The New Sudoku Players' Forum

[m_b_metcalf]

Code: Select all

 1 . . . . . . . 2
 . 3 . . . 4 . 5 .
 . . 6 . . . 7 . .
 . . . 3 . 8 . 4 .
 . . . . 6 5 . . .
 . 8 . 4 9 . . . .
 . . 2 . . . 1 . .
 . 5 . 8 . . . 9 .
 7 . . . . . . . 6   ED=11.5/11.5/11.2

[JPF]

good, but not minimal

JPF

[m_b_metcalf]

good, but not minimal

Oh, well, you can't have everything.

Actually, Tarek's pattern reminded me of the pattern you used for the very first PG:

Code: Select all

 4 . . . . . . . 5
 . 9 . 7 . . . 2 .
 . . 2 . . . 4 . .
 . 8 . 1 . 4 . . .
 . . . . 6 . . . .
 . . . 2 . 5 . 1 .
 . . 1 . . . 2 . .
 . 7 . . . 8 . 6 .
 5 . . . . . . . 8

In that game, the highest submitted rating was 10.7 (10.7/107./3.4 in modern parlance), but was that the best that we could do today?

Mike

[JPF]

After a quick search,

Code: Select all

+-------+-------+-------+
| 1 . . | . . . | . . 2 |
| . 3 . | 4 . . | . 5 . |
| . . 6 | . . . | 7 . . |
+-------+-------+-------+
| . 8 . | 1 . 5 | . . . |
| . . . | . 2 . | . . . |
| . . . | 3 . 9 | . 4 . |
+-------+-------+-------+
| . . 2 | . . . | 9 . . |
| . 5 . | . . 8 | . 3 . |
| 7 . . | . . . | . . 6 |
+-------+-------+-------+  ED=11.3/11.3/3.4


JPF

[m_b_metcalf]

After a quick search,

Code: Select all

 ED=11.3/11.3/3.4


Good quick search. My best was:

Code: Select all

 1 . . . . . . . 2
 . 3 . 4 . . . 5 .
 . . 6 . . . 7 . .
 . 4 . 8 . 5 . . .
 . . . . 6 . . . .
 . . . 9 . 1 . 3 .
 . . 2 . . . 1 . .
 . 8 . . . 3 . 9 .
 7 . . . . . . . 6   ED=11.0/11.0/10.4

[m_b_metcalf]

good, but not minimal

Actually, I have to thank you for drawing this to my attention. Upon investigating the two minimal puzzles that this non-minimal puzzles contains, I discovered this:

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 1 . . . . . . . 2
 . 3 . . . 4 . 5 .
 . . 6 . . . 7 . .
 . . . 3 . 8 . 4 .
 . . . . 6 . . . .
 . 8 . 4 9 . . . .
 . . 2 . . . 1 . .
 . 5 . 8 . . . 9 .
 7 . . . . . . . 6   ED=11.8/11.8/11.2

the highest rating I've ever found. I'll post it on the hardest thread.

Merry Xmas to all,

Mike

[JPF]

All of this takes us back 16 years.

From the basic pattern P of the very first Game mentionned above , a large number of puzzles with very high SE ratings were obtained as follows:
1. Generate minimal puzzles based on the pattern P (Patterns Game on P)
2. Retain only the puzzles with a high SE rating.
3. For each puzzle Q, fill box B5 according to its solution : Q-->Q'
4. Since this puzzle Q' is non-minimal, find all minimal puzzles it contains.
5. The list of minimal puzzles contains the initial puzzle Q ; thus, the highest rating obtained by say Q" is at least equal to the rating of Q.
6. If Q" <>Q vicinity search can be applied on Q" and so on, using pattern of Q" goto 1

It turns out that this method is quite effective for finding puzzles with a high SE rating. (SK loop vs Sudoku Explainer...)

JPF

[urhegyi]

Is this a valid pattern game layout?

Code: Select all

+-------+-------+-------+
| . . . | . . 4 | . . 3 |
| . 8 . | . 2 . | . 9 . |
| . . . | . . . | 7 . . |
+-------+-------+-------+
| 9 . . | 1 . . | . . . |
| . . 7 | . . 3 | . 6 . |
| . 2 . | . 5 . | . . 4 |
+-------+-------+-------+
| . . 4 | . . 6 | . . . |
| 5 . . | 7 . . | 8 . . |
| . 3 . | . 9 . | . . 2 |
+-------+-------+-------+

.....4..3.8..2..9.......7..9..1.......7..3.6..2..5...4..4..6...5..7..8...3..9...2 ED=9.0/8.4/3.4



[m_b_metcalf]

Is this a valid pattern game layout?

I think not. It can be transformed into this:

Code: Select all

 . 8 . . 2 . . 9 .
 . . . . . 4 . . 3
 * . . . . . 7 . .
 . . 7 . . 3 . 6 .
 . 2 . . 5 . . . 4
 9 . . 1 . . . . .
 . . 4 . . 6 . . .
 . 3 . . 9 . . . 2
 5 . . 7 . . 8 . .

which is almost, but not quite (see asterisk) symmetric about the anti-diagonal.

Mike

[m_b_metcalf]

which is almost, but not quite (see asterisk) symmetric about the anti-diagonal.

Actually, the pattern with the exra clue would have been fine for the Patterns Game. Here a few diamonds etc.:

Code: Select all

r3c1 added:
.1..2..3......4..56.....7....8..6.1..9..5...47..3.......3..8....2..7...65..1..9..   ED=8.9/8.9/8.9   
.1..2..3......4..56.....7....3..8.4..5..7...92..6.......9..5....7..3...84..1..2..   ED=9.0/9.0/9.0
.1..2..3......4..56.....7....8..1.9..5..3...27..6.......4..5....3..7...82..9..1..   ED=9.1/9.1/9.1   
.1..2..3......4..56.....7....7..1.2..4..3...68..9.......5..6....3..7...42..8..9..   ED=9.2/9.2/9.2   
.1..2..3......4..56.....7....2..6.8..5..3...97..1.......4..5....9..7...63..8..2..   ED=9.3/9.3/9.3   
.1..2..3......4..56.....7....3..7.2..4..5...89..1.......8..3....7..9...15..6..4..   ED=9.4/9.4/9.4   
.1..2..3......4..56.....7....5..3.4..7..1...81..9.......8..7....2..5...39..8..6..   ED=9.5/9.5/9.5   
.1..2..3......4..56.....7....5..3.7..3..1...81..9.......8..1....2..5...49..8..6..   ED=9.6/9.6/9.6   
.1..2..3......4..56.....2....5..3.6..3..5...78..9.......7..5....2..1...49..3..8..   ED=9.9/9.9/9.9 
.1..2..3......4..56.....7....5..3.1..3..8...98..6.......9..5....8..3...27..8..4..   ED=10.4/10.4/10.4
.1..2..3......4..56.....7....5..3.1..3..8...98..6.......9..5....8..1...27..8..4..   ED=10.5/10.5/10.0

[JPF]

I couldn't resist:
-Edited-

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.1..2..3......4..56.....7....5..3.2..7..5...18..9.......3..5....4..7...67..8..4..   ED=9.4/9.4/9.4
.1..2..3......4..56.....7....8..5.2..4..3...92..9.......9..8....3..5...17..6..4..   ED=9.5/9.5/9.5
.1..2..3......4..56.....7....6..8.2..3..6...74..9.......8..3....7..5...65..1..9..   ED=9.6/9.6/9.6
.1..2..3......4..56.....7....8..5.2..4..3...71..9.......1..8....3..5...64..7..9..   ED=9.7/9.7/9.7
.1..2..3......4..56.....7....3..8.1..5..3...49..6.......7..3....8..5...25..4..9..   ED=9.8/9.8/9.8
.1..2..3......4..56.....7....8..7.1..9..5...32..4.......2..8....5..9...43..1..6..   ED=9.9/9.9/9.9
.1..2..3......4..56.....7....3..5.6..7..3...89..8.......8..3....5..7...47..9..1..   ED=10.0/10.0/10.0
.1..2..3......4..52.....6....3..5.7..4..1...68..9.......7..1....8..6...29..8..5..   ED=10.1/10.1/10.1
.1..2..3......4..15.....6....7..3.2..8..7...44..9.......8..7....4..1...39..6..5..   ED=10.2/10.2/10.0
.1..2..3......4..56.....7....5..8.1..3..5...72..9.......8..3....2..7...41..6..9..   ED=10.3/10.3/10.3
.1..2..3......4..56.....7....3..8.4..5..3...89..7.......6..3....7..5...25..9..1..   ED=10.4/10.4/10.4
.1..2..3......4..56.....7....3..8.2..5..3...49..4.......8..5....9..1...71..9..6..   ED=10.5/10.5/10.5
.1..2..3......4..56.....7....3..8.2..9..3...45..4.......8..9....5..1...72..5..6..   ED=10.6/10.6/10.6
.1..2..3......4..56.....2....7..3.4..8..5...71..9.......1..5....2..3...89..7..6..   ED=10.7/10.7/10.7
.1..2..3......4..15.....6....7..3.2..3..7...58..9.......9..8....8..1...74..6..8..   ED=10.8/10.8/10.0


JPF