The New Sudoku Players' Forum

[m_b_metcalf]

Really? There are, indeed, some little diamonds:

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......3....9.....5.4.2...6.8...9.7...1.3.4.2...4.5...6.8...1.7.5.....9....2......   ED=2.5/2.5/2.5
......1....2.....3.4.5...6.1...7.8...3.6.5.9...9.4...7.6...1.5.3.....9....8......   ED=3.0/3.0/3.0       
......2....3.....7.9.6...1.8...7.6...1.3.4.2...4.9...5.2...3.9.6.....5....1......   ED=7.1/7.1/7.1   

but where are the 10.4+ huge pearls?

Mike

[Hajime]

No 10+ ratings found
this is the best pearl rating I found:

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 . . . . . . 7 . .
 . . 9 . . . . . 8
 . 5 . 6 . . . 1 .
 2 . . . 8 . 9 . .
 . 7 . 1 . 5 . 4 .
 . . 4 . 2 . . . 1
 . 4 . . . 7 . 5 .
 8 . . . . . 3 . .
 . . 6 . . . . . .  ED=9.4/9.4/2.6

[m_b_metcalf]

And this:

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 . . . . . . 1 . .
 . . 2 . . . . . 3
 . 4 . 1 . . . 5 .
 6 . . . 7 . 2 . .
 . 8 . 5 . 4 . 9 .
 . . 9 . 6 . . . 7
 . 9 . . . 8 . 4 .
 3 . . . . . 7 . .
 . . 5 . . . . . .   ED=9.7/9.7/2.6

Mike

[Hajime]

Hi Mike, You are good.
After 44M different potential puzzles with this pattern I run out of memory and my program crashes.
I did not encountered your high pearl. Well done

[m_b_metcalf]

Well, vicinity searches are the name of the game. I found otherwise only curiosities uch as

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...... 1..
.. 2..... 3
. 4. 5... 6.
 5... 7. 2..
. 7. 8. 1. 9.
.. 1. 3... 8
. 9... 6. 5.
 7..... 9..
.. 3......   ED=8.6/7.3/4.4


and the best 9+ with ED>2.6 was

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...... 1..
.. 2..... 3
. 4. 5... 6.
 5... 7. 2..
. 1. 8. 4. 9.
.. 9. 3... 8
. 9... 6. 5.
 7..... 8..
.. 3......   ED=9.1/9.1/6.7

Regards,

Mike

[Hajime]

Well, vicinity searches are the name of the game. Mike

Also I do vicinity search, mostly {-4/+4}.
The first seed is the given puzzle. And the next seed is the highest rated up till then.

My best 9+ with ED>2.6 was

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 . . . . . . 1 . .
 . . 2 . . . . . 9
 . 8 . 5 . . . 6 .
 3 . . . 5 . 2 . .
 . 5 . 6 . 2 . 3 .
 . . 1 . 3 . . . 7
 . 6 . . . 4 . 8 .
 9 . . . . . 3 . .
 . . 7 . . . . . .  ED=9.3/9.3/9.0

What is the curiosity of ED=8.6/7.3/4.4 ?

[m_b_metcalf]

My best 9+ with ED>2.6 was

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 . . . . . . 1 . .
 . . 2 . . . . . 9
 . 8 . 5 . . . 6 .
 3 . . . 5 . 2 . .
 . 5 . 6 . 2 . 3 .
 . . 1 . 3 . . . 7
 . 6 . . . 4 . 8 .
 9 . . . . . 3 . .
 . . 7 . . . . . .  ED=9.3/9.3/9.0

Well done, great rsult!

What is the curiosity of ED=8.6/7.3/4.4 ?

It's a rating never played in the Patterns Game.

Finally, another diamond:

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......1....2.....3.3.1...4.5...6.7...8.4.7.5...1.5...9.4...2.3.9.....5....6......  ED=7.2/7.2/7.2

Regards,

Mike

[dobrichev]

a diamond

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......1....2.....3.3.4...5.6...1.7...5.7.6.2...4.8...5.9...3.7.8.....4....6...... ED=9.0/9.0/9.0


[dobrichev]

Code: Select all

......1....1.....2.3.4...5.1...5.6...7.8.4.1...2.3...9.4...5.7.8.....9....6...... ED=8.8/8.8/8.8
......1....1.....2.3.4...5.6...4.7...1.2.8.4...9.5...1.2...3.8.7.....5....6...... ED=8.5/8.5/8.5
......1....1.....2.2.3...4.3...5.6...1.4.7.5...7.8...9.4...5.2.7.....8....9...... ED=8.4/8.4/8.4
......1....2.....3.3.4...5.6...4.7...2.5.6.8...1.9...2.8...3.4.7.....9....6...... ED=8.3/8.3/8.3
......1....1.....2.2.3...4.5...3.6...7.4.8.1...9.7...8.4...2.3.7.....9....6...... ED=8.2/8.2/8.2
......1....1.....2.2.3...4.3...5.6...7.4.8.1...9.7...8.4...2.5.8.....9....6...... ED=7.3/7.3/7.3
......1....2.....3.4.1...5.6...2.7...7.8.9.4...5.3...8.5...8.7.3.....2....6...... ED=6.7/6.7/6.7
......1....2.....3.3.4...5.4...5.6...7.8.2.3...9.1...8.5...8.7.1.....9....6...... ED=6.6/6.6/6.6
......1....2.....3.3.4...5.6...1.5...7.6.5.8...4.9...2.8...9.7.1.....4....6...... ED=4.4/4.4/4.4
......1....1.....2.3.4...5.4...6.3...1.7.5.8...7.2...9.8...3.4.9.....6....2...... ED=4.2/4.2/4.2
......1....1.....2.2.3...4.1...3.5...6.4.5.7...8.6...9.4...2.3.7.....9....9...... ED=3.6/3.6/3.6
......1....1.....2.3.4...5.1...6.7...5.8.3.9...6.2...4.9...8.3.6.....8....4...... ED=3.4/3.4/3.4
......1....1.....2.3.2...4.1...5.2...5.6.3.7...8.2...9.6...4.3.8.....7....9...... ED=2.8/2.8/2.8
......1....1.....2.3.4...5.1...2.6...5.3.7.4...8.6...9.4...9.7.7.....8....5...... ED=2.3/2.3/2.3
......1....1.....2.2.3...4.1...3.5...6.4.7.8...7.2...9.4...8.6.5.....7....9...... ED=2.0/2.0/2.0


[m_b_metcalf]

Thanks, Mladen, I guess that wraps it up!
Mike

[dobrichev]

Unable to find hard puzzles.

For completeness

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Diamonds
......1....2.....3.4.2...5.6...7.8...9.4.2.1...3.6...7.3...5.9.8.....4....6...... ED=7.0/7.0/7.0
......1....2.....3.3.4...5.6...7.4...5.6.4.8...8.2...9.8...3.2.9.....8....1...... ED=7.4/7.4/7.4
......1....1.....2.3.4...5.1...6.2...7.5.4.8...6.8...9.4...8.3.3.....7....9...... ED=7.5/7.5/7.5
......1....2.....3.3.4...5.6...7.5...2.8.4.7...9.5...2.8...7.3.4.....6....1...... ED=8.9/8.9/8.9

Pearls
......1....2.....3.4.5...6.7...1.5...8.9.4.2...9.7...1.5...9.4.3.....8....6...... ED=9.4/9.4/7.8
......1....2.....3.4.5...6.5...2.6...6.7.3.5...8.5...9.3...4.7.8.....2....1...... ED=9.5/9.5/6.7
......1....1.....2.3.4...5.6...2.5...4.5.7.8...9.6...3.7...8.4.8.....7....6...... ED=9.6/9.6/2.6
......1....2.....3.4.1...5.6...7.2...8.5.4.9...9.6...7.9...8.4.3.....7....5...... ED=9.7/9.7/2.6 by m_b_metcalf, reinvented, for comparison
......1....2.....3.4.5...6.2...7.3...5.8.6.9...8.3...6.8...4.5.9.....7....1...... ED=9.7/9.7/2.6


That is from 1384483 puzzles.

[Hajime]

I could generate 44M puzzles in 36 hours, of which 140K puzzles were valid (1 solution) and minimal.
The 140K were submitted to PGExplainer (2 processes, multi treaded, on my 4 cores laptop), that uses the most elapsed time. You generated 1.4M (valid and minimal?) puzzles, 10 times more as I, and found many more nice solutions.
What is the extra you did or have in such a short time?
BTW, great results.

[m_b_metcalf]

I don't keep count, but I generated in batches, either from scratch or by vicinity searches, not more than 2000 valid puzzles that wre minimal and with ED >= 2.6. Others never saw the light of day.

Regards,

Mike

[dobrichev]

Hi Hajime,

I started by finding all valid minimal puzzles matching the given pattern within the 35 solution grids that have 27+ automorphisms. Only this puzzle appeared and I used it as the only seed for vicinity search.

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......1....1.....2.2.3...4.5...1.6...7.8.9.2...4.6...9.8...2.7.1.....5....3...... ED=1.5/1.2/1.2


Then I followed procedure described here.

I decided to ignore non-minimal puzzles. Utilized 4 CPU cores for less than a day. I did 45 runs from which last 15 gave no improvements. The hardest diamponds appeared somewhere in 10 - 15 run. One run produces one or more puzzle generations and I didn't count them, but likely 100-200 generations were produced.

As usual, {-2,+2} with EP filter was most productive. Ocassionly I tried -+3 or even -+4 on the top few ED or ER.
I gradually decreased EP margin. At the end the filter was ER=any, EP >= 4.0, ED=any, and -+2 produced only garbage.

For a typical for the game pattern, rating millions of 10+/x/y puzzles significantly slows down the process. This wasn't the case for this pattern.

[champagne]

Hi Hajime,

I started by finding all valid minimal puzzles matching the given pattern within the 35 solution grids that have 27+ automorphisms. Only this puzzle appeared and I used it as the only seed for vicinity search.

This is quite unusual for me in the old game.

How did you detect that the pattern fitted with the 27 auto morphisms