.....9..1......1.9.....7.1...5.2....37.9......8..6......13.....2 7.2/7.2/7.2

2..3....6.....473.....9..1......1.9.....7.1...6.2....35.7......4..5......19.....8 7.2/7.2/7.1

6..3....4.....573.....9..1......1.7.....7.5...8.2....39.1......3..4......75.....2 7.2/7.2/7.1

2..3....6.....473.....9..1......1.9.....7.1...6.2....33.7......6..5......19.....8 7.2/7.2/7.1

3..6....2.....473.....9..1......1.9.....7.1...6.2....34.7......8..5......19.....8 7.2/7.2/7.1

2..3....4.....573.....9..1......1.9.....7.1...4.2....34.7......3..6......19.....8 7.2/7.2/7.1

3..6....2.....473.....9..1......1.9.....7.1...6.2....36.7......8..5......19.....8 7.2/7.2/7.1

5..3....2.....973.....4..1......1.4.....7.1...8.5....32.7......8..6......14.....8 7.2/7.2/7.1

2..3....4.....573.....9..1......1.9.....7.1...4.2....34.7......5..6......19.....8 7.2/7.2/7.1

 

Most of these puzzles would surely be solved before the SK loop has been seen. Applying the SK  loop changes them in quite simple puzzles.

 

Another important point is that most of the puzzles having the SK loop seem to have as well some big rank 0 SLG.  A significant percentage have the three main SLG patterns. Some have only 2, other only one, and very few have none.

 

This is quite new to me, There is a lot of redundancy between the sk loop and the SLG’s as far as eliminations are concerned, but not always.

 

In Easter Monster for example the 3 SLG are there, but after the SK loop the immediate assignment and basic eliminations, nothing more come thru the SLG’s.

 

Reversely, in the 2 hardest puzzles shown above (StrmCkr and m_b_metcalf) the SLG’s bring some eliminations not  so easily established after the SK loop eliminations. (both puzzles have the 3 SLG forms)

 

Let’s see the first one, from mb_metcalf with the PM at the start.

 

5      137   1467  |3478  234678 2368  |12    468   9     

346    2     469   |1     34689  35689 |456   7     468   

1467   179   8     |4579  24679  2569  |3     456   12    

--------------------------------------------------------

12378  4     12579 |6     1389   1389  |2579  3589  2378  

123678 13789 12679 |3489  5      1389  |24679 34689 234678

368    3589  569   |2     3489   7     |4569  1     3468  

--------------------------------------------------------

24     157   3     |579   12679  12569 |8     469   1467  

178    6     157   |35789 13789  4     |179   2     137   

9      178   24    |378   123678 12368 |1467  346   5     

 

The sk loop and in red eliminations from the loop

r2c13 r2c79 r13c8 r79c8 r8c79 r8c13 r79c2 r13c2

3946 4658  5846  4639  3917  1758  5817  1739  loop

 

At the start, we have the 2 classical SLG’s on floors 3589.

 

X     3+    X     |38+   38+   38+   |X     8+    X    

3+    X     9+    |X     389+  3589+ |5+    X     8+   

X     9+    X     |59+   9+    59+   |X     5+    X    

 

38+   X     59+   |X     389+  389+  |59+   3589  38+  

38+   389+  9+    |389+  X     389+  |9+    389+  38+  

38+   3589  59+   |X     389+  X     |59+   X     38+  

 

X     5+    X     |59+   9+    59+   |X     9+    X    

8+    X     5+    |3589+ 389+  X     |9+    X     3+   

X     8+    X     |38+   38+   38+   |X     3+    X    

 

 

I give only the sets

 

Rows:    R2 R4 R6 R8   16 sets

Columns: C2 C4 C6 C8   16 sets

Square:  R2 R8 C2 C8   16 sets

 

If we apply these 3 SLG’s the situation at the end is

 

 

5     137  1467  |3478 2467 2368  |12   468  9   

346   2    469   |1    389  3589  |456  7    468 

1467  179  8     |4579 2467 2569  |3    456  12  

-----------------------------------------------

12378 4    12579 |6    1389 389   |2579 3589 2378

1267  389  1267  |3489 5    1389  |2467 389  2467

368   3589 569   |2    3489 7     |4569 1    3468

-----------------------------------------------

24    157  3     |579  1267 12569 |8    469  1467

178   6    157   |3589 389  4     |179  2    137 

9     178  24    |378  1267 12368 |1467 346  5   

 

We have lost also

 

3: r1c5 r5c19 r9c5

8: r1c5 r5c19 r9c5

9: r3c5 r5c37 r7c5

N: r4c6 

 

These eliminations are not too difficult to find after the SK loop, but it is much easier ot get them applying the SLG’s rank 0.

 

Another point is the possibility to have in the same puzzle  a SK loop, an EXOCET and generally some rank 0 logic.

Here some examples coming out of the data base given by tarek in the “new hardest” thread

004000009010003070600000200000008000050030080000105000002000004070300010900070600 tarx0037,tarek

100000000020400060003000501040086000000049080000200000507000300060900040000000007 CloudyBay,coloin  

100000002020000060003400500000805000008030900000904000005003400070000010600000007 dukdiamond1,coloin

 

All three have an EXOCET in the base r46c5 and a SK loop.

The first one has one rank 0 logic, the two next 2 rank0 logic.

 

General way to continue after the SK loop clearings

 

On that point, I already made many comments on my site . The weak point is always along the loop . I’ll come back later in that post thru an edit to repeat what is already in other places