Thanks for you efforts

We now have a number of ways to grade puzzles - not just the hardest step but also an attempt to summate the many hard steps in some puzzles.

I drew a blank on the unavoidable front.......Analysing m_b_metcalfs puzzle not surprizingly there were no insertable clues when you looked at the grid solutions of each [n-1] clues where n = the given clues. When you looked at each clue and the unavoidable sets that they uniquely occupied they envolved all the non given clues

In m_b_metcalf, looking at the clue with the least solutions - the 2 in r4c6 [82 grid solutions] there were 5 unavoidable sets which had between 30 and 50 clues. Of note there didnt tend to be the small unavoidables that you normally have !. The symmetrical nature of the clues must support these large sets. I cant see a way of using this however.

If all these puzzles are difficult because of the chains couldnt we use a more functional method of analysis.

My [sadman] graphical solver solves these difficult puzzle by systematiclly forward tracking on the remaining pencil marks - it takes about 30 seconds with m_b_metcalf's puzzle and 15 seconds with St.Patrick1. This tends to appromimate well to SE !

Here is another variation, possibly up there

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

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

|.2.|1..|.7.|

|..8|...|3..|

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

|.4.|2.7|...|

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

|...|.46|.1.|

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

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

|.6.|..4|.2.|

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

+---+---+---+ SE 10.8 [Seamus5] or [529148#1]

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

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

|.2.|1..|.7.|

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

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

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

|...|821|...|

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

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

|3..|...|8..|

|.6.|..4|.2.|

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

+---+---+---+ SE 11.1 [Edmund5] or [295208#1]

- Code: Select all
`5.......9.2.1...7...8...3...4.......................1...3...8...6...4.2.9.......5[m_b_m]`

5.....3...2.1...7...8.....9.4.......................1.3.....8...6...4.2...9.....5 [Edmund]

5.......9.2.1...7...8...3...4.......................1...9...8...6...4.2.3.......5 [Seamus]

5.......9.2.1...7...8...3...4.......................1.3.....8...6...4.2...9.....5 [Patrick]

295376 sol.

295208 sol.

529148 sol.

414054 sol.

I wonder how many different combinations of Box 3&7 we would have to try....