Thank-you for all your vaid comments ! This isnt a solving technique.

Perhaps its more of sorting out the "route" that a hard puzzle takes initially to be able to determine its solution. [quite a difficult concept].

In easy puzzles there are many solving routes as such.

Allan.....

Absolutely correct, there is no easy way to "see" these eliminations.....except they are there !

The eliminated pms dont occur in any of the [multiple] grid solutions.

The fact that the eliminations are there doesnt necesarily mean that they would be the simplist to find - which you have confirmed [pity

].

Although the fact that they are there probably means that there is a logical way to find them.

eleven......

As i said above you cant see the elimination - you almost need to have T&E glasses ! - The eliminations and insertions are definitely present.

I am not sure of the relevance of uniqueness - In somewhat easier puzzles there will be eliminations present with [n-2] subpuzzles, and indeed we have seen the eliminations in the SK loop in EM where there were visable [and demonstratable] eliminations in the [n-5] subpuzzle.

In the GN puzzle we can proceed following the above 2 clue insertions [we now have a non minimal puzzle] to look at the [n-1] pms and continue to get furthur eliminations - and the solving path will be variable given the multiple eliminations and insertions that are bound to occur.

In harder [well balanced] puzzles there is a tendancy to have few eliminations with the [n-1] analysis. In unbalanced puzzles - with an SKloop - virtually all the puzzles we generated using a 16-clue template and adding clues to a central box

here will have eliminations with the 16 clues alone.

In easier puzzles you tend to get several eliminations with a low number of clues. Trivially you only need 4 clues to insert a clue using a "single" technique.

StrmCkr.....

Removing a clue absolutely leaves unavoidable sets [minimal and non-minimal] uncovered which are specific to each solution grid. We revisited this recently

here. Perhaps there is a distintion here with "real" pm board showing the clues that can be present in all the combinations of "deadly patterns" in all the grid solutions of each subpuzzle.

I am going to see if other puzzles [next is FM] also have an initial insertion which breaks the puzzle. I optimistically expect this to be the case.

..............

- Code: Select all
`+---+---+---+`

|...|...|..3|

|..1|..5|6..|

|.9.|.4.|.7.|

+---+---+---+

|...|..9|.5.|

|7..|...|..8|

|.5.|4.2|...|

+---+---+---+

|.8.|.2.|.9.|

|..3|5..|1..|

|6..|...|...|

+---+---+---+ FM

FM certainly lived up to its name......a very balanced puzzle.

There were no eliminations initially......none. Apart from the insertion of the 5 at r5c5 ! which decimated it, on the first round.

the most obvious elimination leading to an insertion was:

pms @ r2c9 are 249

without 5@r8c4 no 2@r2c9 [bivalue 49@r2c9]

without 5@r2c6 no 4@r2c9 [bivalue 29@r2c9]

therefore an inserted clue will be 9@r2c9..........................

Probably not a move that a solver [computor or

StrmCkr] could make very easily.

C