This is something I have done in the past for “exotic patterns”, but nothing is done for the “tridagon threat” where we have files with millions of puzzles.
To avoid dilution in other threads, I open this one to address the topic.
We are here interested by a “tridagon impossible pattern” coming in the PM of a puzzle.
We know that 3 digits cannot have in four boxes the following pattern
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..x x..
.x. .x.
x.. ..x
x.. x..
.x. .x.
..x ..x
At the end, the solution grid will have or not the digits at the right place in boxes 123 and 2 digits at the right place in box 4 this is commonly called here a “tridagon pattern in the solution grid”.
In the PM, the impossible pattern has the 3 digits plus extra candidates (at least one will be true).
We have a “tridagon threat” if, using a classical set of rules (for me Sudoku Explainer rating), the rating is very high with a small number of extra candidates.
With only one extra candidate, the solution grid will always have a “tridagon pattern in the solution grid”.
And if only one cell of the impossible pattern does not have one of the 3 digits, the puzzle can be morphed to have this in the box4
The corollary property is that if the solution grid does not have the tridagon pattern, then we have a minimum of 2 guardians.
In mith’s file of more than 4.3 million puzzles, ~870 000 puzzles have a solution grid without the tridagon pattern.
For all the puzzles of the file, we have in the PM a tridagon impossible pattern with 2 false extra candidates.
Here is the first in my file
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........1......234....2567...76.2....65.89...8..75.9....8.9...7.52..6...79...8... npuz= 1
623947851579861234184325679937612485265489713841753926318294567452176398796538142
|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|
| 2346 23478 3469 | 3489 346 347 | 58 589 1 |
| 5 178 169 | 189 16 17 | 2 3 4 |
| 134 1348 1349 | 13489 2 5 | 6 7 89 |
|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|
| 9 134 7 | 6 134 2 | 13458 1458 358 |
| 1234 6 5 | 134 8 9 | 7 124 23 |
| 8 1234 134 | 7 5 134 | 9 1246 236 |
|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|
| 1346 134 8 | 25 9 134 | 1345 12456 7 |
| 134 5 2 | 134 7 6 | 1348 1489 389 |
| 7 9 1346 | 25 134 8 | 1345 12456 2356 |
|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|
The reader can see r5c1=2 and r9c3=6 the 2 extra digits.
I am not clear on what can be done here to select a puzzle of the file.
The number of guardians after “easy steps” is surely one possibility, but what else ???
For the 3.7M puzzles of mith’s file where the solution grid has the tridagon pattern, we have clearly 2 cases
One guardian: here the guardian can be assigned and rating the rest we have an idea of the interest of the puzzle,
More than one guardian: then, we are in the same situation as before.
Note ; with one cell having guardians, we can still have several extra candidates.
With 2 guardians, we have a classical simple ‘or’ (not exclusive) between the 2 extra candidates, something known for long in the AIC’s chains, so the cases with more than 2 guardians can be requested by the players.
After theses preliminary thoughts, what I intend to do is to clean files from “ easy after unique cell “ and to split files on the above criterias.
May be some have more precise ideas.
I’ll check the status of “2 TH” threats, but up to now, what I have seen is that only one of the 2 THs have a very small number of extra candidates.
