coloin wrote:Any news on this.

The work continues... I started looking for 17-hint uniquely completable grids with the expectation that if there were large numbers of those, then there would probably be a 16 out there somewhere. Conversely, if there were very few 17s, then that might be the cutoff point.

In order to construct 17s, I also collect a pile of 18s as a sort of by-product.

By now, I have collected 1075 different (ie genuinely different, not just relabellings or rearrangements) uniquely completable 17-hint grids, and about 78000 uniquely completable 18-hint grids.

I have not bunged these on my webpages yet because I need to rewrite my PHP code so that it doesn't attempt to display all 1075 of them at once when someone visits...

I have kept some statistics on how many occurrences of each number there are in these grids. For example

79 x (0^1, 1^2, 2^3, 3^3)

means that there are 79 grids where one number is missing (0^1), two numbers occur once each (1^2), 3 numbers appear two times each (2^3) and 3 numbers occur three times each.

The stats so far are

79 x (0^1, 1^2, 2^3, 3^3)

301 x (0^1, 1^1, 2^5, 3^2)

57 x (0^1, 2^7, 3^1)

1 x (1^5, 3^4)

28 x (1^4, 2^2, 3^3)

308 x (1^3, 2^3, 3^3)

301 x (1^2, 2^6, 3^2)

Things that are "different" from all the others are often interesting mathematically, so here is the single example of type (1^5, 3^4) - notice that there is one each of {1,3,4,8,9} and three each of {2,5,6,7}

- Code: Select all
`+ + + + 6 + + 3 +`

+ + + 8 + + 2 + +

2 + + 5 + + + + +

+ + + 2 9 + 5 + +

+ 7 6 + + + + + +

+ + + + + + 1 + +

+ + + + + 7 + 6 4

5 + + + + + + + +

+ + + + + + + 7 +

How does this rate as an actual puzzle? (I have not yet had time to code up all the "rules" and figure out how to assign a rating to a puzzle...). Probably it cannot be done just using the rules without some backtracking...