999_Springs wrote:i was messing around with sudoku explainer's GUI and tried to make champagne's 11.9/11.9/11.8 hardest ever puzzle even harder by adding pencilmarks to known clues. in this puzzle the only clue that lets you add a candidate to it without invalidating the puzzle is 5r7c4, which can be replaced with (56).
The original (Sudoku) puzzle was: 98.7.....7.....6....6.5.....4...5.3...79..5......2...1..85..9......1...4.....3.2.;11.90;11.90;11.80;GP;champagne dry;1;22;
It is by no means the "hardest ever" puzzle. (SER is meaningful in computing hardness, but the next two measures are totally irrelevant.) See below for the real 3 hardest.
The modified (Sukaku) puzzle is: 98.7.....7.....6....6.5.....4...5.3...79..5......2...1..8(56)..9......1...4.....3.2., with the obvious () notation for the candidate-givens.
AFAIK, the above is the first example of a Sukaku derived from a Sudoku and harder than it in the SE rating. As there's some correlation between SER and my BpB classification - but no systematic correspondence - the natural question for me was: is it also harder in the BpB classification?
It's obvious that in any
rational rating/classification system, this modified Sukaku should be at least as hard as the original Sudoku. But there's no reason why it couldn't be harder. More generally, although all the known Sudokus are in B7B, there's no reason why some Sukakus couldn't be in B8B or even higher in the classification.
As the original Sudoku is in B6B, is the derived Sukaku also in B6B or do we need to go to B7B or even any higher BpB? Such computations are very time consuming and there has been some suspense for me (the more so that, beyond B7B, there may be memory overflow problems if I had to go there).
- My first computations showed that
it cannot be solved in B6B. This required 4 phases of T&E(B6) and a total of 970 candidates tried. (Remember that when the resolution state is changed during a T&E phase, a whole new phase must be tried, so that any candidate has to be tried several times. But it's the first time I see the need for 4 phases. Of course, this may not be meaningful, as the number of phases depends on the order the candidates are tried.)
- And the next computations showed that
it can indeed be solved in B7B - a small disappointment: still nothing to see in B8B
Conclusion:
The derived Sukaku is indeed harder than the original Sudoku puzzle in the BpB classification, but not beyond the hardest known B7B Sudokus.
A more interesting question for me would now be:
can one find a Sukaku not in B7B? First remember that we know only 3 Sudokus in B7B (and 2 of them have SER=11.8, not even 11.9)
..3....8..5....2.17...........5.8..6.9.12....8....3....6.9....5..4....7.....1.6.2 (eleven; 11.9 11.9 02.6)
.2...67..4...8......9.......3.....7.5.8....4..1.3....2....9..5....6.1..3...2..6.7 (eleven; 11.8 01.2 01.2)
5.......9.2.1...7...8...3...4.6.........5.......2.7.1...3...8...6...4.2.9.......5 (m_b_metcalf; 11.80 11.80 03.40)
They might be a good starting point for finding harder Sukakus (not speaking of the more general Sukakus, not derived from a single change in a Sudoku.)
dobrichev wrote:For even harder puzzles, SE gives up after thinking for 2-3 days.
Do you have such examples?
