Hi StrmCkr,

StrmCkr wrote:if i am reading that correct it seems i was going in the same direction.

u are using the avoided sets of pairs that lead to a contradiction in the sk loop. to reduce one of the corners to only being one of 8 possible scenarios.

What has clearly shown my solver is that if you can not solve a puzzle clearing candidates thru AICs nets. Using “avoided sets of pairs” you can crack all known puzzles, but there is an exponential growth of possibilities each time a new field is open.

The question is then to find a feasible process for a player. The general strategy followed in full tagging in to “reduce the count”. The SK loop when it exists has the best chances to offer logical clearings. When you have reached the point to say “I have only 8 scenarios. . .” you already made a lot of work.

StrmCkr wrote:I start with placing the 1 or 2 or 4 or 2 found in box 3 and 7 { limits the scenarios to 2 and 2 possible when u consider the anti parings}

using all 4 possible scenarios but as sets of 2 different functions.(the 1&2 as one and 4&2 as the second)

in conjunction

As you could see, in the solution I published, these cells r1c7 r3c9 r7c1 r9c3 play a key role to establish equivalences (and reduce the count).

Later on, their effect is hidden in the list of the 8 scenarios.

StrmCkr wrote:I test place 6 in: R1C3 & R3C1 with all its legal pairing in the opposite corner R1C3 & R3C1 which can only 1 or 7 - and look for a contradiction (3 legal moves tests)

I test place 4 in: R1C3 & R3C1 with all its legal pairing in the opposite corner R1C3 & R3C1 which can only 1 or 7 - and look for a contradiction.(3 tests)

I test place 7 in: R1C3 & R3C1 with all its legal pairing in the opposite and look for contradictions. (3 legal tests)

This is a very common way for players to face hardest puzzles . The more I work on solution, the more I see that a solver building a net of AICs as mine is doing something equivalent. The main difference is that the solver will limit itself to what can be achieved with strong an weak inferences coming out of an identified set of stuff and constraints.

Again, the number of possibilities to examine is in general very high. In the SK loop, we have tools and good reasons to identify and test a limited number of scenarios.

StrmCkr wrote:corner R1C3 & R3C1 which can only 4 or 6 and look for a contradiction in all of each test numbers scenarios.

the results are R1c3 & R3C1 cannot = 6, 1 and 7 from R1C3, (all 4 scenarios produce a contradiction} contradiction is in the sk loop.

u can repeat this process on box 9 using its properties of

cannot have paid in a row or column. 1-7,3-9,6-4

then from corner to corner (r8c9 & r9C7) pairs 4-6,1-7 cannot be combined.

I know it is a hard job, but showing how you did it would be interesting. Difficult to comment such a general statement.

The way I am working to prepare my solution is very specific. I try to work out a solution the solver could produce in the future. I am very keen to select a path complying with the full tagging process. There is plenty of other paths to solve this puzzle.