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I think the product, rather than the sum, might be a better measure.

Or take the log of the product, if you like.

What do you think of that idea?

--Joshua

Looking at that column 8, the topmost thing can only be 6 or 9. Also in row 7, that spot can only be 6 or 9. Therefore, among those two spots, the 6 and the 9 get used up: 6 and 9 must be the 1st an ...

For the difficulty:

Entropy would be the log of the product of the number of possibilities for each square. That would be a fine measure. The question is, when to measure it? Certainly you should ...

Both programs, yours and my, are solving what can be solved without using a "look ahead" technique (I am almost sure).

I have a feeling that there are still more ideas out there of how to analyze th ...

After crossing off the "obvious" possibilities (that is, eliminating from the row and column all the numbers that are already used) you should find that in that -x- spot you have only 3 and 9 as optio ...

Here an additional one to compare our programs:

020000000
000600003
074080000
000003002
080040010
600500000
000010780
500009000
000000040

For this one it has found "only" 8 numbers.
We can exchange ...

For the first one, my program gives

17 4 3 9 8 67 2 5 167
6 789 1789 4 2 5 138 38 178
2 578 578 37 36 1 68 9 4
9 568 2568 13 13 ...

Indeed, there was a (in hindsight obvious!) bug in the "box rule".

Now, with the two rules I mentioned in the previous post, there's not a sudoku I've found that can't be solved. In fact, I've only ...

Thanks Steve!

I thought I had coded that rule as my rule 2: I call it the "box rule", that if a row intersects a box, and a certain digit only appears as a possibility in the intersection but nowhere ...