Intrinsically Difficult Patterns

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Intrinsically Difficult Patterns

Postby m_b_metcalf » Wed Apr 01, 2009 4:38 pm

I can't imagine that this hasn't come up before, but here goes anyway.

I occassionaly investigate a clue pattern to see whether it might be suitable for the Patterns Game. I recently got off to a good start with a symmetric, 19-clue pattern that quickly yielded a nice, high SE rating:
Code: Select all
 . 1 . . 2 . . 3 .
 4 . . 5 . . 6 . .
 . . . . . . . . .
 . 3 . . 7 . . 1 .
 6 . . 4 . . 5 . .
 . . . . . . . . .
 . 2 . . 1 . . 7 .
 8 . . 6 . . 9 . .
 . . . . . . . . 8   ED=9.8/9.8/3.8

However, a pattern can be submitted to the Game only in the form of a valid puzzle solvable with singles only. This I could not find. In fact, the lowest I got was
Code: Select all
 . 1 . . 2 . . 3 .
 4 . . 5 . . 6 . .
 . . . . . . . . .
 . 3 . . 7 . . 1 .
 6 . . 8 . . 5 . .
 . . . . . . . . .
 . 2 . . 1 . . 7 .
 8 . . 6 . . 4 . .
 . . . . . . . . 8   ED=7.1/1.2/1.2

Assuming this can't be bettered (not obvious, but let's suppose), the challenge arises:

For any given number of clues, n, find that pattern whose lowest SE rating has the highest value.

So, for instance and for n=19, is there a pattern whose lowest SE rating is higher than 7.1 (assuming the value above is really valid)?

It might be that this is already known, or can be easily found, for n=17.

Regards,

Mike Metcalf

    { added by Moderator: re the above Layout of 19,
    blue (2014.May.17) has confirmed that 7.1 is indeed the lowest }
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