That one should be dedicated to discussions on how some “forcing nets” or whatever is the appropriate name of what is explained later, can be (or not) transformed in AICs nets.
I will also use that post to comment some aspects linked on the same example to Allan Barker method described here
I have to apologize but I’ll use freely Allan findings, concentrating mostly on Permutations analysis,
This post is limited to the first topic
Fata Morgana is a puzzle proposed few months ago by Tarek.
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000000003001005600090040070000009050700000008050402000080020090003500100600000000
At the start, Fata Morgana has the following Map of Candidates:
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2458 2467 245678 |126789 16789 1678 |24589 1248 3
2348 2347 1 |23789 3789 5 |6 248 249
2358 9 2568 |12368 4 1368 |258 7 125
----------------------------------------------------------
12348 12346 2468 |13678 13678 9 |2347 5 12467
7 12346 2469 |136 5 136 |2349 12346 8
1389 5 689 |4 13678 2 |379 136 1679
----------------------------------------------------------
145 8 457 |1367 2 13467 |3457 9 4567
249 247 3 |5 6789 4678 |1 2468 2467
6 1247 24579 |13789 13789 13478 |234578 2348 2457
Allan Barker proposed an Initial loop working on Floors 1;3;6 and on the node/cell N42.
I will write the map focusing on these digits in the following way
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+ ..6+ ..6+ | 1.6+ 1.6+ 1.6+ | ...+ 1..+ -
.3.+ .3.+ - | .3.+ .3.+ - | - + +
.3.+ - ..6+ | 136+ - 136+ | + - 1..+
------------------------------------------------
1.3+ 136+ ..6+ | 136+ 136+ - | .3.+ - 1.6+
- 136+ ..6+ | 136 - 136 | .3.+ 136+ -
13.+ - ..6+ | - 136+ - | .3.+ 136 1.6+
------------------------------------------------
1..+ - + | 136+ - 136+ | .3.+ - ..6+
+ + - | - ..6+ ..6+ | - ..6+ ..6+
- 1..+ + | 13.+ 13.+ 13.+ | .3.+ .3.+ +
Each ’+’ represents any candidates “out floors”.
Each ’-’ is a given.
What is established in Allan Model (and checked by my solver) is that in that map, All valid permutation lead to one of the digits ‘136’ in N42.
My preferred explanation is the following (Allan source):
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1r5c46=>1r1c5^1r9c5=> 1r4c2|1r6c8 (^ exclusive or; | non exclusive or)
3r5c46=>3r2c5^3r9c5=>3r4c2|3r6c8
6r5c46=>6r1c5^6r8c5=>6r4c2|6r6c8
As r5c46 is filled by two of these groups, n42 is always assigned (1,3 or 6)
24r5c46 can be eliminated.
This is a mixture between forcing nets and use of “super candidates”. Nevertheless, I do not see a corresponding AIC net.
Super candidates are not a problem. Tests have been delayed by work on Allan model, but it is on the way.
The problem starts with 3r5c46 => 3r2c5^3r9c5.
This is very easy to state in a forcing chain POV.
This is a key point for the next =>.
I have no equivalence in AICs .
It seems to me that once you have that relation, you are not so far from an answer thru AIC’s nets, however, you still have the last difficulty: how do you express in AIC environment the fact that two distant cells (N42,N68) are linked. (in blind mode Any puzzle tailor made practice is forbidden)
I will show in other posts other ways to show that N42 is one of 1;3;6, but if anybody has ideas to express that situation in a kind of AIC’s net, he is welcome.
BTW, one difficulty I face for the time being is to find Allan first loop among other possibilities to show N42={1;3;6}, but this is another story.
