Mauricio wrote:champagne wrote:2) try without the given in excess
. either you solve it now and find the given in the solution, the puzzle was not minimal
. or you fail and then you look for something else.
...
Counterexample to point 2Minimal, not symmetric, remove 1@r6c4 (now multisolution, but symmetric), solve it (assuming uniqueness, wrongly), and you have r6c4=1 in the solution.
- Code: Select all
.....1..2..3.4..5..6.7..8....1....3..4..9.1..7..1....6..5.7.....8.6...9.2....3..4
Now, if you remove one clue, giving it symmetry, solve it, and if the solution is not consistent with the original puzzle, then you now the clue you erased was not redundant; in other words, redundancy allows you to erase a clue, but IMO it is not easier to know if a clue is redundant than to solve the puzzle.
nice counter example, good to have the expert in symmetry.
is it a contradiction with point 2? I am not sure. and your reaction open some doors
Happily, in the wording, I did not stated that the puzzle was not minimal, so I have may be an escape lane.
Here it is a fact that the solution has a symmetry of given.
No easy way to establish it "forward". It could be that easy moves at the start lead to the symmetry, but in all these puzzles, the first move is very tough to establish.
Trying a kind of "backward" symmetry is still valid.
As you say, if the given in excess does not come, you know you could not erase it and you have to find something else..
If the erased given comes, as the puzzle is assumed to have a unique solution, it must be the solution, but it does not bring the probe that that digit was in excess.
Am I right??
champagne
. How far back did the goal posts move 
