tarek wrote:gsf wrote:this minimal puzzle has the minimum (maximum) number of clues out of all minimal puzzles within this solution grid

Thanx gsf, that clears it. Up until now, I thought that Minimum would mean the unique puzzle resulting from removing the largest possible combinations of givens.

its what you thought, so maybe I muddied the waters ...

procedurally (not necessarily efficient)

start with a solution grid (all clues, no holes)

generate all possible minimal puzzles from the grid

keep track of the minimal puzzles with the least and most clues

after all have been generated you will end up with

one or more minimal puzzles with the minimum number of clues and

one or more minimal puzzles with the maximum number of clues

for the specific solution grid

tarek wrote:But if you are talking about "Maximum minimal" then it should be easier.

the 17 (or 16) search is for the "minimum minimal" over all solution grids

and the current discussion is on the "maximum minimal"