The New Sudoku Players' Forum

[Leren]

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| W H O P # M O U E |
| H U R R A Y I N G |
| O R # E N D # B A |
| P R E W A R N E D |
| # A N A X I A L # |
| M Y D R I A T I C |
| O I # N A T # E E |
| U N B E L I E F S |
| E G A D # C E S S |
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Score = 123

Here is another, Leren

<edit>

New Hi Score 131, now 136

Leren

[JPF]

Edit : wrong pattern, again!

JPF

[Leren]

Hi JPF, not quite sure what you mean by your last comment.

I'm sure I have the right pattern but I'm following the agreed protocol of announcing a new high score but not posting a new diagram until you respond.

Still looking, Leren

[JPF]

Hi Leren,
Sorry, my post was not clear.
I posted again a grid with "the" wrong pattern.
When I realized that, I deleted my post and left the comment starting with edit.
In practice, it means that I lost a lot of time and I have to start again a new search.

JPF

[JPF]

With all those mistakes, I am late.
Here is one though:

Score = 135
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Grid 2 - Sol 2.JPG (22.38 KiB) Viewed 1537 times

JPF

[Leren]

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| V R O W # V I B E |
| R H Y O L I T I C |
| O Y # R I Z # D O |
| W O R K F A R E S |
| # L I F T M A N # |
| N I D A M E N T A |
| A T # R A N # A X |
| B I D E N T A T E |
| E C O S # S E E D |
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Score = 136

Leren

[JPF]

easy move

Score = 139
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Grid 2 - Sol 3.JPG (20.21 KiB) Viewed 1526 times

JPF

[Leren]

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| W A A C # B A F F |
| A M Y O T O N I A |
| A Y # N O W # X I |
| C O N Q U E R E R |
| # T O U Z L E D # |
| J O D E L L I N G |
| O N # R E I # E A |
| S I D E D N E S S |
| H A I R # G A S H |
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Score = 143

Leren

<edit> New high score for me : 146

[Leren]

Hi JPF, I'm going to claim that 146 is the maximum score for this pattern with Scrabble letter distribution rules. In any event I've stopped looking.

Are you still looking for a higher score, do you wish to propose another pattern or have you had enough of Crossword Squares for now? I'm still up for it if you are, it's a lot of fun for me.

Leren

[JPF]

Hi Leren,
Congratulations for your 143 and your upcoming 146!
Actually, I am stuck under 140 and yes let's stop with that pattern.

My "solver" is obviously too low and inefficient.
I should rewrite it but i am busy - and lazy - at the moment.

Anyway, here is a new pattern, randomly picked.
Good luck!

Maximum score =160
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Grid 7.JPG (15.67 KiB) Viewed 1496 times

JPF

[Leren]

Well, here is the highest score pattern:

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| Q U A D # S H O W |
| U N D E C E I V E |
| A D # F O P # E L |
| D E F L A T O R S |
| # C O A X I N G # |
| S E P T I M O L E |
| H I # O N O # A Y |
| O V E R G L A Z E |
| W E M S # E Y E N |
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Score = 146

There are a total of 46 similar solutions with this pattern, or 92 in total, counting transposes.

The reason that I think it can't be exceeded is that it's the highest scoring pattern with the two central 7 letter words equal. Why can't there be a higher score with the central words unequal? Well in theory there could be, but in practice I found that this was never the case. Because the black cell pattern is symmetrical about the main diagonal, if it wasn't for the scrabble letter distribution constraint, the highest score would obviously be transposable (the contents of each row would be equal to the contents of the corresponding column). The letter distribution constraint prevents this from being perfectly true, but in practice it just isn't a strong enough constraint to stop the highest score occurring with the two central words equal.

I'll have a look at your new pattern, it's got 2 more black cells, which is good, and is not symmetrical about the main diagonal, which is also good.

Leren

[JPF]

Thanks for the solution!

Here is a solution for the new pattern with a very low score:

Score = 95
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Grid 7 - Sol 1.JPG (19.34 KiB) Viewed 1484 times

My real current score is 154 - edit: 159 now

JPF

[Leren]

Hi JPF. Thanks for the example, it will help me debug the new pattern. As usual it will take me a day or two to respond to a new pattern

Leren

<edit> Up and running - like a freight train. HS only 150 at the moment.....154.... like a bolt out of the blue ... 158 !.... 159 one to go !

Leren

[Leren]

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| B A C K F L I P S |
| A G H A # E V E T |
| J E E # P A Y S # |
| A N C L E S # O M |
| N # H I D E D # Y |
| # F A G # D E M E |
| N I Q A B # V O L |
| A G U N O T # Z O |
| W O O D W A X E N |
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Score = 160

Mount Everest has been conquered !

Leren

<edit>

Corrected diagram to display r3c7 correctly. Leren

[JPF]

Great achievement!
But are you sure you climbed the right mountain?
Your pattern is not the proposed one.

Here is a real solution:

Score = 160
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Grid 7- Sol2.JPG (21.81 KiB) Viewed 1435 times

JPF