you wrote:I havn't explored the minimality of the n=3 puzzles

I got more than 1000 minimal puzzles.

I stopped the search.

Here is an example:

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

|123|...|...|

|4.5|...|...|

|678|...|...|

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

|...|857|..3|

|...|9.3|...|

|7..|216|...|

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

|...|...|156|

|...|...|4.7|

|...|5..|392|

+---+---+---+ SE=7.2

Finding minimal puzzles when 4<=n<=8 seems not too difficult.

Of course, Mauricio's lemma helps to place the clues.

Here is one (out of 4000+) for n=8 having main diagonal and anti-diagonal symmetries which btw implies 180° rotational symmetry

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

|123|4..|..5|

|4.6|...|...|

|578|...|4..|

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

|2..|594|...|

|...|1.2|...|

|...|678|..2|

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

|..4|...|253|

|...|...|1.7|

|7..|..5|864|

+---+---+---+ SE=9.0

I will have a look at n=9+; it seems more challenging!

JPF