gfroyle wrote:Here's a question...

This is the grid with 29 x 17s..

Here is a similar grid... in fact, it is the same except that I have swapped around the elements of an unavoidable set of size 6 in rows 8 and 9..

Does this have a lot of 17s as well?

Hmm. Intuitively I would expect so, but I can't think of a proof. Focusing on that unavoidable set, I looked at the first of the 29 puzzles with 17 clues from the "strangely familiar" grid. It has 2 clues from this unavoidable set. No other choice of 2 clues gives a 17. In the new grid, no choices of 2 clues from the unavoidable set give a 17. So there's no simple transformation, at any rate.

dukuso wrote:24:1.0042

23:1.0154

22:1.0209

21:1.0590

20:1.3187 (240/182)

I would be wary of these ratios since the numbers 240, 182, are too small.

Maybe the ratio for 24 is better since the numbers are bigger (I presume).

In the limit maybe all ratios are 1.

gfroyle wrote:Now, you would have to say that the new grid is actually MORE promising for uniquely completable subgrids than the original...

These numbers seem small for a million tries. dukuso said elsewhere that you have a 60% chance of a puzzle with a unique solution for k=25.

About 40% in general.

Only 2 for the Mosch grid! Interesting. These grids must be highly non-random.