FATA MORGANA V2

 

........3..1..56...9..4..7......9.5.7.......8.5.4.2....8..2..9...35..1..6........

fata morgana tarx0001

 

That new version follows the same general strategy, but copies some ideas of a solution found by abi a French player through a special loop and makes more eliminations within the floors 136

 

To make it shorter in other examples, Ill name that loop abi loop

 

The loop shown has good chances to be found in other exocet or nearly exocet patterns.

It has been developed first by abi on Platinum Blonde. Platinum Blonde is very close to an exocet, but is not one.

 

X 6+ 6+ |16+ 16+ 16+ |X 1+ X

3+ 3+ X |3+ 3+ X |X X X

3+ X 6+ |136+ X 136+ |X X 1+

 

13+ 136+ 6+ |136+ 136+ X |3+ X 16+

X 136+ 6+ |136 X 136 |3+ 136+ X

13+ X 6+ |X 136+ X |3+ 136 16+

 

1+ X X |136+ X 136+ |3+ X 6+

X X X |X 6+ 6+ |X 6+ 6+

X 1+ X |13+ 13+ 13+ |3+ 3+ X

 

In that reduced PM, the exocet is shown in blue. The potential of eliminations just using floors 136 is shown in red.

 

We have 3 scenarios for r5c46: 13r5c46 16r5c46 36r5c46. Only one is valid

 

One can see that elimination of 13r5c46 and 16r5c46 does not appear here.

To achieve such elimination, we need the UR potential.

 

We have to key URs linked to the scenarios

 

r3c46+r5c46

r5c46+r7c46

 

We study the scenario 13c46

 

Then, to avoid the UR pattern, we must have

1r3c9 | 3r3c1

1r7c1 | 3r7c7 These are strong inferences

 

We must also have (due to exocet 13r4c2 13r6c8 )

1r9c2 | 3r2c2 (induced ALS)

1r1c8 | 3r9c8 (induced ALS) strong inferences as well

 

Giving the loop (within the scenario) (this is the abi loop)

 

1r7c1 - 1r9c2 = 3r2c2 3r3c1 = 1r3c9 1r1c8 = 3r9c8 - 3r7c7 = 1r7c1

 

Due to the loop (still within the scenario)

 

3r2c2 3r9c8 => 3r46c5 - 13r5c46 or

1r9c2 1r1c8 => 1r46c5 - 16r5c46

 

<13>r5c46

 

We study the scenario 13c46

 

 

We have a similar abi loop

 

1r7c1 - 1r9c2 = 6r1c2 6r3c3 = 1r3c9 1r1c8 = 6r8c8 - 6r7c9 = 1r7c1

 

And a similar conflict

 

6r1c2 6r8c8 => 6r46c5 - 16r5c46

1r9c2 1r1c8 => 1r46c5 - 16r5c46

<16>r5c46

 

So we have 36r5c46

 

============================

 

This is a very common pattern when an exocet does exists, but it can be found as well with patterns close to an exocet. abi showed it in platinum blonde in a slightly different presentation

 

Ill use as much as possible abis preferred way to show the loop

Here for the first case

 

1r3c9 3r3c1

1r9c2 3r2c2

1r7c1 3r7c7

1r1c8 3r9c8

 

In rows we have the strong inferences

In columns we have the conflicts

In blue odd positions in the loop (starting in 1r3c9)

In red the even positions

===========================================

 

The new reduced PM with exocet eliminations from 36r5c46

 

X 6+ 6+ |16+ 16+ 16+ |X 1+ X

3+ 3+ X |3+ 3+ X |X X X

3+ X 6+ |136+ X 136+ |X X 1+

 

13+ 36 6+ |1+ 1+ X |x X 1+

X 1+ x |36 X 36 |x 1+ X

1+ X x |X 1+ X |3+ 36 16+

 

1+ X X |136+ X 136+ |3+ X 6+

X X X |X 6+ 6+ |X 6+ 6+

X 1+ X |13+ 13+ 13+ |3+ 3+ X

 

We still have some potential eliminations.

 

But we have 2 small loops with the same basis as before

 

6r3c3 - 6r1c2 = 3r2c2 - 3r3c1 = 6r3c3 => <3>r2c1 <6>r1c3

3r8c7 - 3r9c8 = 6r8c8 - 6r8c7 = 3r8c7 => <3>r9c7 <6>r8c9

 

The last red candidates are cleared through these 2 loops

 

3r2c5 - 3r2c2 = 3r4c2 3r6c8 = 3r9c8 3r9c5 = 3r2c5

6r8c5 - 6r8c8 = 6r6c8 6r4c2 = 6r1c2 6r1c5 = 6r8c5

 

 

2458 2467 24578 |12789 16789 178 |24589 1248 3

248 2347 1 |23789 3789 5 |6 248 249

2358 9 2568 |12368 4 1368 |258 7 125

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

12348 36 2468 |178 178 9 |247 5 1247

7 124 249 |36 5 36 |249 124 8

189 5 89 |4 178 2 |379 36 1679

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

145 8 457 |1367 2 13467 |3457 9 4567

249 247 3 |5 6789 4678 |1 2468 247

6 1247 24579 |1789 13789 1478 |24578 2348 2457

 

At that point, SE rating is 9.0.

 

This is a maximum as we know that cells r4c23 r6c8 are in strong link, what still does not know Sudoku Explainer.