Comments and thoughts on solving larger sized Sudoku puzzles
How to Tackle?
Our Sudoku puzzle solver has full support for the larger 16x16 version of the puzzle.
In theory all the same tactics can be used to solve this super-sized puzzle.
However, keeping track of 16 symbols for each square is much harder to do. It's also true to say that using a pencil to mark off possibilities on a printed copy is not really feasible for this number of options - there is just not enough space in the squares to do this.
Are they any new strategies to consider for a big 16x16 Sudoku puzzle?
I guess there aren't really. For the 9x9 my favourite strategy is the two out of three rule.
Look for occurrences of the same symbol in rows or columns in the same region, if you find two then you can work out that the symbol must occur in the other row/column in one of only three squares. Extending that to 16x16 then you should look for three out of four rows or columns. If you are lucky to find this then you know that the remaining row/column must have the symbol in the other column.
You're right, I don't think there are any special rules just the logical adaption of existing rules that are used in the 9x9 grid. Because there are 16 rather than just 9 options it just takes a lot longer to think through the options. That's particularly true of looking for the only choice rule - where for each square you have to look through all options.
I agree that there is nothing that new.
Even the X-Wing and Swordfish can be used, and these are more likely to be useful as there are so many more options.
Looking for groups (twins, triplets etc.) is more challenging too as there are more combinations to think through. Technically speaking it is an NP-complete problem - looking for sub-groups within groups so stepping up from 9 to 16 options is not just a matter of a linear scale up it really does get more complex to spot and there are no short cuts in doing this.
Even on my large sized display I can not read the possibility text at small screen sizes.
To make all the text readable run Sudoku Dragon to use the full screen by just double clicking on the title bar. This makes all the squares large and all the text easy to read.
Here are some other suggestions for making the big grid easier to see.
1. You can use the View | Options to increase the grid display size by switching off the column and row headings and the side panel.
2. Switch off the status bar with View | Status bar and drag the possibility bar so it is alongside rather than below the toolbar.
3. Try another display theme or create your own new one with a clearer font for displaying possibilities
It has been proven by McGuire et al., that a 9 x 9 Sudoku puzzle must have at least 17 clues. Demoen et al. have shown that 6 of the 27 constraints are redundant for 9 x 9 Sudoku.
Now, my question is, does anybody know the lowest number of clues known for a 16 x 16 sudoku?
My suggestion is that it must be at least 48; i.e. 48 if there was no redundancy. But due to redundancy, it will probebly be a few more.
Any answer, also if you have just one example of a 16 x 16 sudoku puzzle with a minimal number near 48 would be nice. By near to 48 I mean 60 or less.
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