Sudoku Players' Forums

[gfroyle]

Here is a 13-clue Sudoku X (ie diagonal + antidiagonal added as extra blocks that must contain no repeated numbers)

[Moschopulus]

It's interesting to see we can go as low as 13. I wonder if there is a 12?

I assume you found this with the same algorithm as for ordinary sudoku? You took the 14 that you posted before, and did some perturbations of it. You must also have modified your solver for sudoku X.

I was wondering about unavoidable sets for sudoku X. Suppose we start with a sudoku-X puzzle that has a unique solution. I suppose we define as before: an unavoidable set (in the solution grid) is a set of cells such that some permutation of those cells results in another valid completed diagonal grid.

All the unavoidable sets from ordinary sudoku will be unavoidables for sudoku X if they do not have any cells on the diagonals.

If an unavoidable set from ordinary sudoku has one cell on a diagonal, for example {11,12,41,42}, then it will definitely *not* be an unavoidable set for sudoku X.

Unavoidable sets from ordinary sudoku that hit the diagonals in two more more cells might remain unavoidable, if the permutation from ordinary sudoku happens to also permute the diagonals. It looks to me that this may or may not happen.

[ihope127]

Wait, just what are the new can't-be-the-same groups?

[gfroyle]

[Moschopulus]

Suppose you have a completed diagonal grid (1-9 on both diagonals), and an unavoidable set for this grid from ordinary sudoku. You want to know if this set remains an unavoidable set for sudoku-X. One way is just to remove the unavoidable set, and run the remaining puzzle through a sudoku-X solver. The set is unavoidable for sudoku-X if and only if the solver says there are at least two solutions.

It looks like most of the unavoidables from ordinary sudoku are lost, so the MCN for sudoku-X will be much smaller then the MCN for the same grid for sudoku.

Edit: for example, the solution grid of the 13 given above is
123984675654713298879625314915432786387561429462897153291356847546278931738149562
The MCN for ordinary sudoku for this grid is 10, whereas the MCN for sudoku-X is 4. For ordinary sudoku there are 24 unavoidables of size 4 or 6, whereas for sudoku-X there are 3 of size 4 or 6 (only 3 of the 24 survive).

[pompy]

[Chessmaster]

that is cool. i doubt you can go lower than that. it is like 17 clues for the regular sudoku

[Ruud]

While everybody is searching for 17-clue Sudokus, I spent this weekend in another niche, using similar searching techniques.

Here's a Sudoku-X with 12 clues:



000000009050000010000005000000000060000007000000004000000100000000920000004000008

A new record, if I'm not mistaking.

I found a few hundred in total, which I will post on my website after canonicalization and filtering out the duplicates.

Searching for an 11 now...

Ruud

[JPF]

Congratulations

JPF

[ravel]

Congrats on that one, Ruud.

It must be an easy one, because i could solve it

[udosuk]

Congrats Ruud! Good luck looking for the 11.

I wonder how close we can get to the minimum 8...

On the other hand, I bet you can do better if you work on Windoku X or DG X...

PS:

A warning for all Simple Sudoku users, don't try to load this puzzle onto that program and start solving, otherwise your CPU will be preoccupied for a long time when SS tries ferociously working out the number of (non-X) solutions. You should start solving on SS using a blank puzzle and then manually key in the 12 clues at the beginning.

Guess the number of non-X solutions for this puzzle hits the "black-hole" range of SS's programming (if SS detects the number of solutions to be over a certain limit, say 1 million, it aborts counting and reports "too many solutions", so if the number of solutions is just below that limit, SS will suck all your CPU power to work it out).

[Ruud]

The current collection can be downloaded from my website at this page, where I also explain my search methods.

The current collection has 1167 canonicalized Sudoku-X puzzles with 12 clues. This collection is exhausted for the -1+1 search method. No elevens were found. I will sleep better if anyone (gsf?) can confirm that the puzzles are unique upto isomorphism.

The first puzzle in the collection (also shown on the page) starts with a series of 33 empty cells.

Ruud

[udosuk]

[gsf]

[ronk]