HP02 Solving “hardest puzzles” continued    

 

P3. Multi floors fish

 

That property that we could call as well “Huge rank0 or nearly rank logic” has been shown by Allan Barker and is typically in the field of application of it’s model.

 

I failed until recently to find a well performing process to locate such logic, so I am missing stats on the relative frequency of that property.

 

Even with the process I am testing, processing time  is much too long to just think of testing huge files.

 

For the time being, I am thinking of testing the frequency of that property in the top list of hardest.

 

Another key point is that the property appeared with a high frequency in the list of puzzles having no SK loop, no Exocet and classified by me as “hardest”  after these 2 properties were applied to crack puzzles;

 

A multi floors fish is a kind of sandwich made of piled “quasi fishes” forming, thru adequate cells links a huge “multi fish”.

 

I’ll take as example the puzzle cola199 where different possibilities exist to build such multi floors fishes.

 

That puzzle has been first studied by Allan Barker here

 

Cola 199 is locked in that position after basic logic.

 

 

3589  4789  345789 |24567 245678 247  |45689 2456  1

158   6     4578   |12457 124578 9    |458   3     258

1589  1489  2      |1456  3      14   |7     456   5689

 

4     1279  679    |8     127    5    |1369  1267  23679

12589 12789 5789   |3     1247   6    |1459  12457 2579

1256  3     567    |9     1247   1247 |1456  8     2567

 

23689 289   1      |2567  25679  237  |3568  567   4

236   5     346    |12467 12467  8    |136   9     367

7     489   34689  |1456  14569  134  |2     156   3568

 

The floors/rookeries of the multi fish are 1;2;4;7.

We can notice the mini column r456c5 made of cells belonging to the multi floors. This is not a must, but a good indicator for a possible big rank 0 or near rank0 logic.

 

An easier way to find such logic is to work, here again, on a reduced PM.

 

 

X    47+  47+ |247+  247+  247  |4+  24+   X    

1+   X    47+ |1247+ 1247+ X    |4+  X     2+ 

1+   14+  X   |14+   X     14   |X   4+    X    

 

X    127+ 7+  |X     127   X    |1+  127+  27+

12+  127+ 7+  |X     1247  X    |14+ 1247+ 27+

12+  X    7+  |X     1247  1247 |14+ X     27+

 

2+   2+   X   |27+   27+   27+  |X   7+    X    

2+   X    4+  |1247+ 1247+ X    |1+  X     7+

X    4+   4+  |14+   14+   14+  |X   1+    X    

 

As far as I can see, a multi fish is usually based on a group of rows/cols or on a square. (sets in Allan Barker model)

 

We have here the three possibilities

 

SLG1  1247r2 1247r5 1247r6 1247r8 r4c5      17 sets

SLG2  1247c2 1247c4 1247c6 1247c8           16 sets

SLG3  1247r2 1247r8 1247c2 1247c8 r456c5    19 sets

 

The link sets are

 

SLG1 12c1 47c3 1247c5 14c7 27c9 r2c4 r5c28 r6c6 r8c4 17 links

SLG2 247r1 14r3 27r7 14r9 r2c4 r4c28 r5c28 r6c6 r8c4 16 links

SLG3 1247C5 147B1 24B3 24B7 17B9 r2c4 r4c28 r5c28 r8c4 19links

 

Eliminations are respectively of 22 candidates, 20 candidates, 20 candidates (non cumulative)

 

With 17 sets made of 4 rows/columns plus one cell, the first SLG seems to be a typical pattern;

 

The third one is also the typical square mode pure rank 0 logic, with a mini column purely in the field, 2 rows and 2 columns are forming an empty square in the other stacks and bands. In that third type, the four boxes outside the stack/band of the mini row have some link sets.

 

 

These examples are pure rank 0 logic, very easy to understand for anybody aware of Allan Barker Model.

 

In the square pattern, if the four intersections are not empty, some SLG are still valid, but they are not rank0. I have  examples with one or 2 intersections not empty.

 

I’ll describe in another chapter how to-day my solver finds such rank 0 or near rank 0 logic.