I've just come across the discussion from way back on Oct/29/2005 (I don't read this group often, someone else pointed me at this thread), regarding the minimum number of clues needed for a 6x6 sudoku's with irregular regions.

The answer is 5, and I have plenty of examples of that at

www.bumblebeagle.org/dusumohBut the answer as to the minimum number of clues necesary depends on the particular layout (i.e. the shapes). For any N there exists an NxN layout with an N-1 clue puzzle. See proof on the site above but note that the puzzle shown in the proof is not very interesting as a puzzle.

There was also mention of my previous post (from who knows when):

In other words, the layout allows only one possibility for the

latin square. The player could just write 1-9 along the top row

and start solving. I believe Mark Thompson found one of these

for 5x5 or 6x6.

I was unable to find the one Mark did, and may have been mistaken, but I recently searched for those myself and found five 6x6's pretty quickly (there may be more) and one 7x7 after a much longer search. There are probably others, but as N gets larger the layouts with low clue puzzles become much much much sparser. Actually the proof mentioned two paragraphs above shows how to create such a "no-clue" layout for any N>=4 (but again, not interesting as a puzzle).

Bob H