## Intrinsically Difficult Patterns

Everything about Sudoku that doesn't fit in one of the other sections

### Intrinsically Difficult Patterns

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 }

m_b_metcalf
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Location: Berlin

### Re: Intrinsically Difficult Patterns

Since 19-clue puzzles are the flavour of the month, here's another pattern I thought might be suitable for the Patterns Game but for which, again, I could find no singles-only version:
Code: Select all
`.1...2..34..5...6...........3...7..1.........8..4...9.......4...7...1..25..9...8.   ED=9.4/9.4/3.8   `

m_b_metcalf
2017 Supporter

Posts: 11140
Joined: 15 May 2006
Location: Berlin

### Re: Intrinsically Difficult Patterns

Hi Mike,
I think that we have a trivial answer with 17 clues patterns where the 17 has a high rating
champagne
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